John Carroll’s Views on Intelligence: Bi-Factor vs. Higher-Order Models

Abstract

The development of factor models is inextricably tied to the history of intelligence research. One of the most commonly-cited scholars in the field is John Carroll, whose three-stratum theory of cognitive ability has been one of the most influential models of cognitive ability in the past 20 years. Nonetheless, there is disagreement about how Carroll conceptualized the factors in his model. Some argue that his model is best represented through a higher-order model, while others argue that a bi-factor model is a better representation. Carroll was explicit about what he perceived the best way to represent his model, but his writings are not always easy to understand. In this article, I clarify his position by first describing the details and implications of bi-factor and higher-order models then show that Carroll's published views are better represented by a bi-factor model.

Construct validity of the Wechsler Intelligence Scale for Children – Fourth UK Edition with a referred Irish sample: Wechsler and Cattell–Horn–Carroll model comparisons with 15 subtests

“…Other researchers maintained that the bifactor model better represents Spearman's (1904Spearman's ( , 1927 and Carroll's (1993) conceptualizations of intelligence (Beaujean, 2015;Frisby & Beaujean, 2015;Brunner et al, 2012;Gignac, 2006Gignac, , 2008Gignac & Watkins, 2013;Gustafsson & Balke, 1993). Beaujean (2015) noted that Spearman's conception of general intelligence was of a factor 'directly involved in all cognitive performances, not indirectly involved through, or mediated by, other factors' (p. 130), and that 'Carroll was explicit in noting that a bi-factor model best represents his theory' (p. 130). Murray and Johnson (2013) suggested that bifactor models might benefit from statistical bias when compared to higher-order models by better accounting for unmodelled complexity.…”

“…Reise (2012) and Canivez (2016) noted several advantages of bifactor models including the direct influences of the general factor are easy to interpret, both general and specific influences on indicators (subtests) can be examined simultaneously, and the psychometric properties necessary for determining scoring and interpretation of subscales can be directly examined. Gignac (2006) also noted that the bifactor model can be considered more conceptually parsimonious because it specifies a unidimensional general factor and this model seems more consistent with Spearman's (1927) and Carroll's (1993) models of intelligence (Beaujean, 2015).…”

Construct validity of the Wechsler Intelligence Scale For Children – FifthUKEdition: Exploratory and confirmatory factor analyses of the 16 primary and secondary subtests

“…For example, Gignac (, ) contended that the most substantial factor of a battery of tests (i.e., g ) should be directly modelled, whereas its full mediation in the higher‐order model demands explicit theoretical justification; that is, a rationale is needed for why general intelligence should directly influence group factors but not subtests. Other researchers have argued that a bifactor model better represents Spearman's () and Carroll's () conceptualizations of intelligence than the higher‐order model (Beaujean, ; Beaujean, Parkin, & Parker, ; Brunner, Nagy, & Wilhelm, ; Frisby & Beaujean, ; Gignac, , ; Gignac & Watkins, ; Gustafsson & Balke, ). Beaujean () elaborated that Spearman's conception of general intelligence was of a factor ‘that was directly involved in all cognitive performances, not indirectly involved through, or mediated by, other factors’ (p. 130) and noted that ‘Carroll was explicit in noting that a bi‐factor model best represents his theory’ (p. 130).…”

“…Other researchers have argued that a bifactor model better represents Spearman's () and Carroll's () conceptualizations of intelligence than the higher‐order model (Beaujean, ; Beaujean, Parkin, & Parker, ; Brunner, Nagy, & Wilhelm, ; Frisby & Beaujean, ; Gignac, , ; Gignac & Watkins, ; Gustafsson & Balke, ). Beaujean () elaborated that Spearman's conception of general intelligence was of a factor ‘that was directly involved in all cognitive performances, not indirectly involved through, or mediated by, other factors’ (p. 130) and noted that ‘Carroll was explicit in noting that a bi‐factor model best represents his theory’ (p. 130). In fact, Jensen and Weng () suggested a bifactor model as the first step in their strategy for identifying general intelligence (Jensen & Weng, ).…”

“…Although EFA was not reported in the WISC‐V Technical and Interpretive Manual, independent EFA of the WISC‐V has not supported the existence of five factors in the total US WISC‐V standardization sample (Canivez et al ., ; Dombrowski, Canivez, Watkins, & Beaujean, ), in four age groups (6–8, 9–11, 12–14, 15–16) with the 16 WISC‐V primary and secondary subtests (Canivez, Dombrowski, & Watkins, ), nor in three of the four age groups (6–8, 9–11, and 12–14 years) with the 10 WISC‐V primary subtests in the US standardization sample (Dombrowski, Canivez, & Watkins, ). In these cases, the fifth extracted factor included only one salient subtest loading.…”