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The Psychometric Structure of GMA and Specific Cognitive Abilities

In IWO psychology the structure of cognitive abilities has been the focus of research for at least 80 years, following the publication of Spearman’s (1904) model. As Schmitt (2014) points out, cognitive abilities are typically hierarchically represented, with a general factor at the top, several broad content abilities on a lower level and the narrowest cognitive

a Spearman’s model of cognitive abilities

Figure 7.1a Spearman’s model of cognitive abilities.

b A g-centric representation of Spearman’s model

Figure 7.1b A g-centric representation of Spearman’s model.

abilities typically represented at the bottom of the hierarchy. Two psychometric models of the structure of cognitive ability have predominated for years: Spearman’s one-general cognitive ability factor and its derivatives (e.g., Vernon’s model, Carroll’s model) and Cattell and Horn’s two-general factor model (Cattell, 1963, 1971, 1987; Cattell & Horn, 1978; Horn, 1989). In the last 20 years, the most dominant model has been the three- strata model developed by Carroll (1993) and its derivatives (e.g., Cattell-Horn-Carroll’s model). However, several alternatives have been proposed, such as Holzinger’s model, Vernon’s model, the Berlin model and Johnson and Bouchard’s VPS model (2005), among others. In order to provide a general overview, the main models of the structure of cognitive ability will be briefly examined as well as more recent theoretical contributions, such as van der Maas and colleagues’ (2006) revitalization of Thomson’s model and Bartholomew, Deary and Lawn (2009).

Spearman (1904, 1927) proposed that every test consisted of a general factor (g), which was common to all tests, and a specific factor (s), which was unique to each test. For this reason, Spearman’s model has often been represented as a large, central circle representing g, and a number of smaller circles arrayed radially, which represent the specific factors or abilities (e.g., Ree & Carretta, 1998; van der Maas et al., 2006). In this sense, Spearman’s model is g-centric. Figures 7.1a and 7.1b represent Spearman’s model. For many years, Spearman refused to accept that ‘group factors’ or ‘specific abilities’ were possible, but eventually admitted they were possible in his key book of 1927.

Spearman’s model has been challenged since its inception, and several researchers have suggested that there are additional factors rather than a single general factor. The first challenge to Spearman’s model was the claim made by the British psychologist Cyril Burt that not one, but several group factors are involved (Burt, 1909). Moreover, Godfrey

Thurstone’s model of primary abilities

Figure 7.2 Thurstone’s model of primary abilities.

Thomson (1916, 1919, 1951) proposed group factors could exist without the need for a general factor to explain the positive manifold by mathematically demonstrating that a general factor could arise randomly.

Some years later, Spearman’s model was again challenged by Leon Thurstone (1938), who proposed a primary mental abilities (PMA) model, with seven orthogonal primary factors and no general factor. Figure 7.2 represents the PMA model. Initially, Thurstone refused to accept a second-order general factor, but admitted the existence of a general factor two years later (Thurstone & Thurstone, 1941). Therefore, both Spearman and Thurstone eventually agreed on the structure of cognitive abilities, although insisting on their respective emphasis on the upper or the lower level of the hierarchy.

Spearman’s model was also challenged by his disciple Karl Holzinger (Holzinger & Swineford, 1937), who proposed there was both a general factor - called the basic factor by Burt - and group factors, but that there was no hierarchical order. Holzinger’s contribution initiated the idea of nested models of cognitive abilities. This proposal was called a bi-factor theory because the group factors are independent of the general factor. In other words, this model assumes that all battery tests measure a common factor (i.e., GMA) but the variance of each test is influenced by an additional and smaller common factor reflected in tests tapping similar aspects of the smaller factor. Therefore, in a bi-factor model tests are free to load on a general factor and a set of group factors. It is important to appreciate that a bi-factor model is not a hierarchical model, as both the general factor and the group factors explain common variance of tests (or items) (Reise, Moore & Haviland, 2010).

Holzinger’s bi-factor model

Figure 7.3 Holzinger’s bi-factor model.

Research undertaken since the 1940s has lent some support to Holzinger’s view (Harman, 1976; Jenrich & Bentler, 2011; Swineford, 1949). Typically, bi-factor models use confirmatory factor analysis (CFA), but Jenrich and Bentler (2011) have proposed a method for conducting exploratory bi-factor analysis. Figure 7.3 represents Holzinger’s view.

Cattell (1963, 1971, 1987) hypothesized that there are two general factors of intelligence rather than one: fluid intelligence (Gf) and crystallized intelligence (Gc). According to Cattell (1971, p. 96), Gc arises from educational opportunities and from motivation and persistence in applying fluid intelligence to approved areas of learning. This means that Gc reflects scholastic and cultural knowledge acquisition, and therefore would be consolidated knowledge. Gf would be most highly loaded in tests like Raven’s matrices, D-48 or verbal tests designed to identify the relationship between words with similar meanings. Gc is the most highly loaded in tests based on scholastic knowledge and tests with a cultural content. Horn (1965, 1989; Cattell & Horn, 1978; Horn and Cattell, 1966), Cattell’s disciple, extended this initial model by including five broad factors (although they are narrower than Gf and Gc): visual inspection speed (Gs), visual-spatial reasoning (Gv), auditory thinking (Ga), quantitative reasoning (Gq) and fluency in recall of learned information (Gr). Figure 7.4 represents the Cattell-Horn model of intelligence. Subsequently, the Swedish researcher Jan-Eric Gustafsson (1988, 1992; Kvist & Gustafsson, 2008) found that a hierarchical factor analysis of a large battery of tests measuring Gf and Gc showed that, when the second-order factor is residualized, Gf disappears and is subsumed in GMA, and the residualized Gc remains as a verbal-numerical- educational factor. This last factor is very similar to the verbal-educational factor of Vernon’s (1957) model of intelligence.

Cattell-Horn’s two-factor theory of intelligence

Figure 7.4 Cattell-Horn’s two-factor theory of intelligence.

Vernon’s (1957, 1971) model consists of three levels, with g at the highest level and two broad factors at the lower level. The first broad factor was termed verbal-educational and the second practical-mechanical. At the primary level, Vernon distinguished six primary abilities: verbal, numerical, abstract, mechanical, perceptual and spatial. The first three abilities can be explained by the verbal-educational factor and the other three by the mechanical-practical factor. According to Carroll (1993, p. 60), Vernon’s model was the first truly hierarchical model of intelligence. Figure 7.5 represents Vernon’s intelligence model.

A further contribution relevant to the structure of intelligence is the Berlin Intelligence Structure (BIS; Jager, 1967, 1982, 1984; see also Beauducel & Kersting, 2002), which is a hierarchical model with multiple facets. A general factor of intelligence is placed at the top of the hierarchy, and below this level a content facet with three abilities: verbal, numerical and figural, with an operation facet of processing speed, memory, creativity and processing capacity. At the lowest level, there are 12 ‘structuples’ (3 contents x 4 operations). These structuples serve to classify the task in the BIS. Beauducel and Kersting (2002) found that the BIS model included Cattell-Horn’s model of Gf-Gc. Figure 7.6 represents the BIS model, including Gf/Gc distinction.

Carroll’s (1993) three-strata model of cognitive abilities is worth a special mention as it is based on an impressive analysis of more than 400 datasets. Carroll (1993) found that cognitive ability can be hierarchically described using three levels or strata. At the highest level there is a general cognitive ability (also referred to as general mental ability, general intelligence, or factor g). At the second level, there are several specific broad cognitive abilities. According to Carroll, specific broad cognitive abilities are: 1) fluid intelligence; 2) crystallized intelligence; 3) general memory ability; 4) visual perception; 5) auditory perception; 6) retrieval ability; and 7) cognitive speed. The first stratum includes a large number of more specific and narrow cognitive abilities, which are more homogeneous than those of the second stratum. Figure 7.7 represents Carroll’s model.

Over the last 15 years several researchers have suggested that Cattell-Horn’s model and Carroll’s model can be combined into a single model, usually denominated the Cattell- Horn-Carroll’s (CHC) model (Alfonso, Flanagan & Radwan, 2005; Flanagan, McGrew & Ortiz, 2000; McGrew, 1997). The CHC model consists of 10 broad cognitive abilities

Vernon’s hierarchical model of cognitive abilities

Figure 7.5 Vernon’s hierarchical model of cognitive abilities.

Berlin’s model of intelligence structure

Figure 7.6 Berlin’s model of intelligence structure.

Carroll’s three-strata model

Figure 7.7 Carroll’s three-strata model.

and more than 70 narrow abilities (see Alfonso, Flanagan & Radwan, 2007, for a complete list of the narrow abilities and their dependence on the broad cognitive abilities). The findings of the Berlin model (Beauducel & Kersting, 2003) and of Kvist and Gustafsson (2008) converge somewhat with the perspective of the CHC model.

Johnson and Bouchard have offered an innovative hierarchical model (Johnson & Bouchard, 2005a, 2005b, 2007, 2011; Johnson et al., 2004), which is an alternative to Carroll’s (1993) three-strata model. Inspired by Vernon’s (1957) model, Johnson and Bouchard’s model proposes a four-strata model. The lowest level consists of primary abilities assessed by tests, such as solving anagrams or simple arithmetical calculations. The second stratum consists of broader but still narrow abilities. The third stratum consists of three factors: a verbal (V) factor, a perceptual (P) factor and an image rotation (R) factor. The factors in the third level are highly correlated, indicating the need for a fourth stratum in which Johnson and Bouchard found a general cognitive factor, which explains why Johnson and Bouchard labelled the model VPR. Figure 7.8 represents the VPR model.

van der Maas and colleagues (2006) and Bartholomew, Deary and Lawn (2009) have proposed models for explaining intelligence structure, which were inspired by Thomson’s sampling theory of intelligence. van der Maas and colleagues (2006) proposed two possible structures of intelligence called the ‘mutualism model’ and the ‘extended

Johnson-Bouchard’s VPR model of intelligence

Figure 7.8 Johnson-Bouchard’s VPR model of intelligence.

The mutualism model

Figure 7.9 The mutualism model.

The extended mutualism model

Figure 7.10 The extended mutualism model.

mutualism model’, which explain the positive manifold without the need for a general factor. Figures 7.9 and 7.10 represent these two structures of intelligence.

Bartholomew and colleagues (2009), after pointing out certain limitations of van der Mass and colleagues’ models, proposed a revised version of Thomson’s model. This revised model supposes that the brain has N ‘bonds’, which can be called on when a person tries to respond to an item. If the bond i is active, then it contributes an amount ei to the total score. This quantity ei is a characteristic of each individual, and if the bond is selected it will contribute that quantity whatever the test items on all occasions. Because the essence of Thomson’s model is to assume that a fixed proportion of bonds, p, are selected when the test item I is selected, then the resulting score is the sum of the es resulting from the sampled bonds. The model also assumes that each bond is selected independently with probability ptI = 1..., N, where N is the number of items. Finally, the model supposes that the final score is arrived at by repeating the sampling process independently, several times.

Together the earlier models converge to the extent that they accept the existence of a general factor. Notwithstanding, whether the general factor is exactly the same or substantially the same when it is extracted from the different test batteries conceptualized and developed for specific cognitive models remains to be ascertained.

Johnson and colleagues (2009) addressed this issue by examining whether the g factor extracted from three test batteries is substantially the same or not. This point is important because, if GMA is not consistently found across batteries, then its theoretical and practical importance will be small (Jensen, 1998) due to its dependence on the specific battery. Johnson and Bouchard (2005a, 2005b, 2007) conducted several comparative studies using three datasets in which they compared the Cattell-Horn model, the g-VPR model and Vernon’s model. In these three datasets, the g-VPR model was a better fit than the others. Another important finding was that the general factor of each battery correlated largely with the others (0.99, 0.99 and 1.00). In other words, the individual differences in GMA were identical for the three different batteries (Deary, 2012).

Woolley and colleagues (2010) have made another contribution to the cognitive ability domain, in this case from the group perspective rather than from the individual one. They claim they have found a collective intelligence factor, which explains how well a group performed tasks, and which is not the mean of the GMA of the group members. Earlier, Heylighen (1999) defined collective intelligence (CI) as the ability of a group to produce better solutions to a problem than group members can work individually. Woolley and colleagues (2010) found that CI was higher in groups where turn-taking in speaking was relatively evenly distributed among members and in groups whose members had higher mean social sensitivity. A practical suggestion from this study is that it can be useful to include CI for selecting team workers.

In short, despite the multiple sub-factors and abilities measured in the various tests and batteries, most of the variance of these measures is due to a general factor, sometimes referred to as g, and sometimes as general mental ability (GMA) or general cognitive ability (GCA). Although computerized and video-based versions of cognitive tests have been developed, there are no relevant differences in their predictive capacity. Thus, there is a general consensus that a general cognitive factor, or GMA, appears to be present in most ability tests and test batteries (Carroll, 1993; Deary, 2012; Hunt, 2011; Schmitt, 2014). There is less consensus regarding the number and type of the narrower abilities, although verbal, numerical, spatial, perceptual and memory abilities are typically found in factor analytic studies.

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