In the previous example, we had two groups and we simply tracked spending behaviors across the groups. With many latent growth curve models, you will want to include a predictor of the intercept and slope; specifically, the variable or construct that would influence the intercept and growth over the time period. Using our environmentally sus- tainable packaging example, let’s say we think that females are going to be more responsive to this type of packaging than males and we want to see if gender has an impact on the intercept and slope. Initially, we are going to draw and label the latent growth model the same as before, but this time we are going to include a gender construct (males coded as a 1, females coded as a 0) and have a path drawn directly from the predictor variable to the unobserved intercept and slope.The path from the predictor directly to the unobservables (slope and intercept) will now change these variables from an independent to a dependent variable. This means you will need to include error terms on the unobservable intercept and slope variable.
Figure 9.12 Latent Growth Curve With Predictor Variable of Gender Modeled
If you are not recreating the model and are just trying to add a predictor to an existing latent growth curve model, you need to delete the existing parameter names for the variance of the intercept and slope.AMOS will give you a warning/error message if you try to have the variances labeled for the unobservable variable while including an error term.You also want to make sure that you correlate the error terms for the intercept and the slope of unobservable variables. If you want to compare the influence of gender across the groups, you will need to uniquely label the parameters from gender to the intercept and slope for each group.You can choose to select the multi-group analysis button again and it will relabel all your parameters again, or you can just label them individually. If you choose to have AMOS relabel all your parameters again, it will give you numerous potential models for comparison. In this example we are really concerned with only two tests:Test 1, which asks if the slope and intercept are different between the groups; and Test 2, which asks whether the influence of gender is significantly different across the groups. All other model comparison tests will not help us much. Once we have formed the model and asked for AMOS to “Estimate means and intercepts” in the output, we are ready to run the analysis.
When you have AMOS label your parameters, two model comparisons will be of primary concern: the structural intercepts, and the structural weights comparison. The “Structural intercepts” comparison will constrain the means for the intercept and slope to be the same, and it will also constrain the parameters from the independent variable (gender) to the slope and intercept.This comparison test will let you know if the intercept and slope are significantly different across the groups with the inclusion of the predictor variable (gender). The second comparison, called the “Structural weights”, will only constrain the parameters from the inde- pendent variable to the intercept and slope.This specific test will allow to you to examine if the predictor variable is having a significant influence in the growth model across the groups.Again, AMOS will give you more models for comparison, but these are the ones you need to focus on going forward. Let’s run the analysis and examine the model comparison link in the output.
Figure 9.13 Manage Models Window Showing Structural Weight and Intercepts Comparison
The results show us that the structural intercept comparison was significant, which means the slope and intercept are significantly different across the two groups when accounting for the influence of gender.The specific test for gender called the structural weights was also sig- nificant, providing evidence that gender had a significant influence across the groups.
Figure 9.14 Chi-Square Difference Test for Structural Weights and Intercepts Model Comparison
After finding a significant difference between the groups, let’s go to the “Estimates” link in the output, where we will examine the results of each group. See Figures 9.15 and 9.16.
In the environmentally sustainable group, you can see that gender has a significant and negative direct influence of the intercept and slope. Remember, males were coded as a 1 and females as a 0.This means females had a stronger influence on the starting intercept and slope than males. In the intercepts section in the output, you will see the intercept is significant and slope for the “SustainPackage” group is positive and significant denoting that spending patterns increased in the positive for this group. Notice that the slope is a little stronger now that we are including the predictor of gender than the first analysis that had no predictors.
Figure 9.15 Estimates Output of the Sustainable Package Group Including Regression Weights of Predictors Along With Intercept and Slope Values
Figure 9.16 Estimates Output of the No Sustainable Package Group Including Regression Weights of Predictors Along With Intercept and Slope Values
In the group that did not have environmentally sustainable packaging listed on their snacks, gender did not have a significant difference on slope or intercept. Additionally, the “NoSustain” group did not have a significant slope denoting that the change over the four time periods was not significant.
Our ultimate results show that the environmentally sustainable packaging had a significant positive “growth” or change over the four-week time period in customers purchasing behavior compared to customers who did not have any sustainability packaging information presented on their snacks. Additionally, female customers responded more strongly to the environmen- tally sustainable packaging than males.
Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer, Singapore.