A Beginner’s Guide to Structural Equation Modeling by Randall E. Schumacker

Author:Randall E. Schumacker
Language: eng
Format: epub
Publisher: Taylor & Francis

Chapter 8

Multiple Group (Sample) Models

Chapter Concepts

Measurement model group difference

Measurement invariance

Structural model group difference

Multiple sample model

Testing for parameter differences

Multiple group models were developed to test whether groups had the same or different theoretical model (Lomax, 1985). This approach can be applied in comparing groups on a measurement model, which is called a test of measurement invariance. Measurement invariance implies that two or more groups have the same measurement model, that is, the same construct or meaning for the latent variables in the measurement model. Byrne and Sunita (2006) provided a step-by-step approach for examining measurement invariance in SEM.

Once a researcher establishes that the latent variable constructs are the same, a comparison of the groups in the structural model can be conducted. A researcher would desire a non-significant chi-square difference between the groups in the measurement model invariance comparison. However, a researcher might want the structural models to be different, thus a significant chi-square difference. For example, adolescent drug use is different between high and low GPA high school students in the structural model, but the self concept and attitude toward drugs constructs in the measurement models are the same.

A researcher could also compare multiple samples of data on a measurement model, thus establishing the validity of a construct. You are basically applying a single specified model to one or more samples of data. Also, samples of data can be applied to a structural model to establish model validity. A unified approach to multi-group modeling is explained in Marcoulides and Schumacker (2001).

A misconception in multiple group modeling is that all paths in the model have to be the same. In fact, the chi-square statistic is a test of global fit; an overall fit of a model. It is possible for a measurement model to be slightly different for each group. Some parameters can therefore be different between the groups in the theoretical model. We can constrain or fix some parameters to be different between the groups, but allow other paths to be tested for equality. You might even consider dropping a single indicator variable that is different between the groups in a measurement model. This type of SEM modeling permits testing for group differences in the specified model without all parameters being tested for equality (Jöreskog & Sörbom, 1993). It is also possible to test for differences in specific parameter estimates.

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