Formative and reflexive parameter bias under instances of continuous partial measurement noninvariance before and after item purification using the multiple indicator multiple causes model

Abstract

The multiple indicator multiple causes (MIMIC) model has been proposed as a powerful technique for the identification of partial measurement noninvariance (pMnI). Typically MI has been explored by comparing response patterns across groups using techniques such as the multiple group confirmatory factor analysis technique. The MIMIC model allows for the exploration of pMnI to be performed in relation to continuous covariates, however the specificity and sensitivity of the MIMIC to identify instances of continuous influenced pMnI is unexplored. This study first explores the bias that instances of continuous pMnI introduce in both formative and reflexive models when estimated within a MIMIC model framework using simulated data. Notable parameter estimation error is observed in extreme instances of both the formative and reflexive models. Next, the ability for the MIMIC model to identify and remove items which possess continuous pMnI are explored, high accuracy is obtained when instances of low and moderate MnI exist although performance degrades as the MnI increases in both magnitude and frequency. Finally, after removing items identified as MnI, parameter bias is again reevaluated in a similar framework noting reductions in parameter estimation bias in the formative model.