Testing strong factorial invariance using three-level structural equation modeling.

Suzanne Jak

doi:10.3389/fpsyg.2014.00745

Abstract

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 group size is relatively small. Jak et al. (2013) showed how strong factorial invariance across large numbers of groups can be tested in a multilevel structural equation modeling framework, by treating group as a random instead of a fixed variable. In the present study, this model is extended for use with three-level data. The proposed method is illustrated with an investigation of strong factorial invariance across 156 school classes and 50 schools in a Dutch dyscalculia test, using three-level structural equation modeling.

Highlights

The purpose of this study is to show how three-level structural equation modeling (SEM) can be used to test for measurement invariance across the Level 2 and Level 3 clustering variables
This means that if there is strong factorial invariance across clusters, the factor loadings are equal across levels, and there is no residual variance at Level 2 ( LEVEL2 = 0)
Adding a residual covariance between Test 1 and Test 2 leads to a better fitting model, χ2(19) = 135.69, p < 0.05, root mean squared error of approximation (RMSEA) = 0.037, comparative fit index (CFI) = 0.97, with close fit according to the RMSEA and good fit based on the CFI

Summary

Introduction

The purpose of this study is to show how three-level structural equation modeling (SEM) can be used to test for measurement invariance across the Level 2 and Level 3 clustering variables. The method is illustrated by testing measurement invariance across school classes and schools in a dyscalculia screening instrument. Testing measurement invariance across in three-level models will be illustrated by testing strong factorial invariance across school classes and across schools in a dyscalculia screening test. Some schools may use more paper and pencil tests than other schools, leading to more experience of the students with a testing situation than others If this is the case, two students that are equal in their levels of dyscalculia, may score differently on a screening test, depending on the school they are in. It is important to establish measurement invariance of an instrument across school classes and schools In this example, strong factorial invariance of a Dutch screening instrument for dyscalculia is tested across school classes and schools

Objectives

Methods

Results

Discussion

Conclusion