Among other advantages, SEM:
- Can control for random errors
- Can model measurement error so the model is more precise
- Can test elaborate models
In general, the SEM starts by looking at all of the relationships in your study. This is known as the perfectly saturated model. All other models are compared to this one. The chi square here should be zero.
From there, it is possible to fix some relationships based on theory. This model is aligning variables to constructs and it is similar to a factor analysis. This model is referred to as the measurement model. If this model is very good, then the chi square will be insignificant. Furthermore, we do not want to have a significant difference between the estimated covariance matrix of the measurement and saturated models. The measurement model is used to asses convergent/discriminant validity. However, this model does not say anything about causality.
It is then possible to specify a causal model using theory. In this case, we also want a low chi square statistic. That would suggest that there is no difference in the estimated covariance matrix from the theoretical model and of the observed.
Last is a further constrained model. This aims to get the most parsimonious model. In this case, some relationships are set to zero. This model should have a larger chi square (bad news), but it is more parsimonious (good news). The goal is to determine if the change in the chi square between the theoretical model and this parsimonious model is significant. If the change is not significant, we should choose the parsimonious model.
From there, it is possible to fix some relationships based on theory. This model is aligning variables to constructs and it is similar to a factor analysis. This model is referred to as the measurement model. If this model is very good, then the chi square will be insignificant. Furthermore, we do not want to have a significant difference between the estimated covariance matrix of the measurement and saturated models. The measurement model is used to asses convergent/discriminant validity. However, this model does not say anything about causality.
It is then possible to specify a causal model using theory. In this case, we also want a low chi square statistic. That would suggest that there is no difference in the estimated covariance matrix from the theoretical model and of the observed.
Last is a further constrained model. This aims to get the most parsimonious model. In this case, some relationships are set to zero. This model should have a larger chi square (bad news), but it is more parsimonious (good news). The goal is to determine if the change in the chi square between the theoretical model and this parsimonious model is significant. If the change is not significant, we should choose the parsimonious model.
(Adapted from course notes)
(Flashcards and other resources here)