Verbal Comprehension. Perceptual Reasoning. Working Memory

Transcription

1 Abstract The German Wechsler Intelligence Scale for Children-Fifth Edition (WISC V; Wechsler, 2017a) includes a five-factor structure (Figure 1), but its Technical Manual (Wechsler, 2017b) CFA analyses were not adequately informative (Boomsma, 2000). No explanation for choice of estimator was provided (perhaps weighted least squares was used like other WISC V versions) and numerous threats to model viability included a general intelligence and Fluid Reasoning standardized path of 1.0, cross loading Arithmetic on three factors (with pathetically low VC AR standardized coefficient of.02!), failure to test rival bifactor models, and failure to provide decomposed variance estimates. Rival bifactor models were not examined for comparison to higher order models as recommended in critiques (Canivez & Watkins, 2014) and independent WISC V analyses with U.S. (Canivez, Watkins, & Dombrowski, 2016, 2017), Canadian (Watkins, Dombrowski, & Canivez, 2017), U.K. (Canivez, McGill, & Watkins, 2018), French (Lecerf & Canivez, 2018), and Spanish (Fenollar-Cortes & Watkins, 2018) standardization samples. This study examined the German WISC V latent factor structure with all 15 subtests using best CFA practices. NCS Pearson, Inc. denied, without rationale, access to the German WISC V standardization sample raw data, so analyses were conducted on the reproduced covariance matrix using subtest correlations, means, and standard deviations from the full German WISC V standardization sample (N=1,087) provided in the Technical Manual Table 5.1 (Wechsler, 2017b). All models presented in the German WISC V Technical Manual were assessed along with rival bifactor models (Figures 2 & 3). Higher-order models were compared to bifactor models to determine the superordinate versus breadth aspects of psychometric g. Confirmatory factor analyses (EQS 6.3) used maximum likelihood estimation. Higher-order and bifactor models among well-fitting models were evaluated and compared. Using Hu and Bentler (1999) combinatorial heuristics, adequate model fit required CFI.90 and RMSEA.08, while good model fit required CFI 0.95 with RMSEA Meaningful differences between well-fitting models were assessed using ΔCFI>.01, ΔRMSEA>.015, and AIC>10 (Burnham & Anderson, 2004; Chen, 2007; Cheung & Rensvold, 2002). Decomposed variance estimates for the best fitting model were calculated. Model based reliabilities were estimated with coefficients omega-hierarchical (wh) and omegahierarchical subscale (whs) using Omega (Watkins, 2013). Table 1 presents maximum likelihood CFA fit statistics for all hypothesized models. Model 1 (g) and Model 2 (V, P), were not well-fitting, but Model 3 (V, P, PS) was adequate (Hu & Bentler, 1999). Models with four or five group factors all fit well, but it appeared that the best model among those tested was Model 4a Bifactor (Figure 4). Table 2 describes local misfit that must be considered beyond global fit. Decomposed variance estimates in Table 4 (Figure 4) and Table 5 (Figure 5) illustrate general intelligence dominance in explaining subtest variance (except for Processing Speed subtests). The omega hierarchical coefficient indicated interpretability of a unit-weighted g factor composite, but small variance portions and low omega hierarchical subscale coefficients for all group factors (except PS) indicated unit-weighted composite scores based on group factors are likely not interpretable independent of g. Implications for German WISC V score interpretation will be discussed.

2 Table 1 Maximum Likelihood CFA Fit Statistics for 15 German WISC V Primary and Secondary Subtests for the Standardization Sample (N = 1,087) Model 1 c 2 df CFI CFI TLI SRMR RMSEA RMSEA RMSEA 90% CI AIC AIC 1 General Intelligence 1, [.103,.114] 76, Higher-Order 2 1, [.100,.111] 76, Higher-Order [.072,.083] 75, a Higher-Order [.039,.051] 75, a Bifactor [.022,.036] 75, a Bifactor (sans FW-PR) [.021,.036] 75, b Higher-Order [.040,.051] 75, c Higher-Order [.037,.049] 75, d Higher-Order [.038,.050] 75, a Higher-Order [.035,.047] 75, a Bifactor [.023,.037] 75, b Higher-Order [.034,.047] 75, c Higher-Order [.032,.044] 75, d Higher-Order [.034,.046] 75, e Higher-Order [.032,.045] 75, Note. CFI = Comparative Fit Index, TLI = Tucker-Lewis Index (Non-normed Fit Index), SRMR = Standardized Root Mean Square (not available in robust estimation), RMSEA = Root Mean Square Error of Approximation, AIC = Akaike s Information Criterion. Bold text illustrates best fitting model. 1 Model numbers correspond to those reported in the German WISC-V Technical Manual Table 5.2 and are higher-order models (unless otherwise specified) when more than one first-order factor was specified. Subtest assignments to latent factors are specified in Figures 2 and Models with local misfit specified in Table 2.

3 Table 2 Local Fit Problems Identified Within Specified Models CFA Model Local Fit Problem 2 Higher-Order V factor and higher-order g factor linearly dependent on other parameters, g factor standardized path coefficient with V factor = Higher-Order g factor standardized path coefficients with V factor (.943) and P factor (.964) were high 4a Higher-Order g factor standardized path coefficients with PR factor (.946) and WM factor (.919) were high 4a Bifactor FW standardized path coefficient with PR (-.005) was not statistically significant; and the MR standardized path coefficient with PR (.136), PS standardized path coefficient with WM (.200), and AR standardized path coefficient with WM (.169) were statistically significant but low 4b Higher-Order g factor standardized path coefficients with FR+WM factor (.945) was high 4c Higher-Order g factor standardized path coefficients with PR+AR factor (.947) was high 4d Higher-Order g factor standardized path coefficients with PR factor (.947) was high, AR standardized path coefficient with VC (.069) not statistically significant, AR standardized path coefficient on PR (.262) was low, removing AR path from VC produces Model 4c 5a Higher-Order FR standardized path coefficient with g (.995) extremely high 5a Bifactor MR and FW had low standardized path coefficients (.090 and.090, respectively) with FR and not statistically significant 5b Higher-Order FR standardized path coefficient with g = 1.0 5c Higher-Order FR standardized path coefficient with g = 1.0 5d Higher-Order FR standardized path coefficient with g = 1.0, AR standardized path coefficient with VC (.151) was low 5e Higher-Order FR standardized path coefficient with g = 1.0, AR standardized path coefficient (.029) with VC not statistically significant, removal of AR loading with VC produces Model 5d Note. g = general intelligence, V = Verbal, P = Performance, VC = Verbal Comprehension, PR = Perceptual Reasoning, WM = Working Memory, VS = Visual Spatial, FR = Fluid Reasoning, FW = Figure Weights, MR = Matrix Reasoning, PS = Picture Span, AR = Arithmetic. Model number indicates the number of group factors included in the model and model number and letter correspond to those reported in the German WISC-V Technical Manual. Bifactor models were added for comparison. Subtest assignments to latent factors are specified in Figures 2 and 3. Wechsler, D. (2017a). Wechsler Intelligence Scale for Children Fifth Edition (WISC-V). Manual zur Durchführung und Auswertung. Deutsche Fassung von F. Petermann. Frankfurt a. M.: Pearson. Wechsler, D. (2017b). Wechsler Intelligence Scale for Children Fifth Edition (WISC-V). Technisches Manual. Deutsche Fassung von F. Petermann. Frankfurt a. M.: Pearson.

4 Table 3 Sources of Variance in the 15 German Wechsler Intelligence Scale for Children-Fifth Edition (WISC V) Primary and Secondary Subtests for the Standardization Sample (N = 1,087) According to a Bifactor Model with Four Group Factors General Verbal Comprehension Perceptual Reasoning Working Memory Processing Speed German WISC V Subtest b S 2 b S 2 b S 2 b S 2 b S 2 h 2 u 2 ECV Similarities Vocabulary Information Comprehension Block Design Visual Puzzles Matrix Reasoning Figure Weights Arithmetic Digit Span Picture Span Letter Number Sequencing Coding Symbol Search Cancellation Total Variance Explained Common Variance w wh /whs Relative w Factor Correlation H PUC.800 Note. b = loading of subtest on factor, S 2 = variance explained, h 2 = communality, u 2 = uniqueness, ECV = explained common variance, wh = Omegahierarchical (general factor), whs = Omega-hierarchical subscale (group factors), H = construct reliability or replicability index, PUC = percentage of uncontaminated correlations. Illustrated in Figure 5.

5 Table 4 Sources of Variance in the 15 German Wechsler Intelligence Scale for Children-Fifth Edition (WISC V) Primary and Secondary Subtests for the Standardization Sample (N = 1,087) According to a Bifactor Model with Four Group Factors with Perceptual Reasoning to Figure Weights Path Removed General Verbal Comprehension Perceptual Reasoning Working Memory Processing Speed German WISC V Subtest b S 2 b S 2 b S 2 b S 2 b S 2 h 2 u 2 ECV Similarities Vocabulary Information Comprehension Block Design Visual Puzzles Matrix Reasoning Figure Weights Arithmetic Digit Span Picture Span Letter Number Sequencing Coding Symbol Search Cancellation Total Variance Explained Common Variance w wh /whs Relative w Factor Correlation H PUC.800 Note. b = loading of subtest on factor, S 2 = variance explained, h 2 = communality, u 2 = uniqueness, ECV = explained common variance, wh = Omegahierarchical (general factor), whs = Omega-hierarchical subscale (group factors), H = construct reliability or replicability index, PUC = percentage of uncontaminated correlations. Illustrated in Figure 6.

6 General Intelligence Verbal Comprehension Visual Spatial Fluid Reasoning Working Memory Processing Speed SI VC IN CO BD VP MR FW AR DS PS LN CD SS CA Figure 1. Publisher preferred higher-order measurement model 5e with standardized coefficients (adapted from Figure 5.1 [Wechsler, 2017b, p. 107]) for the German WISC V standardization sample (N = 1,087). SI = Similarities, VC = Vocabulary, IN = Information, CO = Comprehension, BD = Block Design, VP = Visual Puzzles, MR = Matrix Reasoning, FW = Figure Weights, AR = Arithmetic, DS = Digit Span, PS = Picture Span, LN = Letter-Number Sequencing, CD = Coding, SS = Symbol Search, CA = Cancellation.

7 Figure 2. German WISC V Primary and Secondary Subtest configuration for CFA models with 1 4 factors. VC = Vocabulary, IN = Information, CO = Comprehension, BD = Block Design, VP = Visual Puzzles, MR = Matrix Reasoning, FW = Figure Weights, PC = Picture Concepts, AR = Arithmetic, DS = Digit Span, PS = Picture Span, LN = Letter Number Sequencing, CD = Coding, SS = Symbol Search, CA = Cancellation. All models include a higher order general factor except for the bifactor model. Picture Concepts is listed but not included in CFA models given the ambiguity in the German WISC-V manuals and publisher failure to reply to query.

8 Figure 3. German WISC V Primary and Secondary Subtest configuration for CFA models with 5 factors. VC = Vocabulary, IN = Information, CO = Comprehension, BD = Block Design, VP = Visual Puzzles, MR = Matrix Reasoning, FW = Figure Weights, PC = Picture Concepts, AR = Arithmetic, DS = Digit Span, PS = Picture Span, LN = Letter Number Sequencing, CD = Coding, SS = Symbol Search, CA = Cancellation. All models include a higher order general factor except for the bifactor model. Picture Concepts is listed but not included in CFA models given the ambiguity in the German WISC-V manuals and publisher failure to reply to query.

9 General Intelligence.697*.658*.684*.548*.634*.659*.660*.704*.726*.666*.668*.572*.331*.363*.232* SI VC IN CO BD VP MR FW AR DS LN PS CD SS CA.288*.592*.333*.462*.379*.401*.136* *.409*.200*.405*.643*.715*.456* Verbal Comprehension Perceptual Reasoning Working Memory Processing Speed Figure 4. Bifactor measurement model (4a Bifactor), with standardized coefficients, for the German WISC-V standardization sample (N = 1,087) 15 Subtests. SI = Similarities, VC = Vocabulary, IN = Information, CO = Comprehension, BD = Block Design, VP = Visual Puzzles, MR = Matrix Reasoning, FW = Figure Weights, AR = Arithmetic, DS = Digit Span, PS = Picture Span, LN = Letter- Number Sequencing, CD = Coding, SS = Symbol Search, CA = Cancellation. *p <.05.

10 General Intelligence.697*.659*.684*.548*.634*.658*.660*.703*.726*.666*.669*.573*.331*.363*.232* SI VC IN CO BD VP MR FW AR DS LN PS CD SS CA.287*.592*.333*.461*.377*.405*.138*.169*.409*.199*.405*.643*.715*.456* Verbal Comprehension Perceptual Reasoning Working Memory Processing Speed Figure 5. Bifactor measurement model (4a Bifactor), with standardized coefficients, for the German WISC-V standardization sample (N = 1,087) 15 Subtests without Perceptual Reasoning standardized path to Figure Weights. SI = Similarities, VC = Vocabulary, IN = Information, CO = Comprehension, BD = Block Design, VP = Visual Puzzles, MR = Matrix Reasoning, FW = Figure Weights, AR = Arithmetic, DS = Digit Span, PS = Picture Span, LN = Letter-Number Sequencing, CD = Coding, SS = Symbol Search, CA = Cancellation. *p <.05.