Assessing dimensionality in dichotomous items when many subjects have all-zero responses: an example from psychiatry and a solution using mixture models

William F. Christensen, Melanie M. Wall and Irini Moustaki

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Common methods for determining the number of latent dimensions underlying an item set include eigenvalue analysis and examination of fit statistics for factor analysis models with varying number of factors. Given a set of dichotomous items, the authors demonstrate that these empirical assessments of dimensionality often incorrectly estimate the number of dimensions when there is a preponderance of individuals in the sample with all-zeros as their responses, for example, not endorsing any symptoms on a health battery. Simulated data experiments are conducted to demonstrate when each of several common diagnostics of dimensionality can be expected to under- or over-estimate the true dimensionality of the underlying latent variable. An example is shown from psychiatry assessing the dimensionality of a social anxiety disorder battery where 1, 2, 3, or more factors are identified, depending on the method of dimensionality assessment. An all-zero inflated exploratory factor analysis model (AZ-EFA) is introduced for assessing the dimensionality of the underlying subgroup corresponding to those possessing the measurable trait. The AZ-EFA approach is demonstrated using simulation experiments and an example measuring social anxiety disorder from a large nationally representative survey. Implications of the findings are discussed, in particular, regarding the potential for different findings in community versus patient populations.

Keywords: all-zero responses; AZ-EFA approach; dimensionality assessment; factor analysis; goodness-of-fit metrics; social anxiety disorder; unidimensionality; zero inflated (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 18 pages
Date: 2022-03-01
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Published in Applied Psychological Measurement, 1, March, 2022, 46(3), pp. 167-184. ISSN: 0146-6216

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