Title: Misspecification of Distribution in Multigroup Latent Variable Models

Authors: Stella Bollmann, Irini Moustaki

Affiliation: UZH Zurich, Department of Psychology, Zurich, Switzerland; LSE
London, Department of Statistics, London, United Kingdom

Abstract:
Marginal maximum likelihood estimation for 2PL Item Response Theory (IRT)
models assumes normally distributed latent variables. Previous research has
shown that when this assumption is violated, estimation of item parameters is
biased (Stone, 1992) and estimation of person parameters (i.e. of the latent
variable) is also error-prone (Sass, Schmitt, & Walker, 2008). In this study,
we want to investigate how violation of normality affects the estimation of
the multigroup latent variable model. It includes a grouping variable for
different populations and allows for different parameter estimates in each
group. With this model, measurement equivalence can be tested. Nonequivalence
is operationalized as an association between the group and an item (Kuha &
Moustaki, 2015). The research question of this work is, whether nonequivalence
might be erroneously detected in data sets that are fully equivalent but
exhibit a violation of normality in the latent variable. Non-normality will be
generated using the sn-package by Azzalini (2014). The idea of this work in
progress along with preliminary results will be presented.

References:
Azzalini, A. (2014). The R 'sn' package: The skew-normal and skew-t
distributions (version 1.0-0). Universit a di Padova, Italia.

Kuha, J., & Moustaki, I. (2015). Nonequivalence of measurement in latent
variable modeling of multigroup data: A sensitivity analysis. Psychological
methods, 20 (4), 523.

Sass, D. A., Schmitt, T. A., & Walker, C. M. (2008). Estimating non-normal
latent trait distributions within item response theory using true and
estimated item parameters. Applied Measurement in Education, 21 (1), 65-88.

Stone, C. A. (1992). Recovery of marginal maximum likelihood estimates in the
two-parameter logistic response model: An evaluation of MULTILOG. Applied
Psychological Measurement, 16 (1), 1-16.