JCCES and GAMA: Cognitive Factor Analysis

Whether the Jouve Cerebrals Crystallized Educational Scale (JCCES) and the General Ability Measure for Adults (GAMA, Naglieri & Bardos, 1997) measure distinct cognitive constructs is an empirical question, not a definitional one. Both batteries are routinely administered together in research and clinical contexts on the assumption that they tap separable abilities — JCCES the crystallized side (acquired knowledge and verbal-mathematical skills), GAMA the fluid-nonverbal side (abstract reasoning across figural stimuli). The assumption is reasonable but rarely tested directly with the same respondents completing both batteries. This study uses Pearson correlations and principal factor analysis with Varimax rotation on data from 63 adult respondents who completed both batteries, and recovers a clean two-factor structure that aligns with the crystallized-fluid distinction.

The two batteries and the construct distinction

The JCCES consists of three subtests: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK). All three measure crystallized cognitive abilities — knowledge and skills accumulated through education and experience. VA tests semantic and lexical relationships; MP tests applied numerical reasoning; GK tests factual breadth.

The GAMA consists of four subtests: Matching (MAT), Analogies (ANA), Sequences (SEQ), and Construction (CON). All four are figural and nonverbal, requiring manipulation of visual stimuli rather than retrieval of crystallized knowledge. The construct profile is nominally fluid: pattern recognition, analogical reasoning across visual objects, sequence completion, and shape construction.

The fluid-crystallized distinction (Cattell-Horn theory; Horn & Cattell, 1966) predicts that subtests within a battery should cluster together more tightly than subtests across batteries. Specifically, the JCCES subtests should load on a common factor, the GAMA subtests should load on a different common factor, and the cross-battery correlations should be substantially weaker than within-battery correlations. The factor-analytic test is whether this two-factor pattern emerges from the data without being imposed by hypothesis.

Method

Sixty-three adult participants completed both the JCCES and the GAMA in a quiet, well-lit testing environment. The JCCES was administered first, the GAMA second. Standardized administration procedures were followed for both batteries. Demographic variables (age, gender, ethnicity) were collected but not used in the analysis. No exclusion criteria were applied.

Pearson correlations were computed for all pairs of subtests. Principal factor analysis with Varimax rotation was conducted following Fabrigar, Wegener, MacCallum, and Strahan’s (1999) recommended procedures: initial communalities estimated as squared multiple correlations, convergence criterion 0.0001, maximum 50 iterations. The Kaiser-Meyer-Olkin (KMO) measure was computed to confirm sampling adequacy, and Cronbach’s alpha (Cronbach, 1951) was used to assess factor internal consistency.

Results

Correlation structure

The correlation matrix recovered the predicted within-vs-between battery pattern. The strongest correlations were within the JCCES: VA-GK = 0.712, MP-GK = 0.590, VA-MP = 0.542. All three are moderate to strong positive correlations, consistent with shared crystallized-knowledge variance.

The cross-battery correlations were systematically weaker. The strongest cross-battery pair was MP-MAT (r = 0.427), reflecting that mathematical problems and visual matching share some general cognitive demand. ANA’s correlations with JCCES subtests ranged from 0.141 (ANA-GK) to 0.298 (ANA-VA). SEQ’s correlations with JCCES ranged from 0.076 (SEQ-VA) to 0.391 (SEQ-MP). CON’s ranged from 0.169 (CON-GK) to 0.452 (CON-MP). The pattern is consistent: GAMA subtests correlate moderately with MP (the most fluid-loaded JCCES subtest) but weakly with the more language-dependent GK and VA.

Factor analysis

The KMO measure of sampling adequacy was 0.695, above the 0.6 threshold typically required for stable factor analysis (Fabrigar et al., 1999). Two factors had eigenvalues above 1: Factor 1 with eigenvalue 2.904 (41.482% of variance) and Factor 2 with eigenvalue 1.331 (19.016% of variance), with a cumulative explained variance of 60.498%.

After Varimax rotation, the two factors rebalanced to D1 (32.256% of variance) and D2 (28.242% of variance). The rotated loadings recovered the predicted battery alignment cleanly:

• Factor D1 (nonverbal/fluid): GAMA ANA loaded at 0.685, SEQ at 0.911, CON at 0.841. The GAMA’s three abstract-reasoning subtests anchor this factor.
• Factor D2 (crystallized/verbal): JCCES VA loaded at 0.796, MP at 0.687, GK at 0.845. The JCCES subtests anchor this factor.
• MAT (GAMA): did not load cleanly on either factor and is the perceptual outlier in the GAMA, consistent with the MDS analysis on the same data that placed MAT in its own visual-spatial cluster.

The factor structure is the simple-structure outcome that the construct hypothesis predicted. The two factors collectively explain about 60% of the inter-subtest variance — substantial for a seven-variable analysis with a 63-participant sample — and the rotated loadings show essentially no cross-loading on JCCES subtests onto the GAMA factor or vice versa.

What the structure implies

The factor analysis confirms that the JCCES and GAMA measure separable cognitive constructs in this sample. The crystallized factor (D2) loads exclusively on the three JCCES subtests; the nonverbal/fluid factor (D1) loads primarily on three of the four GAMA subtests. The two factors are nearly orthogonal after rotation, which is the empirical case for treating the two batteries as complementary rather than substitutable.

The result aligns with the Cattell-Horn fluid-crystallized framework and with subsequent factor-analytic work in Carroll’s three-stratum hierarchy (Carroll, 1993): the broad abilities of crystallized knowledge and fluid reasoning emerge as distinct loci that batteries can target separately. Both batteries together provide more comprehensive cognitive coverage than either alone.

The MAT subtest’s failure to load cleanly on either factor is theoretically interesting. MAT is the most perceptual of the GAMA subtests — visual matching of paired stimuli — and the data suggest it taps something distinct from both pure crystallized knowledge and abstract fluid reasoning. The MDS analysis on the same data placed MAT in its own visual-spatial cluster, and the factor analysis recovers the same outlier pattern under different statistical machinery. Convergence across methods strengthens the case that MAT is qualitatively different from the other GAMA subtests.

The MP subtest’s behavior also rewards inspection. MP loads on the crystallized factor (D2 = 0.687) but with the lowest loading among JCCES subtests, and its highest cross-battery correlation is with MAT (r = 0.427). The dual loading is consistent with applied mathematical reasoning straddling the crystallized-fluid boundary: math knowledge is crystallized in the sense that it depends on prior schooling, but applied problem-solving in mathematical contexts recruits fluid-reasoning abilities for novel-problem decomposition.

Methodological caveats

The 63-participant sample is small for an exploratory factor analysis. The KMO of 0.695 is adequate but not strong, and stability of the factor structure across alternative samples is not established. Modern factor-retention recommendations suggest using parallel analysis, MAP test, or fit-index difference values rather than relying solely on the eigenvalue-greater-than-one criterion that Kaiser’s rule provides; the present analysis used Kaiser’s rule, which can over-extract in some conditions but recovered a sensible two-factor solution that the rotation supported.

The lack of demographic data limits the analyzability of how the factor structure varies across age, education, and other relevant moderators. The Varimax rotation enforces orthogonal factors, which is the simplifying default but may understate the genuine correlation between crystallized and fluid abilities; an oblique rotation (e.g., Promax) would test whether the recovered factors are genuinely independent or are correlated as Cattell-Horn theory predicts at higher level. Replication in larger and more diverse samples with explicit oblique-rotation checks would strengthen the inferences.

Implications for assessment practice

For assessors using both batteries: report battery-level composite scores for both JCCES and GAMA, and treat the two as complementary measures of distinct cognitive domains rather than as overlapping measures of a single underlying ability. The factor analysis confirms that the JCCES composite captures crystallized intelligence and the GAMA composite captures nonverbal fluid reasoning; combining them gives broader coverage than either alone but does not collapse into a single composite without losing information.

For test developers building new cognitive batteries: the JCCES + GAMA pairing provides a methodological template. A test pairing that targets distinct cognitive domains and supports clean two-factor recovery is doing something the construct theory predicts; a pairing that fails this test should prompt a closer look at whether the batteries are measuring what their construct definitions claim.

The findings, like all single-sample factor-analytic results, should be replicated in larger and demographically diverse samples before being treated as definitive. The convergence with the MDS analysis on the same data is encouraging but does not substitute for independent replication on different respondents.

Frequently Asked Questions

Why factor analysis instead of multidimensional scaling?

Factor analysis posits a measurement model — observed subtests load on latent factors with quantifiable loadings — and tests how well that model fits the correlation matrix. MDS makes weaker assumptions, representing inter-variable distances geometrically without specifying a measurement model. The two methods are complementary; MDS on the same data recovered a similar structure under different assumptions, and the convergence strengthens the empirical case.

What does a KMO of 0.695 indicate?

The Kaiser-Meyer-Olkin measure assesses sampling adequacy for factor analysis. Values above 0.6 are typically considered adequate, above 0.8 are good, and above 0.9 are excellent. A value of 0.695 indicates that the sample is adequate for factor analysis but not large enough that the factor structure can be considered highly stable.

Why does MAT not load cleanly on the fluid factor?

MAT is a visual-matching subtest, the most perceptual of the GAMA tasks. The data suggest it taps a perceptual or visual-spatial process that is somewhat distinct from the abstract reasoning that ANA, SEQ, and CON share. The same outlier pattern emerges under MDS analysis on the same dataset, suggesting the result is methodologically robust rather than an artefact.

What does it mean that MP loads on the crystallized factor?

MP loads cleanly on the crystallized factor (D2 = 0.687), confirming that mathematical-problem-solving in the JCCES sample is more closely related to acquired mathematical knowledge than to fluid reasoning. The cross-battery MP-MAT correlation (0.427) is the highest in the cross-battery cells, suggesting some shared general cognitive demand, but the primary loading is crystallized.

How should JCCES and GAMA be reported in research?

Report both battery-level composite scores and the inter-battery correlation. The factor analysis supports treating the two as measures of distinct cognitive constructs, so combining them into a single composite collapses information. For granular reporting, the seven-subgroup decomposition recovered in the MDS analysis offers more detail than the two-factor decomposition.