Bayesian Structural Equation Modeling of the WISC-IV with a Large Referred US Sample

(1)

Poster

Reference

GOLAY, Philippe, et al.

Abstract

When investigating the structure of cognitive ability measures like the WISC-IV, subtest scores theoretically associated with one latent variable could also be related to other factors.

The objective of this study was to determine whether secondary interpretation of the 10 WISC-IV core subtests in a large referred US sample could be justified or whether a simple and unambiguous interpretation was more appropriate. To achieve this goal, the influence of each latent factor on subtest scores was estimated using Bayesian structural equation modeling (BSEM). A major drawback of classical confirmatory factor analysis (CFA) is that the majority of factor loadings needs to be fixed to zero to estimate the model parameters. This unnecessary strict parameterization can lead to model rejection and cause researchers to perform many exploratory modifications to achieve acceptable model fit. BSEM overcomes this limitation by replacing fixed-to-zero-loadings with “approximate” zeros that translates into small, but not necessary zero, cross-loadings. Because all relationships between factors and subtest scores are estimated, both the [...]

GOLAY, Philippe, et al. Bayesian Structural Equation Modeling of the WISC-IV with a Large Referred US Sample. In: 122nd Annual Convention of the American Psychological Association, Washington, DC, August 7-10, 2014, 2014

Available at:

http://archive-ouverte.unige.ch/unige:39203

Disclaimer: layout of this document may differ from the published version.

1 / 1

(2)

INTRODUCTION

CONCLUSIONS

RESULTS – MODELS COMPARISONS

Contact: Philippe.Golay@unige.ch 122^nd AMERICAN PSYCHOLOGICAL ASSOCIATION ANNUAL CONVENTION – WASHINGTON D.C. – AUGUST 7-10, 2014

Bayesian Structural Equation Modeling of the WISC-IV with a Large Referred US Sample

Philippe Golay

^1,2

, Thierry Lecerf

¹

, Marley W. Watkins

³

& Gary L. Canivez

⁴

1University of Geneva, ²University of Lausanne, ³Baylor University, ⁴Eastern Illinois University

•

The Wechsler Intelligence Scale for children, 4^th edition (WISC-IV) remains the most widely used test in the field of intelligence assessment.

• General intelligence has been conceptualized as a superordinate factor (higher order models) or as a breadth factor (bifactor models). Numerous studies have supported exploratory and confirmatory bifactor structures of the WISC-IV in US, French, and Irish samples.

• Many controversies remain on the nature of the constructs measured by each subtest score : subtest scores theoretically associated with one latent variable

could also be related to other factors. It is crucial to determine whether secondary interpretation of the 10 WISC-IV core subtests could be justified or whether a

simple and unambiguous interpretation is more appropriate.

1. Results on a sample of 1130 referred US children showed that the bifactor model fit was better than the higher order solution. Models including small cross-loadings were more adequate.

2. BSEM suggested a simple and parsimonious interpretation of the subtest scores

3. Loadings of the subtests scores on the g-factor were systematically higher than their respective loadings on the four index scores. Index scores

represented rather small deviations from unidimensionality and did not

necessarily provide additional and separate information from the Full Scale IQ score (FISQ).

4. BSEM allowed us to estimate models that were closer to theoretical assumptions.

5. BSEM also permits to test more complex models that are not possible to estimate through maximum likelihood estimation.

SAMPLE DESCRIPTION

LIMITATIONS OF CONFIRMATORY FACTOR ANALYSIS (CFA)

 With classical confirmatory factor analysis (CFA) the majority of factor loadings need to be fixed to zero to estimate the model parameters.

 Although needed for model identification, these restrictions do not always faithfully reflect the researchers’ hypotheses. Small but not necessarily zero loading could be equally or even more compatible with theory.

 This unnecessary strict parameterization can contribute to poor model fit, distorted factors and biased factor correlations (Marsh, et al., 2010). It also may cause researchers to perform many exploratory modifications to achieve acceptable model fit. Extensive specification searches can lead to unjustified overfitting of data, with loss of meaning for indices of statistical significance (Carroll, 1995)

• WISC-IV data were obtained from 1130 US children who were referred for evaluation of learning difficulties.

• As it appears to be common in clinical assessments, only the 10 core subtests were

administered. Only children with complete data for all core subtests were included in the analyses.

Sample N % Male Minimum Age Maximum Age Mean Age (SD)

US 1130 62% (696) 6-0 16-11 10.24 (2.51)

GOALS OF THE PRESENT STUDY

o The first goal of this study was to compare indirect (higher-order) versus direct (bifactor) hierarchical models of the 10 WISC-IV core subtests from a large referred US sample.

o The second objective was to determine more precisely which constructs are measured by each core subtest score of the WISC-IV : can secondary interpretation of some subtest scores be supported by the data ?

Model

Number of free parameters

Posterior Predictive

P-Value

Difference between observed &

replicated Χ² 95% C.I.

DIC

Estimated number of parameters Lower 2.5% Upper 2.5%

1. WISC-IV - higher order model 34 0.000 34.732 90.485 25983.228 33.785 2. WISC-IV - higher order model with

cross-loadings (priors variance = 0.01) 64 0.151 -15.168 45.585 25941.978 40.471

3. WISC-IV - bifactor model 40 0.000 21.281 76.965 25963.109 27.042

4. WISC-IV - bifactor model with cross-

loadings (priors variance = 0.01) 70 0.388 -27.095 35.638 25913.312 23.009

RESULTS – WISC-IV BIFACTOR MODEL WITH CROSS-LOADINGS

o Higher Posterior Predictive P-Value and Lower DIC indicates better fit to the data.

o The WISC-IV bifactor model with small cross-loadings showed the better fit overall.

Latent variable

Subtest Subtest Subtest Subtest Subtest Subtest

0 0 0

-1 -0.5 0 0.5 1

Diffuse non informative priors zero mean and

infinite variance

Informative priors zero mean and

small variance

Bayesian estimation combines prior distributions for all parameters with the experimental data and forms posterior distributions via Bayes' theorem.

The posterior distribution of Bayesian estimation was achieved through Markov Chain Monte Carlo (MCMC) algorithm with the Gibbs sampler Method.

Three MCMC chains with 50’000 iterations were used with different starting values and different random seeds.

The prior variance was 0.01 which results in 95% credibility interval of ± 0.20 (small cross-loadings).

g

Verbal Comprehension

VCI

Perceptual Reasoning

PRI

Working Memory

WMI

Processing Speed

PSI

Similarities

Comprehension

Block Design

Matrix Reasoning Picture Concept

Digit Span

Letter Number

Coding

Symbol Search Vocabulary

WISC-IV Higher order model WISC-IV Bifactor model

g

Verbal Comprehension

VCI

Perceptual Reasoning

PRI

Working Memory

WMI

Processing Speed

PSI

Similarities

Comprehension

Block Design

Matrix Reasoning Picture Concept

Digit Span

Letter Number

Coding

Symbol Search Vocabulary

Loadings estimates (median) ^G ^VCI ^PRI ^WMI ^PSI

95% CI 95% CI 95% CI 95% CI 95% CI

Similarities ^0.756* ^0.380* ^0.052 ^-0.008 ^-0.051

0.680 0.823 0.202 0.504 -0.074 0.184 -0.134 0.132 -0.156 0.054

Vocabulary ^0.796* ^0.488* ^0.007 ^0.043 ^-0.014

0.713 0.887 0.267 0.606 -0.142 0.145 -0.127 0.187 -0.138 0.102

Comprehension ^0.691* ^0.394* ^-0.049 ^0.007 ^0.020

0.603 0.779 0.160 0.521 -0.186 0.153 -0.141 0.157 -0.095 0.133

Block Design ^0.699* ^-0.025 ^0.408 ^-0.050 ^0.034

0.592 0.800 -0.176 0.130 -0.198 0.608 -0.209 0.153 -0.109 0.162

Picture Concepts ^0.691* ^0.012 ^0.148 ^0.001 ^-0.024

0.601 0.767 -0.150 0.163 -0.159 0.394 -0.165 0.188 -0.146 0.087

Matrix Reasoning ^0.752* ^0.005 ^0.285 ^0.029 ^0.002

0.671 0.822 -0.127 0.125 -0.097 0.479 -0.116 0.162 -0.119 0.112

Digit Span ^0.637* ^0.022 ^-0.010 ^0.256 ^0.026

0.566 0.710 -0.116 0.149 -0.151 0.134 -0.178 0.502 -0.084 0.131

Letter-Number Sequencing ^0.738* ^0.039 ^-0.006 ^0.311 ^0.044

0.663 0.816 -0.113 0.175 -0.156 0.141 -0.200 0.600 -0.088 0.162

Coding ^0.691* ^-0.030 ^-0.027 ^0.036 ^0.554*

0.603 0.779 -0.171 0.108 -0.172 0.126 -0.127 0.179 0.341 0.811

Symbol Search ^0.621* ^-0.002 ^0.071 ^0.019 ^0.472*

0.539 0.699 -0.135 0.124 -0.085 0.204 -0.116 0.151 0.302 0.714

Note. Loadings in bold were freely estimated. Other loadings were estimated with small (0.01) variance priors. G = General Factor; VCI = Verbal

Comprehension Index; PRI = Perceptual Reasoning Index; WMI = Working Memory Index; PSI = Processing Speed Index; CI= credibility interval; * = statistically significant because 95% CI does not contain zero.

BAYESIAN STRUCTURAL EQUATION MODELING (BSEM)

•

BSEM overcomes CFA’s limitations by replacing fixed-to-zero-loadings with

“approximate” zeros that translates into small, but not necessary zero, cross- loadings.

• Approximate zeros often reflect more accurately theoretical assumptions and facilitate unbiased estimations of the model parameters.

• Because all relationships between factors and subtest scores are estimated this

approach eliminates the need for comparisons of many competing models. It is also possible to determine the precise nature of the constructs measured by the core

subtest scores of the WISC-IV

o The majority of the expected loadings were supported. However the loadings of Block

Design, Picture Concepts, Matrix Reasoning on PRI and the loadings of Digit Span and Letter- Number Sequencing on WMI were not statistically significant.

o Loadings of the subtests scores on the g-factor were systematically higher than their respective loadings on the four index scores.

o No cross-loadings were supported; thus, no secondary interpretation of subtests scores was supported by the data.