# Chapter 4: Structural Equation Models

### Research questions

The main focus in analyzing structural equation models is usually on answering questions about the structural model, such as the following:

- What are the signs and strengths of the relationships between the variables in the model?
- Are any of these relationships absent (i.e. can they be set to 0)?
- If substantive theory hypothesizes that some relationships are absent, is this justified?

We may also want to know how answers to these questions vary between groups such as countries. This can be assessed using multigroup structural equation modelling. It is discussed at the end of this chapter.

It is also important to remember that these relationships, as estimated from a SEM fitted to observed data, are estimated statistical associations, not causal effects. The substantive theory which informs the specification of the form of the structural model will often include hypotheses about causal relationships between the constructs, which in part determine the ordering of the variables and their relationships in the structural model. However, the act of specifying such a model, drawing a path diagram for it, and estimating its parameters does not in itself imply that the results can then be interpreted as estimated causal effects. For such a claim to be justified, the data and the research design that produced them will always need to satisfy additional assumptions which cannot be checked from the analysis of the data alone. In this respect the situation for a SEM remains the same as it is for any inference on causal effects from any kind of statistical analysis on observed data.