Ignoring a Multilevel Structure in Mixture Item Response Models: Impact on Parameter Recovery and Model Selection

Abstract

The current study investigated the consequences of ignoring a multilevel structure for a mixture item response model to show when a multilevel mixture item response model is needed. Study 1 focused on examining the consequence of ignoring dependency for within-level latent classes. Simulation conditions that may affect model selection and parameter recovery in the context of a multilevel data structure were manipulated: class-specific ICC, cluster size, and number of clusters. The accuracy of model selection (based on information criteria) and quality of parameter recovery were used to evaluate the impact of ignoring a multilevel structure. Simulation results indicated that, for the range of class-specific ICCs examined here (.1 to .3), mixture item response models which ignored a higher level nesting structure resulted in less accurate estimates and standard errors (SEs) of item discrimination parameters when the number of clusters was larger than 24 and the cluster size was larger than six. Class-varying ICCs can have compensatory effects on bias. Also, the results suggested that a mixture item response model which ignored multilevel structure was not selected over the multilevel mixture item response model based on Bayesian information criterion (BIC) if the number of clusters and cluster size was at least 50, respectively. In Study 2, the consequences of unnecessarily fitting a multilevel mixture item response model to single-level data were examined. Reassuringly, in the context of single-level data, a multilevel mixture item response model was not selected by BIC, and its use would not distort the within-level item parameter estimates or SEs when the cluster size was at least 20. Based on these findings, it is concluded that, for class-specific ICC conditions examined here, a multilevel mixture item response model is recommended over a single-level item response model for a clustered dataset having cluster size $>20$ and the number of clusters $>50$ .