Multi-group Analysis in AMOS

Multi-group analysis in structural equation modeling (SEM) is another form of moderation analysis but using categorical variables or grouping variables (e.g. Male and Female). This process is straightforward in AMOS as the grouping variable is already specified in the dataset.
In cases where available data are continuous (e.g. Age) or ordinal (e.g. Likert scale responses), conducting Multi-group analysis is also possible. However, you need to convert first these variables into categorical ones, for them to be used in AMOS. This is done in SPSS. You may refer to these posts on how to convert continuous and ordinal variables into categorical. 
Estimating multi-group effects can be done using the (A) indirect (using the Chi-square difference test) or (B) direct method (through user-defined estimand). In the direct method, you need to install first the estimand for a smooth process. Let us see how it’s done below.

File to use: Causal Model Imputed

Dataset to use: Imputed dataset (_C)

A. Using the Chi-square difference test (Indirect method)

1. In the imputed causal model, remove any moderator variables, since you will use groupings of them instead.
2. Assign groupings (e.g. High and Low Knowledge) according to your hypothesized model.
3. Click the ‘Select Data’ button, and locate and load the dataset:
   • Set the Grouping variable and the Grouping value;
   • Then Click OK.
   • Save this file as “8 Path Multigroup indirect”.
4. Click the Multi-group analysis button.
   • A warning will appear, but click OK.
   • Default parameters will appear, leave it as it is, and click OK.
5. Go to the Models section and you will see 4 models.
   • Retain only the ‘Unconstrained’ and ‘Structural weights’ models.
     • Double click on ‘structural covariances’ model and delete.
     • Double click on ‘structural residuals’ model and delete.
     • Then Close.
   • The ‘structural weights’ model shows the paths that are the same in every group.
6. Check for the overall model significance.
   • Go to ‘Run’ — Outputs — Model comparison.
   • If the P-value is NOT significant (greater than 0.50 or 0.10), then the model is the same across groups. This must be the result at the model level.
7. Check for the single path significance.
   • Go back to the model. Double click on ‘structural weights’.
   • Consider only the path to be estimated, and retain it in the box.
     • Just cut the other paths, do not delete them as you need to paste them back to estimate other paths.
     • Click Close.
   • Go to Analysis properties — check ‘standardized estimates’ and ‘squared multiple correlations’ — Run.
   • In the Outputs, go to Model comparison.
   • If the P-value is significant (less than 0.50 or 0.10), then the path is different across groups. This must be the result at the path level.
     • Note the ‘standardized estimates’ of each group (adjacent to arrows or at the outputs section).
     • Conclude that one group is stronger than the other.
8. Do step No. 7 with one path at a time to estimate other paths.

Multi-group analysis using Chi-square difference test in AMOS

B. Using an estimand (Direct method)

Do steps No. 1 to No. 3 above but save the file as “8 Path Multigroup direct”.

1. Go to the bottom-left part of AMOS.
   • Click ‘Not estimating any user-defined estimand’.
   • Choose ‘Select estimand’.
   • Locate the estimand — then click Open.
     • The estimand’s name is “MyGroupDifferencesAmosEstimandVB”
   • This will appear in the bottom left: ‘Estimating MyGroupDifferences’.
2. Double click on the path you want to estimate.
   • A box will appear. Uncheck ‘All groups’.
   • Name the regression weights as A and B for both groups, respectively.
3. Set the following in ‘Analysis properties’.
   • Bootstrap — Perform bootstrap — 2000 samples — Bias corrected — 90 confidence level — Exit.
   • Check for ‘Standardized estimates’ and ‘Squared multiple correlations’.
   • Save — Run.
4. In the Outputs, view the value of the Estimate.
   • Go to Estimates — Scalars — User-defined estimands.
     • It gives the value of the Estimate.
   • Go down to Estimates/Bootstraps — Bias corrected-percentile method.
     • It gives the Estimate and the P-value for the differences between two groups for that specific path.
5. Report and interpret the result.
   • List the estimate (standardized indirect effect or AxB)
   • List the p-value (must be less than 0.10 at least or 0.50)
   • Is the hypothesis supported?
6. Do steps No. 3 to No. 6 one at a time to estimate other paths.

Multi-group analysis using User-defined Estimand in AMOS

In summary, multi-group analysis is another type of moderation analysis but involving categorical variables. You can estimate multi-group effects using the indirect (using the Chi-square difference test) or direct method (through user-defined estimand). In the direct method, you need to install first the required estimand for a smooth process. Hope this helps.

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