Examining Differences of Invariance Alignment in the Mplus Software and the R Package Sirt

Abstract

Invariance alignment (IA) is a multivariate statistical technique to compare the means and standard deviations of a factor variable in a one-dimensional factor model across multiple groups. To date, the IA method is most frequently estimated using the commercial Mplus software. IA has also been implemented in the R package sirt. In this article, the performance of IA in the software packages Mplus and R are compared. It is argued and empirically shown in a simulation study and an empirical example that differences between software packages are primarily the cause of different identification constraints in IA. With a change of the identification constraint employing an argument in the IA function in sirt, Mplus and sirt resulted in comparable performance. Moreover, in line with previous work, the simulation study also highlighted that the tuning parameter ε=0.001 in IA is preferable to ε=0.01. Furthermore, an empirical example raises the question of whether IA, in its current implementations, behaves as expected in the case of many groups.