Education and Human Sciences, College of (CEHS)


First Advisor

James A. Bovaird

Date of this Version



Svoboda, E. A. (2017). Multilevel metric invariance: A Monte Carlo simulation (Master's thesis). Retrieved from DigitalCommons@University of Nebraska - Lincoln.


A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Arts, Major: Educational Psychology, Under the Supervision of Professor James A. Bovaird. Lincoln, Nebraska: December, 2017

Copyright (c) 2017 Elizabeth Svoboda


Multilevel measurement invariance determines the extent to which a construct is measured in the same way across multiple hierarchical nested levels in the context of the current study. Lower-level parameter estimates may differ from parameter estimates based on higher-level aggregates in applied research settings. Multilevel metric invariance is a method to detect the presence of a noninvariant factor loading.

The purpose of the current study was to determine the utility of multiple-group multilevel – confirmatory factor analysis (MGM-CFA) for detecting metric noninvariance in nested data. The example context is noninvariance occurring between treatment and control classrooms with students (i.e., level-one) nested within classrooms (i.e., level-two). Noninvariance was simulated to occur at level-two only with a magnitude of 0.5 for the Replication Study, between level-one and level-two simultaneously with a magnitude of 0.5 for Extension Study 1, and between level-one and level-two simultaneously with a magnitude of 0.25 for Extension Study 2. MGM-CFA was used to detect the presence of metric noninvariance in the multilevel data under various conditions of intraclass correlation coefficients (ICC), number of clusters (j), and cluster size (nj). A level-two grouping variable, which represented treatment versus control classrooms with noninvariance at level two between classrooms was generated using a Monte Carlo simulation. Type I error and statistical power were examined for overall model fit through the use of the chi-square difference test (Δχ2), change in root mean squared error of approximation (ΔRMSEA), and change in comparative fit index (ΔCFI).

Results indicated the ΔCFI nearly always detected the simulated noninvariance in the factor loading, leading to artificially inflated Type I errors. Multiple-group multilevel-CFA was recommended as a powerful procedure for detecting metric noninvariance in nested data with the ΔCFI.

Adviser: James A. Bovaird