Dedifferentiation Hypothesis Statement

Abstract

Existing representations of cognitive ability structure are exclusively based on linear patterns of interrelations. However, a number of developmental and cognitive theories predict that abilities are differentially related across ages (age differentiation-dedifferentiation) and across levels of functioning (ability differentiation). Nonlinear factor analytic models were applied to multivariate cognitive ability data from 6,273 individuals, ages 4 to 101 years, who were selected to be nationally representative of the United States population. Results consistently supported ability differentiation, but were less clear with respect to age differentiation-dedifferentiation. Little evidence for age modification of ability differentiation was found. These findings are particularly informative about the nature of individual differences in cognition, and the developmental course of cognitive ability level and structure.

Keywords: Differentiation, Dedifferentiation, Spearman’s Law of Diminishing Returns, Intelligence, Nonlinear Factor Analysis

Differentiation of Cognitive Abilities across the Lifespan

In the first of a series of empirical and methodological undertakings to evaluate whether “the abilities commonly taken to be ‘intellectual’ had any correlation with each other” (Spearman, 1930, p. 322), Charles Spearman (1904) made the observation that many diverse measures of cognitive performance were indeed positively interrelated. This lead him to develop a “two factor” theory of intelligence, in which he proposed that a given individual’s level of performance on a given cognitive task was determined by a general ability (“g”) that could be diversely applied to many sorts of cognitive tasks, and one of many specific abilities (“s”) that could only be applied to the task in question. This theory was supported by Spearman’s demonstration that the correlations observed among a number of cognitive tests could be closely approximated from a model in which every test was assumed to be related to an unobserved common “g” factor. Elaborations of this method have come to be termed common factor analysis.

Over the hundred years since Spearman’s original (1904) work, factor analyses have continued to be applied to correlation/covariance matrices from cognitive test batteries. Based on such works, it is now clear that sets of cognitive tests tend to cluster into several “broad” ability factors, including what might be described as processing speed, episodic memory, visual-spatial thinking, fluid reasoning, and comprehension knowledge (i.e. crystallized intelligence). The interrelations among these broad abilities can in turn be accounted for by a higher order common factor that is statistically analogous to Spearman’s original conception of general intelligence. Such a contemporary representation of cognitive ability structure was termed the Three Stratum Theory by Carroll (1993), referring to fairly specific factors at the first stratum, broad abilities at the second stratum, and a general factor at the third stratum. This theory is largely based on, and very similar to, the Horn-Cattell theory of fluid and crystallized intelligence (Cattell, 1941; Cattell, 1987; Horn, 1965) which, in addition to fluid intelligence and crystallized intelligence, includes factors such as visualization, retrieval, and cognitive speed. Because such theories presume more specific factors nested within more general factors, they are generally termed hierarchical.

Contemporary hierarchical representations of cognitive abilities are supported by a number of basic findings: 1) patterns of convergent validity (high covariation among measures of the same factor), discriminant validity (more moderate covariation among measures of different factors), and face validity (measures designed to indicate a particular factor often do so); 2) differential patterns of relations of the various abilities with various external variables, including school and job performance, educational attainment, personality, and demographic indicators (e.g. Gottfredson, 2003; McGrew, 2009); 3) quantitative genetic estimates of heritability and environmentality specific to the various abilities (e.g. Petrill, 1997); 4) differential patterns of relations between the various abilities and neuroanatomical/neurobiological indices (e.g. Colom et al, in press); and 5) ability-specific developmental trajectories across both childhood and adulthood (presumably biologically-based abilities tend to grow in childhood, peak at late-adolescence/early adulthood, and decline into later adulthood; knowledge-based abilities tend to grow until mid-to-late adulthood and either stabilize or decline thereafter; Li, Lindenberger, Hommel, Aschersleben, Prinz, & Baltes, 2004; McArdle, Ferrer-Caja, Hamagami, & Woodcock, 2002; McGrew & Woodcock, 2001).

This final line of evidence is of particular relevance to the current investigation. The enterprise of cognitive developmental research is concerned with the striking changes in the quality and extent of cognitive performance as children grow and adults mature. For example, the effect size of increasing age on declining speed of information processing in adults has been listed among the largest effects in all of behavioral research (uncorrected meta-analytic estimated bivariate correlation = −.52; Meyer et al., 2001). Given that levels of cognitive performance differ so dramatically as functions of chronological age, it is very possible that the structural organization of cognitive abilities differs with age as well. A related possibility is that the structural organization of cognitive abilities differs with ability level. These two hypotheses have been the topic of much theoretical speculation for quite some time.

In fact, it was Spearman (1927; see Deary and Pagliari, 1990) who was the first researcher to propose that the relations among cognitive abilities may not be constant, but rather a diminishing function of ability level (what he called “the law of diminishing returns”). He reasoned that at low ability levels, a scarcity of domain general resources constrains multiple modes of cognitive functioning, but that at high ability levels, cognitive functioning is instead constrained by the levels of domain-specific resources. He supported this hypothesis by demonstrating that the mean correlation among 12 ability tests in 78 normal children was .466, but in 22 “defective” children was .782. Here this hypothesis is referred to as the ability differentiation hypothesis.

Referring to others’ works, Spearman (1904, 1927) also speculated that the magnitudes of ability relations may differ according to age. It was Garrett (1938; 1946) who introduced the age differentiation hypothesis, that with child development “an amorphous general ability” gradually breaks down “into a group of fairly distinct aptitudes” (Garrett, 1946, p. 375). Elaborating on this hypothesis to include both child development and adult aging, Balinsky (1941, p. 227) argued for a “greater specialization up to a certain point, followed by a later reintegration of the various abilities into a flexible whole.” This hypothesis, which has come to be termed the age differentiation-dedifferentiation hypothesis, was supported by Balinsky’s finding that a single common factor accounted for a decreasing amount of variance in the Wechsler-Bellevue test battery with older childhood age groups and an increasing amount variance with older adult age groups.

Lienert and Crott (1964) noted that age and ability based differentiation/dedifferentiation may not be independent phenomena. Because cognitive abilities are known to increase with childhood age and decrease with adult age, they explained that age differentiation-dedifferentiation could potentially be explained by ability differentiation. Nevertheless, the two hypotheses have often been examined independently of one another.

As will be discussed subsequently, the two somewhat separate bodies of literature on the topics tend to support ability differentiation, but are much more mixed with respect to age differentiation-dedifferentiation. Extant studies, however, have been typified by a number of shortcomings, outlined briefly below.

  1. Past studies of age differentiation have primarily been isolated to segments of childhood or adulthood, and past studies of ability differentiation have primarily been isolated to samples containing even narrower age ranges. Given that the age differentiation-dedifferentiation hypothesis posits a specific pattern of shifts in ability interrelations across the lifespan, it is advantageous to examine it in lifespan samples. Moreover, the investigation of ability differentiation in age-heterogeneous samples would allow for inquiry as to whether it is a developmentally emergent phenomenon.

  2. No study has estimated models that simultaneously allow for both age and ability differentiation. This is particularly important given that a single mechanism might be responsible for both phenomena.

  3. Although it is well recognized that the hypotheses are inherently nonlinear, previous studies have been based on comparisons of linear relations across subgroups. Moreover, the arbitrary division of continuous variables (i.e. age and ability level) for the purpose of subgroup classification is marked by selection effects that threaten the validity of cross-group comparisons.

  4. Although the assumption of interval measurement is a requisite for the comparisons of relational magnitudes, previous studies have not paid sufficient attention to the measurement properties of the tests employed.

In this article, the above shortcomings are discussed and nonlinear factor analysis of carefully scaled data is offered as a preferable alternative to other recently applied methodologies. Results of such an application to a large nationally representative lifespan sample of individuals, measured on a broad array of well-established cognitive abilities, are reported. First, recent theories and examinations of ability differentiation and age differentiation-dedifferentiation are reviewed. For more comprehensive reviews of older studies, see Deary, Egan, Gibson, Austin, Brand, & Kellaghan (1996) and Reinert (1970).

Ability Differentiation: Recent Theory and Research

Several cognitive theories have been invoked to explain ability differentiation. Anderson’s (1992; c.f. Anderson, 2001) theory of minimal cognitive architecture is perhaps the theory that is most explicit in postulating a mechanism that would lead to such a pattern. It suggests that independent cognitive algorithms differentially contribute to various domains of intellectual performance, but that because the complexity of each of these algorithms is constrained by a single basic processing mechanism, performance across different domains is correlated. Among people for whom the basic processing mechanism is more efficient (i.e. faster), the independent algorithms are less constrained, and performance levels across disparate domains become less correlated. This view bears resemblance to that of Spearman (1927), who argued that general intelligence can be conceptualized as fuel for engines that perform task-specific functions, reasoning that constant increments in fuel only result in diminishing increments in engine efficiency. Detterman and Daniel (1989) have similarly reasoned that if “central processes are deficient, they limit the efficiency of all other processes in the system. So all processes in subjects with deficits tend to operate at the same uniform level. However, subjects without deficits show much more variability across processes because they do not have deficits in important central processes.”

Ability differentiation has conventionally been examined by dividing samples into high and low ability groups, and comparing the magnitudes of correlations or the proportion of variance accounted for by a common factor, across the groups. Detterman and Daniel (1989), for example, compared the average cognitive ability test intercorrelations in mentally retarded versus college students, and low versus high IQ high school students and found substantially lower intercorrelations in the mentally retarded/low IQ groups than in the college/high IQ groups. They similarly divided the standardization samples from the WAIS-R and WISC-R into 5 ability groups, and found that the average subtest intercorrelations decreased from about .7 in the lowest ability groups (IQ equivalent less than 78) to about .4 in the highest ability groups (IQ equivalent greater than 122).

Using a novel method to create similarly distributed subsamples of low and high age and ability individuals from a parent sample of 10,500 school children (ages 14–17), Deary et al. (1996) found that the first principle component accounted for a greater percentage of variance (about 2% more) in low ability groups than in high ability groups, but accounted for a similar percentage of variance in younger and older adolescent age groups. Abad, Colom, Juan-Espinosa, & García (2003) applied this method to 3,430 university applicants, and 823 adults (ages 20–54) composing the Spanish standardization sample of the WAIS-III. They found that a single common factor accounted for greater percentages of variance in low ability groups than in high ability groups (a difference of about 2% in the university applicants and about 12% in the WAIS-III sample). Kane, Oakland, and Brand (2006) applied this method to the standardization sample of the WJ-R (N=6,359, ages 2–95 years) and found that a single common factor accounted for 52% of the variance in test scores in the low ability group and 29% of the variance in test scores in the high ability group. In an examination of the KABC-II (N =2,375, ages 6–18 years) Reynolds and Keith (2007) fit a number of hierarchical ability models with confirmatory factor analysis, and found that a higher order common factor accounted for about 10% more variance per variable in the low ability group than in the high ability group. One notable study not supportive of ability differentiation was a sophisticated set of analyses by Nesselroade and Thompson (1995). A series of nested linear factor models were compared across high and low ability groups of adult twins (ages 49 to 92 years), with only 1 twin from each pair per analysis, and the co-twin in a second set of cross-validation analyses. Results indicated that both the number of factors and the magnitudes of their loadings were invariant across ability groups.

Only one study seems to have implemented nonlinear models to examine either of the differentiation hypotheses. Der and Deary (2003) used polynomial regressions to predict scores on a test of reasoning from simple and complex reaction times. Whereas a linear model adequately described the relation between reasoning and complex reaction time, a quadratic model was incrementally descriptive of the relation between reasoning and simple reaction time in the direction predicted by the ability differentiation hypothesis.

Age Differentiation-Dedifferentiation: Recent Theory and Research

A number of recent cognitive developmental and aging theories have made specific predictions supportive of age differentiation-dedifferentiation. Cattell’s (1987) investment theory proposes that individuals begin life with a single general (fluid) ability that through experience and development is invested in the formulation and elaboration of knowledge-based (crystallized) abilities. As environmental and non-cognitive (e.g. interest, motivation) influences on knowledge acquisition accumulate with age, and as cognitive functions become automatized, fluid and crystallized abilities increase in their relational independence. A number of researchers (Baltes & Lindenberger, 1997; Li et al., 2004; Lövdén, Ghisletta, & Lindenberger, 2004) have expanded upon this hypothesis. They have proposed that during childhood, heterogeneous contributions to development and learning result in increases in ability levels and associated increases in ability independence, whereas during adulthood, more global biological constraints result in broad declines in ability levels and associated increases in ability interrelations. Li and colleagues (Li & Lindenberger, 1999; Li, Lindenberger, & Sikstrom, 2001) have proposed that such aging related biological constraints may be attributable to decreases in neurotransmission that result in increased noise in information processing. When such constraints are simulated with computational models, the results are decreases in cognitive performance, increases in cognitive performance variability, and increases in the relations among cognitive abilities. These emphases on the age-based operation of broad constraints bear theoretical similarity to the cognitive theories described above (see Tucker-Drob & Salthouse, 2008, for a discussion and review).

A separate area of empirically based developmental theory predicts patterns inconsistent with the age differentiation-dedifferentition hypothesis. A number of behavioral genetic investigations have established that the proportion of individual differences in cognitive performance that can be attributed to genetic sources increases monotonically across the childhood and adult lifespan. These findings have been described as “among the most striking and strongly substantiated findings of behavioral genetics in recent years” (Jensen, 1998, p. 179). It has been proposed (e.g. Dickens, unpublished manuscript; Dickens and Flynn, 2001; Scarr & McCartney, 1983) that these findings result from individuals self-selecting into environments that are compatible with their ability levels, and which proportionally amplify their many abilities. The notion that multiple sources of individual variation dynamically interact to produce increasing intercorrelations with childhood age has also been proposed by van der Maas, Dolan, Grasman, Wicherts, Huizenga, & Raijmakers (2006) in their theoretical model of the “positive manifold of intelligence by mutualism.” Therefore, to the extent that broad and dynamic determinants of cognitive abilities (including the self selection into environments that proportionally amplify cognitive abilities) operate across the lifespan, one would expect that the relations among cognitive abilities might increase concomitantly.

Similar to examinations of ability differentiation, age differentiation-dedifferentiation has conventionally been examined by contrasting correlations, or the proportion of variance accounted for by a common factor, across age groups.

Some of the most recent support of age differentiation-dedifferentiation comes from Li et al. (2004) who divided a population based sample of 291 individuals into six age groups ranging from 6 to 89 years of age and found that the correlations between fluid and crystallized intelligence in the adolescent, young adult, and middle adult groups were smaller in magnitude than the correlations in the young children and two older adult groups, and that a similar trend was present in the percentage of variance in cognitive and intellectual measures explained by the first principal component. De Frias, Lövdén, Lindenberger, and Nilsson (2007) compared covariances among levels of cognitive ability measures across 5 cohorts of individuals (aged 35–80) and found evidence for age-related increases in ability interrelations beginning after about 65 years of age, reasoning that this is the age range in which broad and severe determinants of cognitive decline begin to dominate.

Others have been unable to support age differentiation-dedifferentiation. In a sample of 2,087 adults (ages 65 and older) Anstey, Hofer, & Luszcz (2003) examined differences in intercorrelations among Verbal, memory, Vision, & Hearing factors across low, middle, and high ability groups, young-old, mid-old, and old-old age groups, and across 8 years of longitudinal change (791 participants retained). They found some evidence for ability differentiation but little evidence for age-dedifferentiation. Analyzing data from the WJ-R (N=2,201), Bickley, Keith, & Wolfle (1995) found that neither the intercorrelations among subtests, nor the hierarchical factor structure, differed significantly across 8 age groups ranging from 6 to 79 years of age. Juan-Espinosa, García, Escorial, Rebollo, Colom, & Abad (2000), examined the Italian, Spanish, and American standardization samples of the WPPSI and the WISC-R in 17 age groups ranging from 4 to 16 years of age and found no evidence for systematic age-related differences in the percent of variance accounted for by a single factor, or in the average inter-test correlation. In a similar investigation of adults, Juan-Espinosa, García, Escorial, Rebollo, Colom, & Abad (2002) divided the Spanish standardization sample of the WAIS-III (N=1,369) into six age groups ranging from 16 to 94, and after correcting for group differences in ability range found no evidence for systematic age-related differences in the percentage of variance accounted for by a common factor. Using Deary et al.’s (1996) method to sample similarly distributed young and old subsamples from two parent populations of N=6,980 (ages 12–16) and N=11,448 (ages 15–24) Hartmann (2006) found no evidence for differences in the average magnitude of test intercorrelations, or percent of variance accounted for by the first principal component or single common factor, across age groups. These patterns of results unsupportive of age differentiation-dedifferentiation Juan-Espinosa et al. (2002, p. 407), to provide an anatomical metaphor in concluding that “basic structure does not change at all, although, like the human bones, the cognitive abilities grow up and decline at different periods of life.”

Age Modification of Ability Differentiation

Facon (2006) investigated the unique hypothesis that ability-differentiation may not be an age-invariant phenomenon, but rather emerges with childhood development. Facon split the French standardization sample of the WISC-III into 3 age groups ranging from 7 to 15 years, and split the age group into low and high ability groups. He found that the strength of the relations among subtests, as indexed by the median intercorrelation differed more greatly between low and high ability groups for older ability group pairs. Facon (2004), examined the same hypothesis in 4 to 9 year olds (N=574), in comparing subtest intercorrelation matrices across low and high ability groups, and because he did not find evidence for ability differentiation, concluded that the phenomenon must emerge later in development. Arden and Plomin (2007) have made similar speculations.

Goals of Current Investigation

Three major questions were addressed for the current project.

  1. To what extent do the relations among cognitive abilities differ across the lifespan?

  2. To what extent do the relations among cognitive abilities differ according to ability level?

  3. Given the substantial age-related trends in cognitive ability levels, to what extent are (1) and (2) independent of one another? Moreover, to what extent does (2) differ according to age?

In the following sections, key methodological and conceptual issues are surveyed, and the analytic approach for addressing the above questions is described.

Methodological Considerations

Linear Factor Analysis and Nonlinear Factor Analysis

A three outcome1 version of the conventional common factor model is depicted as a path diagram in Figure 1. In this diagram, measured outcomes are represented as squares, unobserved (theoretical) variables are represented as circles, and linear regression relationships (e.g. factor loadings) are represented as single headed arrows. This basic model, on which most existing structural representations of cognitive abilities are based, relies on the assumptions that the pattern of observed interrelations among the outcomes can be fully accounted for by their relations to an unobserved (theoretical) common factor, and that patterns of relations that the outcomes have with external variables are fully attributable to the mediation of the common factor (although these assumptions can be relaxed in some more advanced models). To the extent that more than three outcomes per factor are included, or relations with external variables are included, such models are empirically falsifiable. A further assumption of this basic model that is also amenable to empirical falsification (but which is rarely actually scrutinized) is that all relations are linear in nature. This is represented by the three plots at the bottom of Figure 1, in which it can be seen that each outcome is assumed to have a linear relation to the common factor. Put in other words, this basic model assumes that individuals’ abilities are related to their performance on a given outcome to the same extent regardless of ability level, or level of some other variable (e.g. age). It is precisely these latter assumptions that the ability differentiation and age differentiation-dedifferentiation hypotheses call into question.

Figure 1

The conventional common factor model assumes that performance on a given outcome is a linear function of the score on the common factor. In this hypothetical factor analysis, λA, λB, and λC are factor loadings, which correspond...

The typical approach that has arisen for scrutinizing the assumption of constancy of relations, particularly with respect to age and ability level, is one in which the basic factor model depicted in Figure 1 is fit to two or more groups that have been formed based on fairly arbitrary criteria (i.e. above and below a certain test score or age), and allowing the linear structural interrelations to differ across the two groups. Such an approach has been criticized on a number of grounds, including the application of a linear model to examine an inherently nonlinear hypothesis, the arbitrary nature of dividing a continuous variable into groups and the associated artifacts of such division (e.g. unequal ranges of scores), and the use of observable indices of ability level to form ability groups, when the unobservable true ability is the variable of theoretical interest. See Deary et al. (1996) for a more detailed discussion of these methodological issues.

An alternative to the multiple group approach is one that represents structural interrelations as occurring within a single group and along continuous dimensions, but in nonlinear and interactive ways (see, e.g., Bauer, 2005). Such an approach can help to diminish the above described threats that are associated with multiple group approaches. Moreover, whereas the division of samples into discrete age groups almost inevitably results in groups that also differ in ability level (and vice versa), a continuous approach can allow for a great deal of flexibility in simultaneously modeling the effects of age and ability level.

Figure 2 depicts the results of an analysis of simulated data that illustrates how nonlinear factor analytic methods can be employed in examining the differentiation hypotheses. In the left plot a single nonlinear function describes the relationship between outcome and the common factor. It can be seen that by fitting separate linear regressions to participants scoring below and above the mean on the outcome, the nonlinear relationship is approximated, but suggests lack of measurement invariance (i.e. a single model cannot adequately account for the relation in both groups). Alternatively, a single measurement invariant nonlinear model is a preferable depiction of the relationship. In the center plot a single nonlinear function again best describes the relation between the common factor and the outcome. In this case, when separate linear models are fit to young and old adult groups (assuming that old adults perform more poorly on average than young adults), the results again approximate the nonlinear relationship, and suggest lack of measurement invariance. In the right plot, the nonlinear loading is modeled separately for young and old adults, allowing for inferences to be made regarding both ability differentiation and age differentiation-dedifferentiation. The approach taken in the current study is most analogous to that depicted in the right plot, in which nonlinear loadings, and age-modification of loadings are simultaneously modeled. In the current study, however, both ability level and age are considered as continuous variables.

Figure 2

Left: Simulated Data. Linear regressions fit to High and Low scoring individuals. Although a single (nonlinear) population function applies, a two group linear approach indicates measurement noninvariance across ability groups. Middle: Simulated Data....

The Importance of a Proper Measurement Model

In order to examine influences that may potentially modify the relational magnitudes among variables, it is important for each variable to be measured on a scale for which the distance between any two values has the same meaning as a distance of the same magnitude between any two other values. Put another way, in order for differences in relational magnitudes to be meaningfully examined, the variables should be measured on interval scales. This is because the magnitude of a relation can be conceptualized as a magnitude of change in the expected value of one variable, given a unit of change in the value of another variable. Therefore, only if it is meaningful to compare magnitudes of differences at different areas along the scales, is it meaningful to compare the magnitudes of relations at different areas along the scales.

Whereas most extant examinations of the ability differentiation and age differentiation-dedifferentiation hypotheses have failed to consider the measurement properties of the instruments, the current analyses are of Rasch-scaled ability estimates, which are based on the logistic item response model, and which can be considered to have interval measurement properties. The advantage of the Rasch model is illustrated by analyses of simulated data, results of which are presented in Figure 3. The top row contains plots of sum scores (total number of items correct) as functions of the true ability scores that were generated in the simulation. The bottom row contains ability estimates obtained using an Item Response Theory, Rasch (1 parameter logistic), measurement model as functions of the true scores. The columns represent conditions in which the distribution of item difficulties is either balanced, disproportionately easy, or disproportionally difficult. It can be seen that only when the distribution of item difficulties is balanced relative to the population measured, is interval measurement is maintained such that a sum score is an appropriate indication of the true score. Moreover, by simply adding easy or difficult items to a test, the sum score loses its interval properties and can instead artifactually create an impression of ability-differentiation or even, what might be described as ability dedifferentiation (i.e. the relation between the true score and the sum score becomes nonlinear). However, by applying a Rasch measurement model to the data, interval properties are well maintained in all cases. For a more detailed discussion of the advantages of Rasch scaling to achieve interval measurement properties, see Embretson & Reise (2000).

Figure 3

Simulated Data. The item composition of a measure can influence the quality and magnitude of its interrelations. A sum score is particularly problematic when the distribution of item difficulties does not match the distribution of person abilities. Rasch...

Method

The current investigation is based on analyses of the standardization sample of the Woodcock-Johnson III (WJ-III) Tests of Cognitive Abilities (Woodcock, McGrew, & Mather, 2001). The WJ-III test battery was constructed based on an integration of Cattell’s and Horn’s theory of Fluid and Crystallized intelligence (Cattell, 1941; Cattell, 1987; Horn, 1965), and Carroll’s (1993) three-stratum theory of cognitive abilities. This integration has been termed Cattell-Horn-Carroll (CHC) theory, and is represented as a three-stratum hierarchical structure in Figure 4. The main focus of the current investigation is on the relations between the second stratum abilities and the higher order common (g) factor, as demarcated by the dashed box in the figure. The second stratum abilities are described below (adapted from McGrew & Woodcock, 2001).

Figure 4

A graphical depiction of the theoretical structure on which the WJ-III Tests of Cognitive Abilities was based. This Horn-Cattell-Carroll Model assumes that cognitive abilities are organized in a hierarchy containing three strata, with variables in contiguous...

Comprehension-Knowledge (Gc), also termed crystallized intelligence, refers to knowledge (especially verbal knowledge) that is autobiographically acquired from a culture through experience and learning. It includes factual information, comprehension, concepts, rules, knowledge of relationships, and procedural knowledge that has become automatized.

Visual-Spatial Thinking (Gv) refers to the ability to integrate, perceive, store, recall, rotate and mentally manipulate, and reason with visual patterns and representations.

Fluid Reasoning (Gf) refers to the ability to inductively and deductively reason in novel ways, and with unfamiliar information, by identifying relations, drawing inferences, forming concepts, and identifying conjunctions and disjunctions.

Processing Speed (Gs) refers to the ability to quickly and efficiently perform cognitive tasks requiring focused attention.

Short-Term Memory (Gsm) refers to the ability to apprehend and store information in immediate awareness before it is retrieved or applied.

Long-Term Retrieval (Glr), also termed episodic memory, refers to the ability to encode information and later retrieve it. Between encoding and retrieval, the information departs from immediate awareness.

Auditory Processing (Ga) refers to the ability to integrate, synthesize, discriminate, and process auditory stimuli that may or may not be distorted or obscured.

Whereas the conventional CHC model of cognitive abilities is based on linear patterns of relations, the current investigation examines the possibility that these relations are nonlinear, such that they are functions of age and ability level. This is achieved using nonlinear factor analytic methods, in which potential age and ability level modification of common factor-broad ability relations are evaluated as empirical questions (i.e. the three questions posed earlier).

Participants

The WJ-III sample was recruited from over 100 geographically diverse communities to be nationally representative of the United States population, as indexed by the 2000 census projections (McGrew & Woodcock, 2001). Participants were selected using a stratified sampling design that controlled for census region, community size, sex, race, Hispanic vs. non-Hispanic, type of college/university (for college and university students), educational attainment (for adults), employment status (for adults), and occupation (for adults). Although this design produced samples with distributions of participants closely approximating the U.S. population, individual subject weights2 were applied for all models reported here in order to obtain the most precisely representative parameter estimates possible. Note that results from models in which subject weights were not applied were very similar to those reported here.

Because recruitment was carried out separately for school-age (kindergarten through 12th grade), college and university, and adult (nonstudent) subsamples, data from these three subsamples were analyzed separately in the current project3. The interested reader can refer to the online supplement to this paper for detailed results of a single group analysis (of data aggregated across all three subsamples). Those results were very similar to the ones reported here.

Table 1 presents key descriptive statistics for the three subsamples. Note that in order to avoid extreme influences and sparse data in some areas of the multivariate distributions (e.g. older adults who were still in college), age and grade inclusion criteria were set for each subsample (see starred cells of Table 1). Moreover, participants were only included if they had data available for at least one broad ability cluster score (described below).

Measures

Analyses are based on seven cluster scores corresponding to the seven second stratum broad abilities depicted in Figure 4. Each cluster scores is based on the average of two W-scaled tests representative of the respective ability. The W-scale is a transformation of the Rasch (1 parameter logistic) Item Response Theory model, which has been centered such that 500 corresponds to the approximate level of performance of ten year olds, and scaled to have interval properties such that at any level of functioning (a) a difference between person ability and item difficulty (ability minus difficulty) of 0 corresponds to 50% probability of success, (b) a difference between person ability and item difficulty of 10 corresponds to a 75% probability of success, and (c) a difference between person ability and item difficulty of −10 corresponds to a 25% chance of success (McGrew, Werder, & Woodcock, 1991).

The tests used to measure each ability are described in Table 2. Reliabilities of the cluster scores by age groups are provided in Table 3. The reliabilities of the cluster scores were very high for all age groups, and there was very little evidence that the reliabilities systematically differed according to age. This is important, because systematic differences in variable interrelations could be due to systematic differences in variable reliabilities, if they exist. This possibility was also considered with respect to differences in reliability by ability level. It is well known in modern test theory that ability estimates are less accurate for ability regions that are measured by fewer items. Because the WJ-III tests contain greater item representation at the middle of the scales than at the extremes, ability estimates are likely to be less accurate for extremely high and low functioning participants. It can be inferred that the findings reported in this paper were not biased by this phenomenon, as models that only included individuals scoring within one standard deviation of the sample mean’s general intellectual ability composite score (approximately the middle 68%, where items are evenly and abundantly distributed) produced very similar patterns of results as those reported here.

Table 2

Descriptions of Measures of Broad Abilities

Table 3

Estimated Reliabilities of Cluster Scores by Age Group.

Finally, it is possible that nonlinear trends can be artifactually produced by ceiling and floor effects of the measures. The WJ-III tests underwent a rigorous development process to ensure, among other things, that all ability levels could be sensitively measured. The success of this procedure was confirmed here, by examining histograms of each of the cluster scores. For no variable was there evidence for a disproportionate frequency of scores at the extremes of the scales, or a truncation of the distribution.

Analyses

All models were run in Mplus (Muthén & Muthén, 1998–2007) with Full Information Maximum Likelihood (FIML) estimation procedures using a numerical integration algorithm that permits estimation of interactive effects (see Appendix A for an example script). FIML is also able to accommodate missing data under the missing at random assumption (McArdle, 1994; Muthén & Muthén, 1998–2007). Given the large number of statistical comparisons, alpha values were set to .01.

Sets of stepwise models were separately applied to school-age, college and university, and adult subsamples. In these equations, [x] indicates that a term is specific to each broad ability. For example, G[x] represents the broad abilities Gc, Gv, Gf, Gs, Gsm, Glr, and Ga. Also note that υ represents ability intercepts, α1[x] and α2[x] represent the regression coefficients of the broad abilities on age and age squared4, g represents the higher order common factor, λ1[x]-λ4[x] represent loadings on g, and u[x] represents the (unique) component of each broad ability that is not accounted for by the other terms in the model. The subscript n denotes that a term varies between individuals. In all models, g and u[x] are allowed to have between-person variances σ2g and σ2u[x] respectively. To define the metric of g, σ2g was set to 1 for all models. However, as a result of the differential recruitment procedures for the three subsamples, is likely that the school-age, college and university, and adult subsamples, differed in the magnitudes of the variation in their latent abilities5. Therefore, the parameters for the subsamples were likely not on comparable scales, and across subsample comparisons of parameter values should not be made. However within subsample age-comparisons are of course a main topic of inquiry.

Age was centered for each subsample by subtracting its mean, and the mean of common factor (g) was fixed to 0 for each subsample. This helped to reduce nonessential multicollinearity among the main effects, quadratic effects, and interactive effects of age and g, thus facilitating model estimation and interpretability.

Step 1

In the first step of model fitting, each ability was simultaneously predicted by linear and quadratic age trends, and linear loadings on the common factor (g). This model is equivalent to conventional (linear) common factor models. It is written as

G[x]n = υ[x] + α1[x] · agen + α2[x] · agen2 + λ1[x] · gnu[x]n .

(Eq. 1)

Step 2

In the second step, two parallel models were constructed: one with the addition of terms for quadratic common factor loadings, and a second with the addition of terms for age-modification of the linear common factor loadings. The former model examines the ability differentiation hypothesis, and is written as

G[x]n = υ[x] + α1[x] · agen + α2[x] · agen2 + λ1[x] · gn + λ2[x] · gn2u[x]n.

(Eq. 2)

The latter model examines the age differentiation-dedifferentiation hypothesis, and is written as

G[x]n = υ[x] + α1[x] · agen + α2[x] · agen2 + λ1[x] · gn + λ3[x] · agen · gnu[x]n .

(Eq. 3)

Step 3

In the third step, quadratic common factor loadings and age-modification of the linear common factor loadings were simultaneously estimated. This model simultaneously examines both the ability differentiation and age differentiation-dedifferentiation hypotheses. It is written as

G[x]n = υ[x] + α1[x] · agen + α2[x] · agen2 + λ1[x] · gn + λ2[x] · gn2 + λ3[x] · agen · gnu[x]n .

(Eq. 4)

Step 4

In a final step, terms for age-modification of the quadratic factor loadings were added. In addition to examining the ability differentiation and age differentiation-dedifferentiation hypotheses, this model examines the possibility that ability-differentiation may be modified by age (e.g. that differentiation may emerge with development). The full model is written as

G[x]n = υ[x] + α1[x] · agen + α2[x] · agen2 + λ1[x] · gn + λ2[x] · gn2 + λ3[x] · agen · gn + λ4[x] · agen · gn2u[x]n

(Eq. 5)

or in expanded form as

where G[x] represents the broad abilities, υ[x] represents ability-specific intercepts, α1[x] represents the linear components of the age trends in each ability, α2[x] represents the quadratic components of the age trends in each ability, λ1[x] represents the linear influences of g on each ability, λ2[x] represents the quadratic (nonlinear) influences of g on each ability (ability differentiation), λ3[x] represents age modification of the linear influence of g on each ability (age differentiation), λ4[x] represents age modification of the quadratic influence of age on each ability (age modification of ability differentiation), and u[x] represents unique ability-specific factors.

Results

Model implied age trends in the broad factors are depicted in Figure 5. These were produced using the terms α1[x] and α2[x] of the full models from each group, but the parameters were very similar for each step of the model fitting. Note that because linear and quadratic trends were fit separately for the school-age, college and university, and adult subsamples, elaborate lifespan age trends were able to be captured with these fairly simple functions6. Such trends would ordinarily require much more complex functions (e.g. high degree polynomials, or the dual exponential model that was fit by McArdle et al., 2002) had the lifespan age trends not been modeled in three segments. The trends are consistent with those found in many cross sectional (e.g. Li et al., 2004) and longitudinal (e.g. McArdle et al., 2002) examinations of similar variables. In particular, all abilities except for Gc increase in level during childhood development, peak during late adolescence/early adulthood, and decrease in level across adulthood, whereas Gc increases in level through childhood and until middle adulthood, where it peaks and decreases thereafter. Also of prominence in Figure 5 is the positive selection of college and university participants that is often of concern in psychological research. This thorough modeling of lifespan age-trends is of particular importance for the current project, because covariational patterns can often be influenced by common (or discrepant) mean age trends in the data if they are not modeled and controlled for (see, for example, Hofer & Sliwinksi, 2001; Kalveram, 1965; Salthouse & Nesselroade, 2002).

Figure 5

Model implied lifespan age trends in the broad abilities. These cross sectional trends are based on three models, fit to school age, college and university, and adult (nonstudent) subsamples separately. The discontinuity in the trends apparent surrounding...

Comparisons of, and fit indices for, the stepwise models are reported in Table 4. For all three subgroups, stepwise model comparisons indicated that the full model fit the data best. A number of observations are particularly relevant. First, larger increments in model fits were associated with the addition of the terms corresponding to ability differentiation (λ2[x]), whereas fairly modest increments in model fits were associated with the terms corresponding to age differentiation-dedifferentiation (λ3[x]). In the case of the college and university subsample, increments in model fits associated with the age differentiation-dedifferentiation step were not significant, which is not surprising, given that this sample did not include a very wide age range.

Table 4

Fit Indices and Comparisons of Stepwise Models.

Although the stepwise model comparisons indicated that the addition of terms corresponding to both ability level and age modification of factor loading magnitudes significantly improved model fits, it is important to inspect the direction and statistical significance of each of the terms in order to evaluate whether the ability differentiation and age differentiation-dedifferentiation hypotheses were supported. To accept such support, the parameters should be in directions indicative of lower loadings at high ability levels, lower loadings with increasing childhood age, and higher loadings with increasing adult age. Moreover, the effects should not be isolated to a single broad ability, but should instead be statistically significant and consistent in direction for multiple abilities.

Parameter estimates from the baseline and intermediate stepwise models are reported in Table 5. It is useful to examine the parameter estimates from each of these models in turn. Because it served as the baseline model of which all other models were elaborations, the linear (Step 1) model merits particular scrutiny. It can be seen that all linear loadings (λ1) were highly significant, as none of their 99% confidence intervals included zero. The magnitudes of these linear loadings were moderate to large, all having standardized values greater than 0.50, indicating convergent validity of the common “g” factor. Moreover, the linear model fit the data from each subgroup well in absolute terms (School Age Subsample RMSEA=0.044, CFI=.0994, TLI=0.986; College and University Subsample RMSEA=0.063, CFI=0.925, TLI=0.812; Adult Subsample RMSEA=.039, CFI=.992, TLI=.980). Note that because all subsequent (nonlinear and interactive) models do not produce sample-level covariance expectations, these absolute fit indices are not available for them.

Table 5

Key Parameter Estimates (and 99% Confidence Intervals) from Baseline and Intermediate Models.

Results from the nonlinear model include terms corresponding to ability level modification of the factor loadings (λ2) that were negative for all abilities and statistically significant for 4 of 7 abilities in the school age subsample, 2 of 7 abilities in the college and university subsample, and 5 of 7 abilities in the adult subsample, a finding consistent with ability-differentiation. Results from the age-modification model include terms corresponding to age modification of factor loadings (λ3) that were statistically significant for 2 of 7 abilities in the school age subsample, 1 of 7 abilities in the college and university subsample, and 3 of 7 abilities in the adult subsample. Interestingly, these significant λ3 terms were in the directions opposite to those predicted by the age differentiation-dedifferentiation hypothesis, and instead indicate a pattern of larger factor loadings with childhood development and smaller factor loadings with adult aging. The ability differentiation hypothesis is therefore supported by these data, but the age differentiation-dedifferentiation hypothesis is not supported (instead, an age dedifferentiation-differentiation pattern seems to be evident). Similar patterns persisted when the nonlinear (λ2) and age-modification (λ3) terms were estimated in a single model.

Parameters from the full model for the three subsamples are reported in Table 6. It can be seen that there was very little evidence that ability differentiation was modified by age, as the corresponding terms were only significant for 2 of 7 abilities in the school age subsample (and in opposite directions to one another), 1 of 7 abilities in the college and university subsample, and 0 of 7 abilities in the adult subsample. Note that because the main effects of age were controlled for, and because age and g were centered at their means, multicollinearly was greatly reduced7 and the estimates for the λ1, λ2, and λ3 parameters were very similar to those from the models fit in the intermediate steps (reported in Table 5). That is, the patterns of results in the full model were again consistent with ability differentiation and inconsistent with age differentiation-dedifferentiation, with some indication of an age dedifferentiation-differentiation pattern.

Table 6

Parameter Estimates (and 99% Confidence Intervals) from Full Model.

Figure 6 illustrates the findings with respect to ability differentiation in the 3 subsamples (based on parameter estimates from the full model). The left column of plots displays the model implied quadratic relations between the broad abilities and the common (g) factor. It can be seen that because the trends are concave downward, the slopes of the functions diminish with increasing ability level (note that because g is on the Z metric, the ability levels in these plots range from the 7th percentile to the 93rd percentile). These trends can also be expressed as communalities for the broad abilities, where communality is defined as the percentage of age-independent variance in the ability that is accounted for the common factor (see Appendix B for formulas). In the right column it can be seen that, consistent with the ability differentiation hypothesis, the communalities decrease with ability level in all cases. This is also apparent in the total proportion of standardized age-independent variance in the broad abilities that is accounted for by the common factor. Consistent with ability differentiation, this proportion differs by between approximately twenty and forty-five percentage points, in the range from the 7th percentile to the 93rd percentile of functioning.

Figure 6

Model implied relations between the score on the “g” factor and each broad ability (left column), and communalities in each broad ability (right Colum), in grade school (top row), college and university (middle row), and adult (bottom...

Figure 7 illustrates the findings with respect to age trends in broad ability communalities in the child and adult subsamples (based on parameter estimates from the full model). Although the trends are less apparent than those that are displayed in Figure 6, the general pattern is one of increasing communalities in childhood (significant age trends in the loadings of Gc and Gv on g), and decreasing communalities in adulthood (significant age trends in the loadings of Gc, Gv, and Glr on g).

Figure 7

Model implied relations between age and communalities in each broad ability) in grade school (top) and adult (bottom) subsamples. Communalities are based on age- and age squared-partialled variances. Contrary to the age differentiation-dedifferentiation...

Finally, it is of note that in addition to the models reported here, a number of higher order mediation models (examples of linear forms of which can be found in Salthouse & Ferrer-Caja, 2003, and Salthouse, 1998) were considered. Such models consider the common higher order (g) factor as a mediator of the age-related influences on each ability (ability-differentiation can therefore be conceptualized with respect to absolute ability level instead of age-controlled ability level), with direct effects from age to the individual abilities allowed as needed. These models produced very similar patterns of results to those reported here (weaker factor loadings at higher ability levels, stronger factor loadings with childhood age, and weaker factor loadings with adult age). Such models are suspect, however, as they may potentially produce nonlinear factor loading estimates as artifacts of the nonlinear age-trends that are apparent in Figure 5. These results are therefore not reported.

Discussion

Summary of Findings

The results reported here provide consistent support for the hypothesis that cognitive abilities are less related to each other at higher ability levels, and less clear support for hypotheses that cognitive abilities systematically change in their degrees of independence across the human lifespan. In fact, contrary to the conventional age differentiation-dedifferentiation hypothesis that abilities become less related with childhood development and more related with adult aging, there was partial evidence of the reverse- some factor loadings showed increases in their magnitudes with childhood age and decreases in their magnitudes with adult age.

Introduction

During the last decade, it has been a growing interest in aging research to explore the evolving relationship between cognitive and motor performance decline over time (Li and Lindenberger, 2002; Schäfer et al., 2006; Schaefer and Schumacher, 2010), with the underlying hypothesis that few causal mechanisms might act as pacemakers of cognitive-motor coupling (Lindenberger and Baltes, 1994; Baltes and Lindenberger, 1997). Age-related behavioral slowing, which is observed in both cognitive and motor tasks, is a good entry point in this respect since it constitutes a proxy of processing speed in the central nervous system (CNS; Salthouse, 1996, 2000; Deary et al., 2010; Eckert et al., 2010; Eckert, 2011).

In the cognitive domain, it is currently considered that behavioral slowing is mediated by a generalized deficit in processing speed of the CNS, which might be at origin of performance decline in a large variety of tasks (Birren, 1965; Birren et al., 1980; Cerella, 1985, 1991, 1994; Bashore, 1994; Salthouse, 1996; see Deary, 2000 for a discussion). In support of this hypothesis, meta-analyses using Brinley regression functions (Brinley, 1965) showed roughly constant slowing ratios between response latencies of young and older adults (i.e., 1.4–1.6), independent of the type of task (Cerella et al., 1980; Cerella, 1985). These findings supported the so-called general slowing hypothesis (GSH) in the cognitive domain (Cerella, 1985, 1991, 1994).

Most authors assumed that sensori-motor processing speed is irrelevant to the GSH because it is relatively spared by age-related alteration of the CNS and is included in behavioral slowing as an additive peripheral contribution (for detailed theoretical and methodological arguments, see Cerella, 1985, 1991; Bashore, 1993, 1994). This view was based on the segregation between the slowing of computational (central) and peripheral (sensori-motor) components of the cognitive tasks, which generally involve a simple motor response. However, age-related behavioral slowing is also pervasive in most motor tasks requiring complex movements (Ketcham et al., 2002; Watson et al., 2010; Mielke et al., 2012; Rey-Robert et al., 2012; Temprado et al., 2013). Since brain activity underlying programming and control of complex movements is currently considered as a computational, information-processing activity (Welford, 1977; Schmidt, 1988; Light, 1990), slowing of motor behavior presumably reflects decrease in processing speed in sensori-motor neural structures of the CNS. Thus, the question arises of whether the GSH can be extended to the motor domain. A critical question in this respect is whether behavioral slowing observed in cognitive and motor tasks dedifferentiate that is, if they become of comparable magnitude in older adults (Birren and Fisher, 1995). It might be the case because processing speed in cognitive and motor tasks becomes progressively supported by common neural resources during aging. Evidence supporting this view does exist in the literature. For instance, age-related increase in co-variation of cognitive and motor performance observed in correlation studies (Lindenberger and Baltes, 1994; Baltes and Lindenberger, 1997) suggested the existence of common neural factors to decline of both functional domains (Lindenberger and Ghisletta, 2009). This hypothesis is consistent with the pioneering observations by Birren and Botwinick (1951), who reported increased correlation (i.e., dedifferentiation) between calculation time and writing time in older adults, relative to their young participants. Recent behavioral and brain-imaging studies also showed that cognitive permeation of the motor domain becomes more accentuated during aging (Li and Lindenberger, 2002; Schäfer et al., 2006; Schaefer and Schumacher, 2010), presumably since cognitive and motor systems shared more common brain structures in older adults than in young participants (Heuninckx et al., 2005, 2008). In addition, because some of the neural underpinnings of decrease in processing speed (e.g., white matter changes) are neither specific to cognitive nor to motor areas (Penke et al., 2010; Reuter-Lorenz and Park, 2010; Eckert, 2011), one can predict to observe a generalized slowing of behavior in cognitive and motor tasks. The present study addressed this issue.

To achieve this objective, we compared response times recorded in two representative task paradigms of cognitive and motor domains that is, choice reaction time (CRT) and rapid aiming movement tasks, respectively. In this perspective, the CNS as a model human processor (MHP) composed of cognitive and motor functional sub-systems, each characterized by a specific principle of operation (Card et al., 1986) that is, Hick–Hyman’s law (Hick, 1952; Hyman, 1953) and Fitts’ law (Fitts, 1954; Fitts and Peterson, 1964), respectively. Hick–Hyman’s law and Fitts’ law capture the linear relationship between response time and task-related complexity variables defined in reference to quantitative theory of information processing (i.e., index of difficulty, ID in bit), in CRT and aiming movement tasks, respectively.

In reaction time (RT) tasks, the number of possible S–R associations (i.e., N alternatives) is manipulated, while the complexity of the motor response is maintained constant and minimal (Henry and Rogers, 1960; Sanders, 1990; Klapp, 1996). Thus, when low error rate is preserved in the different conditions (Pachella, 1974; Wickelgren, 1977), CRT is a reliable measure of the time needed by the CNS to reduce the uncertainty conveyed by the imperative signal. Accordingly, the index of difficulty (ID = Log2Na, ID is in bit, with Na being the number of alternatives) quantifies the amount of information (in bit) to be processed to produce a correct response. It is noticeable that RT also includes the central duration of motor response generation processes (Henry and Rogers, 1960), which are however maintained constant, minimal and independent of the duration of central processing related to response selection (Welford, 1977; Cerella, 1985; Jensen, 1987; Bashore, 1993).

Hick (1952) and Hyman (1953) showed that RT is linearly related to ID according to the following relation: RT = a + b × ID, with a and b as constants. This ID–RT linear relation – so-called Hick–Hyman’s law – reflects the efficiency function (EF) of information processing in the CNS. The slope of the EF is currently referred to as a measure of central processing, while the influence of peripheral factors on RT is assessed by changes in the intercept (Welford, 1984; Cerella, 1985; Bashore, 1993). Thus, the steeper the slope of Hick–Hyman’s law, the longer it takes to process a fixed amount of information by the CNS. In this respect, small slope values (30–40 ms/bit) have been currently reported in the literature, thereby suggesting that the RT task weakly loaded information-processing capacity of the CNS (Cerella, 1985; Jensen, 1987; Birren and Fisher, 1995; see below).

According to the framework of information theory, age-related slowing of RT reflects a decrease in central processing speed (e.g., Hale et al., 1987; Amrhein et al., 1991; Fozard et al., 1994; Earles and Salthouse, 1995; Salthouse, 1996; Hultsch et al., 2002). However, the effect of aging on the slope Hick–Hyman law has been scarcely described in the literature. In its extensive review, Jensen (Jensen, 1987) only referred to unpublished data (Ananda, 1985, unpublished doctoral dissertation, University of California, Berkeley) reporting a slight increase (about 10 ms/bit) in the slope of Hick–Hyman law in elderly people that is, 20–25% of the processing capacities currently observed in young adults. On the basis of a review of 11 RT studies, Welford (1984) reported estimated age-related slowing ratio to about 16% (see Cerella, 1985, for a consistent estimation). These values were smaller than those currently reported for cognitive processing speed (1.4–1.6; Cerella et al., 1980; Cerella, 1985), and close to those reported for task conditions involving weak computational requirements (1.2/1.3; Cerella et al., 1980; Cerella, 1985). A plausible explanation is that, when compatible S–R associations are used, central executive functions (EFs) associated with response selection were weakly loaded and RT tends to predominantly reflect more peripheral components (Birren and Fisher, 1995; see Yordanova et al., 2004; Falkenstein et al., 2006; Kolev et al., 2006 for supporting evidence). This raises the question of whether “pure” processing speed of the CNS (and, consequently, age-related slowing ratios) can be estimated independently of the modulating effect of EFs, which are more or less systematically involved in most cognitive tasks and are very sensitive to aging. Unfortunately, as noted by Verhaeghen and Cerella (2002), appropriate paradigms are lacking to resolve the form of the influence of executive control processes on processing speed (but see Albinet et al., 2012 for an elegant attempt in this respect). We contend that the use of incompatible S–R associations in Hick–Hyman paradigm might permit to move beyond this limitation by imposing additional load to EFs (e.g., Smulders et al., 1999; Meiran and Gotler, 2001; Eppinger et al., 2007; Vu and Proctor, 2008) and then, to get a more reliable measure of processing speed of the CNS. Indeed, it has been shown increasing S–R incompatibility – i.e., altering the natural mapping between the spatial stimulus array and the spatial response array (Fitts and Seeger, 1953; Fitts and Deininger, 1954) – significantly increased the slopes of the RT-ID EFs relative to those observed in compatible S–R associations (Welford, 1984; Sanders, 1990; see Jensen, 1987 for a review). Accordingly, Jensen (1987) recommended the use of incompatible S–R associations when assessing cognitive processing speed through Hick–Hyman’s law.

Information-processing speed can also be measured in aiming movement tasks through Fitts’ law. Fitts’ law is calculated on the basis of response times measured in rapid aiming movement tasks, consisting of moving from a home position toward a target placed at a given distance. The width (W) and/or distance (D) of the target can be varied to modulate task difficulty. In the framework of information theory, the index of difficulty (ID = Log2(2 × D/W), in bit) measures the amount of information to be processed to produce a fast and accurate movement in discrete and cyclic aiming tasks (Fitts, 1954; Fitts and Peterson, 1964). Accordingly, movement time (MT) was proven to be linearly related to the ID, hence to D and W, according to the following relation: MT = a + B × ID, with a and b as constants (Fitts, 1954; Fitts and Peterson, 1964). The ID–MT linear relation – so-called Fitts’ law – reflects the EF of information processing in the CNS to control the aiming movement. The steeper the slope, the longer it takes to process a fixed amount of information. Compared to constraints related to increasing movement accuracy (i.e., W manipulation), those related to movement amplitude (i.e., D manipulation) have been shown to result in a steeper ID–MT slope (Welford et al., 1969; Heath et al., 2011; Sleimen-Malkoun et al., 2012) that is, to globally impose greater processing demands to the information-processing system. Slopes values comprised between 60 and 100 ms/bit were currently observed in young adults, depending on whether IDs are obtained via target distance or target size manipulation (for illustrative examples, see Rey-Robert et al., 2012; Temprado et al., 2013). In addition, several studies showed longer MTs (Welford et al., 1969; York and Biederman, 1990; Haaland et al., 1993; Teeken et al., 1996; Ketcham et al., 2002) and steeper slopes of Fitts’ law (130–150 ms/bit) in older participants relative to young adults (Rey-Robert et al., 2012; Temprado et al., 2013).

In the MHP framework, Hick–Hyman and Fitts’ laws are hypothesized to quantify information-processing efficiency of cognitive and motor functional sub-domains, by expressing it under the same form (i.e., linear relations between response times and IDs) and in the same metrics (bit/s) and that, independently of the details of the mechanisms involved in RT and aiming movement tasks (Card et al., 1986). Differences between slope values currently reported in the literature on Hick–Hyman and Fitts’ laws support the hypothesis of functional separation of cognitive and motor principles of operation in young adults. Indeed, the longer time necessary to process one bit of information in aiming tasks relative to CRT tasks suggests that the sensori-motor structures are less efficient in processing information than the cognitive ones. We contend however that this conclusion could be misleading since it does not take into account the possible contamination of processing speed measured by Fitts’ law by cognitive EFs. In other words, larger slope values observed for Fitts’ law could simply reflect the fact that aiming task included a significant contribution of EFs – i.e., planning, up-dating information and inhibitory processes (see Jurado and Rosselli, 2007, for an extensive review on EFs) – which was not (or only weakly) involved in the RT task, when compatible S–R associations were used. This hypothesis is consistent with recent studies showing that EFs are currently involved in complex motor tasks (e.g., locomotion; Yogev-Seligmann et al., 2008; Verghese et al., 2010). Slowing ratios observed in aiming movement tasks (1.4/1.5; Rey-Robert et al., 2012; Temprado et al., 2013) also suggested that cognitive/executive processes are largely involved in the control of aiming movements. Indeed, these values were of comparable magnitude with those previously reported in meta-analyses of the cognitive literature, for a large variety of non-motor tasks (1.4/1.6; Cerella et al., 1981; Cerella, 1985). According to these findings, we concluded that, to test the GSH in both cognitive and motor domains, one should compare Fitts’ law with Hick–Hyman’s law calculated on the basis of response times recorded for incompatible S–R associations in CRT tasks.

The main objective of the present work was to extend the GSH to the motor domain. To achieve this objective, we compared speed of information processing measured by Hick–Hyman’s law and Fitts’ law, in young and older adults. As a prerequisite, we predicted to observe: (1) increase in the slope of the efficiency of Hick–Hyman law in young adults when using incompatible S–R associations relative to compatible ones; (2) longer response times in older adults, in both CRT and aiming movement tasks, and (3) steeper slopes for both laws in older participants. Moreover, our main hypothesis was that, due to the dedifferentiation of cognitive and motor processes during aging, aiming movement task should become more contaminated by the engagement of EF in older than in young participants. Accordingly, we predicted that the slopes of Hick–Hyman’s law and Fitts’ law should be closer (or even similar) in older adults than in young participants.

Materials and Methods

Participants

Twenty-four right-handed subjects, separated in two age groups, participated in this experiment: 10 young adults (five men, mean age = 26 ± 3 years) and 14 older adults (seven men, mean age = 78 ± 7 years). Young participants were recruited among students of Aix-Marseille University. Older participants were recruited in a leisure and retirement club. They all lived independently and declared to be physically active. Autonomy was assessed using the six-item Katz index (Katz, 1983) and the Older American Resources and Services (OARS; Fillenbaum and Smyer, 1981) for basic (ADL) and for instrumental activities of daily living (IADL), respectively. Physical activity level was assessed using the Canadian Study of Health and Aging Risk Factor Questionnaire (RFQ; Davis et al., 2001). All participants completed a self-report to ensure that they did not suffer from cognitive or sensori-motor troubles that might bias their performance in the experimental tasks. In addition, a standardized geriatric assessment (SGA) was supervised by a medical doctor. It allowed the assessment of: (i) vision (using self-report visual functional test described by Cacciatore et al., 2004), (ii) depression (using the four-item Geriatric Depression Scale (mini GDS); Clément et al., 1997), (iii) cognition (using the clock drawing test; Shulman, 2000), (iv) pain (upper limbs or neck pain due to osteoarthritis), and (v) medication and co-morbid conditions. These assessments attested that older participants did not suffer from pathological cognitive and motor impairments. They all had their vision corrected and none of them was depressive. Twelve participants of the elderly group were practicing a regular physical activity, consisting in walking for at least 30 min three times per week; the remaining two participants walked one time per week for at least 30 min. For ADL, 13 participants had a maximum score (6/6) and one had a score of 5/6. For IADL, 12 participants had a score of 14/14, one had a score of 13/14 and one a score of 12/14. None of the older participants presented any deficits leading to their exclusion from the study. Informed consents to participate in the study were obtained from all young and older participants. None of them had a prior experience with the experimental tasks. The protocol was approved by the local ethic committee of Aix-Marseille University, and has therefore been in accordance with the ethical standards laid down in the Declaration of Helsinki.

Apparatus and Task

Participants were seated in an adjustable height chair at a table in a bright room and no noise disturbance. They had to perform a discrete rapid-aiming task (Fitts’ task) and a RT task (Hick–Hyman’s task). The order of presentation of these two tasks was counterbalanced.

Aiming Task

The task consisted in making home-to-target aiming movements with the right arm by sliding a hand-held non-marking stylus (Wacom, Generation 2 tip sensor) over the surface of a Wacom graphic tablet (Intuos4 XL) placed on the tabletop directly in front of the participants (portrait orientation). The home position was marked by a black square (5 mm × 5 mm) and the target was symbolized by a black horizontal rectangle (40 mm × 7 mm). They were both printed on a white paper sheet and inserted under the tablet’s transparent plastic film cover. Home position and target center were aligned and located at 14.5 cm from the left side of the tablet’s sensitive area. Sliding movements were performed in the anterior–posterior direction and were executed with a combination of shoulder flexion and elbow extension. Participants were instructed to constantly keep their back against the chair support to prevent trunk compensations. The graphic tablet was connected (via a USB port) to a portable PC (Dell, Latitude D420). A customized software was used to acquire and save the kinematic data generated by the displacements of the stylus on the tablet with a sampling frequency of 250 Hz.

Reaction Time Task

The RT task was performed on a response console similar to “Jensen’s box” (1987). The console consisted of a metal panel (360 mm × 400 mm × 4 mm) tilted at a 30° angle. A home capacitive touch sensor switch (CSE 16, Schurter, diameter: 20 mm) was located at the lower center of the panel. It was surrounded by 16 equidistant (17°) similar buttons arranged in a semi-circle, on an arc of 255°, with a radius of 8 cm. All buttons were screwed on the metal plate. Each response button on the panel was associated with a red and a green flat LED (Agilent Technologies, diameter: 5 mm). The red LED was used for pre-cuing the potential responses; the green LED was used to indicate the effective response that is, the button to reach. Three centimeters above the central home button were placed three yellow flat LEDs (Agilent Technologies), which were used as warning signals for the preparation period. The ignition sequence of the LEDs was the following: (1) pre-cuing of response alternatives (red LED, duration: 2 s), (2) preparatory period of 1000, 1250, 1500, or 1750 ms presented randomly (yellow LEDs blanking three times); and (3) response signal (green LED staying on until reaching of the response button). Correspondingly, participants held their right index finger on the home button, then, at the onset of the imperative stimulus (IS), they were instructed to move as fast as possible and press the corresponding response button (see below for description of compatible and incompatible S–R association conditions).

An acquisition card (NI USB 6608) was used to record the data and another one (NI USB 6501) to control the LEDs by managing digital inputs and outputs. Both cards were connected to a laptop (Dell, Latitude D420) via USB ports. The whole display was controlled by an interface developed under LabVIEW (version 10.0, National Instruments), which allowed the experimenter to start the ignition sequence of the LEDs.

Procedure

Aiming Task

Experimental conditions consisted of five ID levels, ranging from three to seven bits by increments of 1.0 bit. Task difficulty was scaled via the manipulation of target distance from home position. Five distances were used: 28 mm (ID3), 56 mm (ID4), 112 mm (ID5), 224 mm (ID6), and 448 mm (ID7). At the start of each trial, the stylus was placed on the home position. Participants were instructed to preserve optimal speed–accuracy trade-off that is “to move as fast as possible from the starting position toward the target and to stop on it without making any (overshoot or undershoot) errors.” For each of the five ID conditions, participants were allowed three unrecorded practice trials then requested to complete a block of 16 trials. The order of presentation of the conditions was randomized in-between participants. In order to help participants to adjust the adopted speed–accuracy trade-off, the experimenter provided verbal feedbacks after each condition. In each ID condition, the allowed error rate was 12.5% (maximum 2 trials out of 16). If more than two trials were missed, the missed trials were repeated at the end of the condition. In this respect, one young participant had to repeat three trials at ID4, and another four trials at ID6. Only one older participant repeated three trials at ID7.

Reaction Time Task

A pilot experiment was carried out with a group of six young participants (25–30 years) with three IDs (0, 1, and 3 bits) to verify the conformity of RT data to Hick–Hyman’s law and to determine the most appropriate experimental conditions of S–R compatibility. These participants were not included in the subsequent experiment.

In the pilot experiment, we conformed to the procedure recommended by Jensen (1987) and the results were similar to those reported in his review. Specifically, they confirmed that: (1) both individual and collective (group mean) RT data followed Hick–Hyman’s law, (2) RT did not depend on the response button position on the panel, and (3) learning effect on RT did not occur for a small number of trials (<30). In addition, we tested the effect of S–R compatibility on RT (Fitts and Seeger, 1953). In incompatible conditions, participants were requested to reach the response button opposite to the button cued by the green LED, with respect to the central symmetry axis of the button arrangement. Results showed that the slope value of the EF (31 ms/bit) was the same as that calculated by Jensen (1987) for a sample of nine studies in young participants (27 ms/bit). Similar values were also observed for the intercepts (300 ± 15 and 270 ms, respectively). In incompatible conditions, RTs also followed Hick–Hyman law but the slope of EF (RT–ID relationship) increased (68 ms/bit) and approached those observed for Fitts’ law in previous studies (Rey-Robert et al., 2012; Temprado et al., 2013). Thus, as predicted, incompatible S–R associations increased the slope of Hick–Hyman law, presumably by loading central EF associated with response selection.

In the subsequent experiment, five levels of difficulty of incompatible S–R associations were selected: ID = 0, 1, 2, 3, and 4 bits, which corresponded to 1, 2, 4, 8, and 16 possible responses. It is noticeable that, due to task specificities, difficulty levels in both tasks were different. Our objective was not to compare similar IDs in the two tasks. It did not preclude however the comparisons between the slopes of Hick–Hyman and Fitts’ laws.

Participants had to react as quickly as possible and move their finger toward the button that was opposite to the one corresponding to the lightened green LED, with respect to the central symmetry axis of the panel. Sixteen trials were carried out in each ID condition. Following the recommendations provided by Jensen (1987), the ID conditions were always presented in the same order to compare the differences between groups. Accordingly, the order of presentation was: 3/0/1/4/2 bits. The locations of effective responses on the button panel were also balanced across trials so that all the different locations were used in each ID condition. To encourage participants to perform the task as quickly as possible, participants were informed of their total response time (TR + TM) after each trial. Trials in which participants anticipated the response signal (<100 s), moved in the wrong direction, or missed the target button, were considered as response errors. In each ID condition, the allowed error rate was 12.5% (maximum 2 trials out of 16). If in any ID condition more than two trials were missed, these trials were repeated. This was the case for only one young participant who had to repeat three trials at ID4.

Variables and Data Processing

Aiming Task

The pen-tip raw data were filtered using a second-order dual pass (no phase-lag) Butterworth filter with a cut-off frequency of 10 Hz. Time series of position and velocity profiles were then computed. Movement onset and offset were determined on the basis of velocity profiles using the optimal algorithm of Teasdale et al. (1993). The critical velocity threshold was obtained by multiplying peak velocity by 0.04. MT, defined as the elapsed time between movement onset and offset, was then computed.

Reaction Time Task

Reaction times and MT were recorded. RT was defined as the time elapsing between the lighting of the green LED and the release of the home button. RT values above three times the standard deviation (SD) were discarded from the analysis. MT was defined as the time elapsing between the release of the home button and the touch of the response button. Participants were instructed to respond as fast as possible but they were not informed that RT and MT were recorded and analyzed separately.

Statistical Analyses

Two-way ANOVA (group × ID) with repeated measures on ID has been carried out on all variables. The sphericity of the data was verified for each analysis with the test of Mauchley and, in case of violation, the Greenhouse–Geisser correction was applied to the degrees of freedom (df). Accordingly, the reported df correspond to the nearest whole number. The effect size was calculated as: η2=SS explained/SS total. Post hoc analyses were carried out using Newman–Keuls test.

To compare response times observed in CRT and aiming movement tasks, EFs and Brinley functions (BF) were calculated. EFs quantified the relation between the ID and the temporal variables recorded in each task (RT and MT). They were determined by using linear regressions carried out on mean group values in each task. EFs representing Fitts’ law were conducted on MT data and those representing Hick–Hyman’s law on RT data. Linear regressions of BF (Brinley, 1965) were calculated after plotting mean values of MT and RT observed in young participants (abscissa) against those observed in elderly (ordinate). Thus, it resulted in two BF: one for Fitts’ task and one for Hick–Hyman task.

Efficiency and BF differed in their purpose and, hence, were complementary. By comparing between the slopes of the different EFs, we assessed information-processing capacities in each age group (in bit/s). BFs, on the other hand, allowed the estimation of age-related slowing ratios, which were measured by the slope values of the regression functions. The comparison between the calculated slopes in each task allowed determining if sensori-motor and cognitive processes presented the same slowing ratios with aging. In all regression analyses Student’s t-statistic was used to compare between slopes. For all statistic tests the used threshold of significance was 0.05.

Results

Mean and SDs values of response times observed in each ID level along with the statistics of ANOVA are summarized in Table 1.

TABLE 1. Mean and standard deviation values of response times and ANOVA results.

Aiming Movement Task

Analysis of Variance on Movement Time

The ANOVA carried out on MTs revealed a main effect of group [F(1,22) = 23.13, p < 0.001, η2 = 0.2], with older participants being slower, and of ID [F(2,47) = 324.93, p < 0.001, η2 = 0.55]. It also showed a significant group × ID interaction [F(2,47) = 9.56, p < 0.001, η2 = 0.02]. Post hoc decomposition of the interaction showed that MT increased with ID for both groups (p < 0.001). In addition, MTs were longer in older adults and the difference between the two groups was larger for the higher difficulty level (ID7, p < 0.05).

Efficiency Function

Linear fittings of ID–MT relation in each age group, along with the corresponding equations, can be found in Figure 1. Fitts’ law fitted well MT data in both groups (Ryoung2 = 0.98; Relderly2 = 0.96). However, EF of the group of older participants presented a significantly steeper slope (147 vs. 105, p < 0.05), with no significant difference between the intercepts (-100.3 vs. -111.5, p > 0.05).

FIGURE 1. Efficiency functions for movement time in Fitts’ task. Young participants’ data and linear regression estimates are presented in gray and those of older participants in black.

Choice Reaction Time Task

Analysis of Variance

The ANOVA carried out on RTs showed main effects of group [F(1,22) = 32.62, p < 0.001, η2 = 0.21], and ID [F(2,43) = 122.83, p < 0.001, η2 = 0.28], with a group × ID interaction [F(2,43) = 10.39, p < 0.001, η2 = 0.004). Older participants were slower than young participants with a significant inter-group effect for ID3 and ID4 (post hoc decomposition, p < 0.001). The ID significantly increased RTs with significant inter-conditions differences for both groups (post hoc decomposition, p < 0.01) except for ID3–ID4 in the young group (p > 0.05).

We also analyzed MTs associated with RTs. Results showed a main effect of age [F(1,22) = 20.11, p < 0.001, η2 = 0.31], but no significant effect of ID [F(1,32) = 3.07, p > 0.05, η2 = 0.04], nor a significant group × ID interaction [F(1,32) = 0.52, p > 0.05, η2 = 0.007]. Hence, older participants were slower than young participants. In addition, for both young and older participants, MT was not significantly changed across the ID levels.

Efficiency Functions

Efficiency functions were estimated for mean RTs in each group (Figure 2). Coefficients of determination were higher than 95% (Ryoung2 = 0.97; Relderly2 = 0.99). The EF of older participants showed a significantly steeper slope (134.9 vs. 76.9, p < 0.001) and a greater intercept (396.5 vs. 316.7, p < 0.01) compared to those observed for young participants

FIGURE 2. Efficiency functions for reaction time in Hick–Hyman’s task. Young participants’ data and linear regression estimates are presented in gray and those of older participants in black.

Since the results of the ANOVA showed that RT did not significantly increase after ID4 in the young group, ID–RT relation was re-evaluated for the difficulty range between zero and four bits (Ryoung2 = 0.99; Relderly2 = 0.99). The exclusion of ID4 increased the slope of the young’s EF but it remained significantly inferior to the older one (89 and 134.9, respectively, p < 0.001).

Comparison Between Fitts’ Law and Hick–Hyman Law

Efficiency Functions

We compared the slopes of EFs calculated for Hick–Hyman and Fitts’ laws in each group of participants. Results showed that the slope of Fitts’ law was significantly larger than that of Hick–Hyman’s law in young participants, independent of whether three or four IDs were considered in the CRT task (105.4 vs. 77 and 89, respectively, p < 0.05). Conversely, the slopes of Fitts and Hick–Hyman’s laws observed in older adults did not differ from each other (147.1 and 134.9, respectively, p > 0.05). As for the intercepts, in both groups, Hick–Hyman’s law presented the largest values (p < 0.001).

Brinley Functions

Brinley functions were calculated for MT and RT, allowing a quantification of age-related changes in performance in each task, which was then compared. The estimates of BFs are reported in Figure 3. For both tasks the slopes of BFs were significantly different from 1 (1.4 for the aiming task and 1.7 for the CRT task, p < 0.001). However, although the slope of BF calculated in the cognitive task was 20% larger than that observed in the motor task, they were not significantly different from each other (p > 0.05). When the analysis was conducted between ID0 and ID4 the inter-group difference in slope was reduced (1.33 for MT with R2 = 0.99, and 1.44 for RT with R2 = 0.98; see Figure 4).

FIGURE 3. Brinley plots. Data and linear regression estimates of reaction time (observed in Hick–Hyman’s task) are presented in gray and those of movement time (observed in Fitts’ task) are presented in black. Each data point corresponds to an ID condition (from the easiest to the hardest).

FIGURE 4. Brinley plots without the hardest ID condition. Data and linear regression estimates of reaction time (observed in Hick–Hyman’s task) are presented in gray and those of movement time (observed in Fitts’ task) are presented in black. Data points correspond to the first four ID conditions of each task, respectively.

Discussion

One of the most reliable findings in aging literature is that older adults respond more slowly than younger adults in both cognitive and motor tasks. Hence, several studies attempted to quantify slowing ratios between response latencies of older and younger adults in cognitive tasks (e.g., Cerella et al., 1980; Cerella, 1985) and, more recently, in rapid aiming movement tasks (Rey-Robert et al., 2012; Temprado et al., 2013). However, until now, it had never been explored whether similar slowing ratios could be observed in cognitive and motor domains, in the same group of participants. It could be the case because, due to the dedifferentiation of neural information-processing resources during aging, the two operation principles presumably related to separate cognitive and motor sides of the MHP in young adults become related to one another in later life (Lindenberger and Baltes, 1994; Birren and Fisher, 1995; Lindenberger and Ghisletta, 2009). The present experiment addressed this issue in young and older adults by comparing Hick–Hyman and Fitts’ laws.

Results observed in the pilot experiment of the present study confirmed that, in the CRT task, the use of incompatible S–R associations led to steeper slope of Hick–Hyman’s law. This result was consistent with those reported by Jensen (1987) and confirmed our prediction with respect to the effect of load imposed to EFs on cognitive processing speed. This result did lend credence to the strategy used in the present study to investigate the GSH. Specifically, it consisted of assessing processing speed in a cognitive task where EFs were strongly involved to further compare it with that observed in a motor task, also involving EFs. This strategy is different from those consisting of isolating the contribution of EF and processing speed since they are hypothesized to be the two critical and separate mediators of age-related decline of performance in a wide range of tasks (Verhaeghen and Cerella, 2002; Lindenberger and Ghisletta, 2009; see Albinet et al., 2012) for an elegant contribution in this respect). Our results are however consistent with the hypothesis that “pure” cognitive processing speed is rather difficult to quantify in isolation since it is often more or less contaminated by the involvement of EF, even in most cognitive tasks (see Cerella, 1985; Salthouse, 1996 for a converging point of view). Thus, using incompatible S–R associations in the choice reaction task allowed estimating a more specific measure of cognitive processing speed than the use of compatible S–R conditions (see Jensen, 1987 for a converging point of view).

Effects of Aging on Hick–Hyman’s Law and Fitts’ Law

As a prerequisite, we explored the effects of aging on Hick–Hyman’s law and Fitts’ law, thanks to the use of a large range of ID values in both RT and aiming movement tasks.

Results showed that RTs perfectly followed Hick–Hyman law in both young and older adults. An exception to the linear increase in response time with ID was noticed in the RT task, for young participants, between ID3 (eight S–R pairs) and ID4 (16 S–R pairs). Such discontinuity was not observed in older adults. In addition, aging resulted in steeper slope and slightly greater intercept of Hick–Hyman law, thereby suggesting that central components were more loaded by incompatible S–R associations than peripheral ones (Welford, 1984). The analysis carried out on MTs showed that older adults were significantly slower than young participants. On the other hand, MTs were not affected by ID increase. This result showed that participants did not strategically trade RT and MT to make a part of the decision while moving toward the endpoint target, when ID increased (Jensen, 1987).

In Fitts’ task, results observed for MTs were consistent with those observed in our previous studies (Rey-Robert et al., 2012; Temprado et al., 2013). Indeed, regression functions showed that aging resulted in steeper slopes of Fitts’ law in older adults. It is noticeable that intercepts were larger in older adults than in young participants. This result is not surprising however; it suggests that musculo-skeletal peripheral factors were also affected by aging, thereby lengthening additively MTs (Allen et al., 2004).

Overall, as predicted: (1) response times were significantly lengthened in older adults in both the CRT and aiming movement tasks, and (2) difference of response times observed between young and older adults increased with ID in both the cognitive and motor tasks, thereby revealing a previously described age-complexity effect (Birren, 1965; Cerella et al., 1980; Cerella, 1985). These results suggest that processing speed decreased in a quantifiable amount (in bit/s) in older adults, in both the RT and aiming movement tasks. This hypothesis was confirmed by the analysis of slowing ratios.

Age-Related Slowing Ratios in Reaction Time and Aiming Movement Tasks

Brinley functions allowed determining whether behavioral slowing observed in CRT and aiming movement tasks were of comparable magnitude, independently of whether the slope of Hick–Hyman’s law and Fitts’ law were different or not. Indeed, it could be that the effects of aging would be of comparable magnitude, even if the underlying neural resources involved in the two tasks were different. Brinley regression functions indicated equivalent slowing ratios for MT and RT (1.3–1.4). These results confirmed that simple mathematical (linear) functions can predict the latencies of older adults from the latencies of younger participants, independent of the details of information-processing mechanisms involved in CRT and aiming movement tasks. The comparison of magnitude of the slowing ratios observed for RT and MT and those reported by Cerella et al. (1980) suggest that mental information-processing resources were significantly involved in both tasks. Indeed, in their review, Cerella et al. (1980) analyzed 18 studies that included a wide range of information-processing tasks and reported a mean slowing ratio of 1.36. However, they also noticed a smaller ratio (1.15) when only sensori-motor tasks were considered, thereby suggesting that these tasks were relatively unaffected by aging because they only weakly loaded the information-processing resources that are altered in the aging brain (Kail, 1986, 1988). Accordingly, slowing ratios observed in the present study suggested that: (i) computational components were strongly involved in both RT and aiming movement tasks, and (ii) aging similarly affected information-processing speed in both tasks. If one accepts the classic hypothesis of functional separation of cognitive and motor domains, this result was rather unexpected. The comparison between Hick–Hyman law and Fitts’ law allowed testing the dedifferentiation hypothesis, which might explain the equivalent slowing ratios observed in both tasks.

Comparison of Hick–Hyman Law and Fitts’ Law in Young and Older Adults

Results observed in young adults showed that the slopes of Hick–Hyman’s law and Fitts’ law were significantly different. Specifically, the slope of Fitts’ law was larger than those of Hick–Hyman law. One can conclude from this result that neural information-processing resources were more loaded in aiming movement task than in CRT task. In addition, the difference between the slopes of the two laws strongly suggested that, in the aiming movement task, the lower processing speed reflected the conjunction of constraints imposed to cognitive EFs and sensori-motor mechanisms while, in the CRT task, processing speed prominently reflected the efficiency of EFs with minimal influence of sensori-motor mechanisms (Cerella, 1985; Jensen, 1987). Thus, the results observed in young adults are consistent with the MHP, namely that cognitive and motor sides are governed by similar but functionally separated operation principles (Hick–Hyman’s law and Fitts’ law), which rely on different information-processing resources in the CNS.

As predicted, results observed in older adults were different. Indeed, contrary to young adults, in the elderly, no significant difference was observed between the slopes of Hick–Hyman’s law and Fitts’ law. This result supported the GSH that is, the existence of a general limitation of processing speed in the aging brain, which acts as a common cause to behavioral slowing in RT and aiming movement tasks. According to the dedifferentiation hypothesis, a plausible explanation is that, with age, neural resources involved in CRT and aiming movement tasks become less specific and aiming movement task engage a compounded system in which cognitive and motor resources are closely intertwined. Possible candidates in this respect are frontal structures, which are known to be involved in numerous functions, including response selection and movement control (Stuss and Benson, 1983, 1984; Bashore, 1993; Schretlen et al., 2000). Accordingly, because frontal structures might be more and more involved in the control complex movement tasks during aging (Heuninckx et al., 2005, 2008; Yogev-Seligmann et al., 2008), age-related structural and functional alterations of frontal lobes might mediate changes of comparable magnitude in processing speed in both cognitive and motor tasks (Bucur et al., 2008; Eckert et al., 2010; Eckert, 2011). Of course, in the lack of detailed exploration of brain activity, evidence of neural dedifferentiation was indirect and only supported by the comparison of slopes of Hick–Hyman’s law and Fitts’ law that is, by the equivalent slowing ratios observed in CRT and aiming movement tasks.

Conclusion and Perspectives

The present study investigated, for the first time to our knowledge, the relationship between cognitive and motor aging in the framework of MHP (Card et al., 1986

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