Model-Based Person Fit Statistics Applied to the Wechsler Adult Intelligence Scale IV

An important task in clinical neuropsychology is to evaluate whether scores obtained on a test battery, such as the Wechsler Adult Intelligence Scale Fourth Edition (WAIS-IV), can be considered "credible" or "valid" for a particular patient. Such evaluations are typically made based on responses to performance validity tests (PVTs). As a complement to PVTs, we propose that WAIS-IV profiles also be evaluated using a residual-based M-distance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> ) person fit statistic. Large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> values flag profiles that are inconsistent with the factor analytic model underlying the interpretation of test scores. We first established a well-fitting model with four correlated factors for 10 core WAIS-IV subtests derived from the standardization sample. Based on this model, we then performed a Monte Carlo simulation to evaluate whether a hypothesized sampling distribution for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> was accurate and whether <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> was computable, under different degrees of missing subtest scores. We found that when the number of subtests administered was less than 8, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> could not be computed around 25% of the time. When computable, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> conformed to a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>χ</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> distribution with degrees of freedom equal to the number of tests minus the number of factors. Demonstration of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> index in a large sample of clinical cases was also provided. Findings highlight the potential utility of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>ri</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> index as an adjunct to PVTs, offering clinicians an additional method to evaluate WAIS-IV test profiles and improve the accuracy of neuropsychological evaluations.