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Factorial Design

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Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...

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Factorial invariance in multilevel confirmatory factor analysis.

¹Department of Psychology, Boston College, Chestnut Hill, USA.

The British Journal of Mathematical and Statistical Psychology

|May 21, 2013

Summary

This study introduces a new method for testing factorial invariance in multilevel models, addressing challenges with level-1 group dependencies. The procedure offers a reliable approach for complex data structures in multilevel confirmatory factor analysis.

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Area of Science:

Psychometrics
Multilevel Modeling
Structural Equation Modeling

Background:

Multilevel confirmatory factor analysis (MCFA) is essential for understanding nested data structures.
Standard factorial invariance testing procedures face limitations with level-1 group dependencies.
Accurate invariance testing is crucial for valid cross-group comparisons in MCFA.

Purpose of the Study:

To present a novel procedure for testing factorial invariance in MCFA, specifically addressing level-1 group membership issues.
To offer a robust method for handling dependencies within level-1 groups in invariance testing.
To evaluate Muthén's maximum likelihood (MUML) estimation as an alternative to traditional maximum likelihood estimation for multilevel invariance.

Main Methods:

Development of a procedure to extend standard factorial invariance testing to MCFA with level-1 group membership.
Application of the proposed procedure to test invariance across level-1 and level-2 groups.
Comparison of Muthén's maximum likelihood (MUML) estimation with standard maximum likelihood estimation.

Main Results:

The proposed procedure effectively addresses the dependency issues in level-1 groups for factorial invariance testing.
MUML estimation is demonstrated as a viable alternative for testing multilevel factorial invariance.
Empirical examples illustrate the successful application of the procedure for both level-1 and level-2 group invariance.

Conclusions:

The presented procedure offers a significant advancement for factorial invariance testing in MCFA, particularly for complex nested data.
Researchers can confidently apply this method to ensure measurement invariance across different levels of grouping.
Provided SAS macros and Mplus syntax facilitate the practical implementation of the proposed methodology.