JCCES and GAMA: Multidimensional Scaling Analysis

Cognitive batteries that combine verbal and nonverbal subtests routinely report a single composite score, but the underlying structure — how the subtests relate to each other, where the boundaries fall between domains, and which tasks are pulling on shared cognitive processes — is rarely made explicit. The Jouve Cerebrals Crystallized Educational Scale (JCCES) and the General Ability Measure for Adults (GAMA, Naglieri & Bardos, 1997) jointly span both the crystallized verbal and the nonverbal fluid sides of cognitive ability, which makes them a natural pairing for examining how individual tasks cluster when both batteries are administered to the same respondents. This study used multidimensional scaling (MDS) to examine that structure on data from 63 adult respondents who completed both the JCCES and the GAMA, and found a seven-group cluster structure with substantive interpretive consequences for how the two batteries should be used together.

The two batteries and what they measure

The JCCES measures crystallized cognitive abilities through three subtests: Verbal Analogies (VA), Mathematical Problems (MP), and General Knowledge (GK). The construct draws on Cattell’s distinction between crystallized intelligence — accumulated knowledge and skills shaped by education and cultural exposure — and fluid intelligence, the capacity for abstract reasoning and problem-solving independent of prior knowledge (Horn & Cattell, 1966). The JCCES tasks index the crystallized side: vocabulary structure for VA, applied numerical reasoning for MP, factual knowledge for GK.

The GAMA is a standardized nonverbal cognitive battery (Naglieri & Bardos, 1997) with four subtests: Matching (MAT), Analogies (ANA), Sequences (SEQ), and Construction (CON). All four are figural, requiring the respondent to manipulate visual stimuli rather than language. The construct profile is heavily fluid-loaded — abstract pattern recognition, analogical reasoning across visual objects, sequence completion, and shape manipulation — though the nonverbal medium does not by itself entail purely fluid demand.

The fluid-crystallized framework predicts a clear bifurcation: the JCCES subtests should cluster on one side, the GAMA subtests on the other, and the relationship between the two batteries should largely reduce to a global verbal-vs-nonverbal contrast. The MDS analysis tests this prediction directly. If the framework is correct, the seven subtests should arrange in a recognizable two-cluster structure with the JCCES tasks on one side and the GAMA tasks on the other.

Method

Sixty-three adult participants completed both the JCCES and the GAMA in a quiet, well-lit testing environment. Each battery was administered according to its standardized procedures, with the JCCES first and the GAMA second. Demographic variables (age, gender, ethnicity) were collected but not used in the analysis. No exclusion criteria were applied beyond willingness to complete both batteries.

The seven subtest scores per participant were submitted to nonmetric multidimensional scaling (MDS) using XLSTAT, with Kruskal’s stress (1) as the goodness-of-fit measure (Kruskal, 1964). Solutions of dimensionality 1 through 7 were estimated with random initial configurations, ten repetitions per dimensionality, and convergence and iteration limits of 0.00001 and 500 respectively. The 2-dimensional solution was selected based on stress (0.100) and explained variance (RSQ = 0.942); higher dimensionalities did not yield substantive improvements in fit.

Results

The 2-dimensional MDS solution revealed a diagonal separation between the GAMA nonverbal subtests (MAT, ANA, SEQ, CON) and the JCCES verbal subtests (GK, VA), with the JCCES Mathematical Problems subtest (MP) positioned closer to the verbal cluster but somewhat separate from both. The diagonal — rather than orthogonal — separation indicates that the verbal-vs-nonverbal contrast is the dominant axis but is not orthogonal to a secondary axis that pulls some subtests away from the centroid of their nominal cluster.

Closer inspection of inter-subtest proximities identified seven recognizable groups across the configuration:

• Crystallized intelligence cluster: MP, GK, VA. The three JCCES subtests cluster together, consistent with their shared crystallized-knowledge construct.
• Fluid intelligence cluster: ANA, SEQ, CON. Three of the four GAMA subtests cluster together, reflecting their shared abstract-reasoning load.
• Visual-spatial cluster: MAT alone. The Matching subtest is the most directly perceptual of the GAMA tasks and stands apart from the other three.
• Quantitative cluster: MP alone. Mathematical Problems sits closer to the verbal side than the nonverbal but pulls partly away from the GK-VA pairing toward an axis that captures applied numerical reasoning.
• Language-development cluster: GK and VA. The two most overtly language-dependent subtests pair tightly, consistent with shared lexical and semantic demand.
• Abstract-reasoning-and-pattern subgroup: SEQ and CON. Within the fluid cluster, these two share the strongest pattern-extrapolation and spatial-manipulation overlap.
• Nonverbal analogical reasoning: ANA. Within the fluid cluster, ANA pulls farther from SEQ-CON, reflecting its heavier load on relational mapping rather than pattern extrapolation.

The verbal and nonverbal sides are clearly separated, but the structure is more granular than a binary split. The seven-group decomposition tracks recognizable cognitive subdomains documented in Carroll’s three-stratum framework (Carroll, 1993) and the McGrew (2009) CHC consolidation: crystallized knowledge, fluid reasoning, visual-spatial processing, and quantitative reasoning each emerge as distinct loci.

What stands out

Two findings deserve particular attention. The first is the position of CON. Despite being a constructional/spatial task at face value, CON cluster proximity placed it within the fluid-reasoning subgroup with ANA and SEQ rather than with MAT in a visual-spatial subgroup. The interpretation: CON’s task demands extend beyond visual-spatial manipulation to include abstract pattern recognition and assembly logic, which align it more closely with fluid reasoning than with MAT’s purer perceptual matching.

The second is the differentiation within the fluid cluster between SEQ-CON and ANA. SEQ and CON share pattern-extrapolation demands — identifying the underlying logic of a sequence or a constructional rule — while ANA is more cognitively distinctive, requiring relational mapping between figurative pairs (Gentner, 1983). The structure-mapping demands of analogical reasoning are not the same as the rule-extraction demands of sequence completion, and the MDS configuration recovers this distinction empirically.

The position of MP — Mathematical Problems — adds a third notable feature. MP nominally belongs to the JCCES crystallized cluster but lies somewhat apart from GK and VA in the configuration, partly aligned with the fluid side. Quantitative reasoning has long been recognized as straddling the crystallized-fluid boundary (McGrew, 2009): mathematical knowledge is crystallized in the sense that it depends on prior schooling, but applied mathematical problem-solving recruits fluid reasoning abilities for novel-problem decomposition. The MDS placement reflects this dual loading.

Implications for using the two batteries together

The MDS configuration argues against treating the JCCES and GAMA as fully independent measures of crystallized and fluid intelligence respectively. The diagonal separation indicates that the two batteries are jointly informative about a richer cognitive structure, not just the bipolar verbal-nonverbal contrast that a separate-administration framing implies. The seven subgroups suggest that a combined JCCES + GAMA administration can support more granular cognitive profiling than either battery alone.

For applied use, the implication is that combined scores can be reported across the seven subgroups for individual respondents, identifying relative strengths and weaknesses across crystallized knowledge, fluid reasoning, visual-spatial, and quantitative loci rather than collapsing everything into a single composite. The increased granularity has practical consequences for educational, clinical, and research settings where the cognitive profile matters more than the global score.

The findings should be read with the limitations in mind. The 63-participant sample is small for an MDS analysis, the recruitment was non-probability based, and the MDS assumptions of interval-scaled data and Euclidean representation may not hold exactly. Replication in larger and more demographically diverse samples would strengthen the inferences. The seven-group structure is also somewhat method-dependent: a confirmatory factor analysis with the same data would test the structure under a different statistical model, and convergent findings across methods would be the strongest evidence for the underlying structure.

Frequently Asked Questions

What is multidimensional scaling and why use it for cognitive batteries?

MDS is a statistical technique that represents the relationships among a set of variables as distances in a low-dimensional space, preserving the relative similarities of the original data. For cognitive batteries, MDS shows how subtests cluster geometrically based on their inter-correlation pattern, often revealing structure that a single-summary correlation matrix obscures.

How does MDS differ from factor analysis for the same purpose?

Factor analysis assumes that the observed variables load on a small number of latent factors and decomposes the correlation matrix into factor loadings plus residuals. MDS makes weaker assumptions: it asks only that the inter-variable distances be approximately reproducible in the low-dimensional space. The two methods can complement each other; factor analysis on the same JCCES + GAMA data tests whether the MDS structure replicates under a different statistical model.

What does the diagonal separation in the MDS configuration mean?

A diagonal separation indicates that the verbal-nonverbal contrast is one important dimension but not the only one — a second dimension pulls some subtests away from their nominal cluster. In this analysis, MP (a JCCES verbal subtest) is pulled toward the nonverbal side; SEQ and CON (GAMA nonverbal subtests) cluster together away from MAT. Both effects reflect substantive cognitive content, not statistical artefact.

Why is the sample size of 63 a concern?

MDS results stabilize with larger samples; smaller samples produce configurations that may not replicate. Sixty-three is on the low end of recommended sample sizes for a 2-dimensional MDS solution with seven variables. The substantive interpretation of the configuration is plausible but should be confirmed in larger and more demographically diverse samples before being treated as definitive.

How should JCCES and GAMA be used together in practice?

The MDS findings suggest reporting subgroup-level scores rather than a single combined composite. The seven subgroups identified — crystallized intelligence, fluid intelligence, visual-spatial, quantitative, language development, abstract reasoning and pattern, nonverbal analogical reasoning — each support different inferences about an individual’s cognitive profile. Combining the batteries into a single composite collapses information that the granular structure preserves.