Invariance and factorial models

Invariance and Factorial Models

Two factors having the same set of levels are said to be homologous. This paper aims to extend the domain of factorial models to designs that include homologous factors. In doing so, it is necessary rst to identify the characteristic property of those vector spaces that constitute the standard factorial models. We argue here that essentially every interesting statistical model speciied by a vec...

Factorial Invariance: Historical Trends and New Developments

Within-level Group Factorial Invariance with Multilevel Data: Multilevel Factor Mixture and Multilevel MIMIC Models

This study suggests two approaches to factorial invariance testing with multilevel data when the groups are at the within level: multilevel factor mixture model for known classes (ML FMM) and multilevel multiple indicators multiple causes model (ML MIMIC). The adequacy of the proposed approaches was investigated using Monte Carlo simulations. Additionally, the performance of different types of ...

Factorial Invariance of a Pan-Hispanic Familism Scale

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Testing strong factorial invariance using three-level structural equation modeling

Within structural equation modeling, the most prevalent model to investigate measurement bias is the multigroup model. Equal factor loadings and intercepts across groups in a multigroup model represent strong factorial invariance (absence of measurement bias) across groups. Although this approach is possible in principle, it is hardly practical when the number of groups is large or when the gro...