Advances in statistical methods have resulted in a complex set of techniques to examine models that specify a set of relationships among variables using quantitative nonexperimental methods (see Raykov & Marcoulides, 2000; Ullman, 2007). Structural equation modeling (SEM) is a general term to refer to these techniques. The methods of SEM are beyond the scope of this book but you will likely encounter some research findings that use SEM; thus, it is worth-while to provide an overview. A model is an expected pattern of relationships among a set of variables. The proposed model is based on a theory of how the variables are causally related to one another. After data have been collected, statistical methods can be applied to examine how closely the proposed model actually “fits” the obtained data.
Researchers typically present path diagrams to visually represent the models being tested. Such diagrams show the theoretical causal paths among the variables. The multiple regression diagram on attitudes and intentions shown previously is a path diagram of a very simple model. The theory of reasoned action evolved into a more complex “theory of planned behavior” that has an additional construct to predict behavior. Huchting, Lac, and LaBrie (2008) studied alcohol consumption among 247 sorority members at a private university. They measured four variables at the beginning of the study: (1) attitude toward alcohol consumption based on how strongly the women believed that consuming alcohol had positive consequences, (2) subjective norm or perceived alcohol consumption of other sorority members, (3) perceived lack of behavioral control based on beliefs about the degree of difficulty in refraining from drinking alcohol, and (4) intention to consume alcohol based on the amount that the women expected to consume during the next 30 days. The sorority members were contacted one month later to provide a measure of actual behavior—the amount of alcohol consumed during the previous 30 days.
The theory of planned behavior predicts that attitude, subjective norm, and behavior control will each predict the behavioral intention to consume alcohol. Intention will in turn predict actual behavior. The researchers used structural equation modeling techniques to study this model. It is easiest to visualize the results using the path diagram shown in Figure 12.12. In the path diagram, arrows leading from one variable to another depict the paths that relate the variables in the model. The arrows indicate a causal sequence. Note that the model specifies that attitude, subjective norm, and behavioral control are related to intention and that intention in turn causes actual behavior. The statistical analysis provides what are termed path coefficients—these are similar to the standardized weights derived in the regression equations described previously. They indicate the strength of a relationship on our familiar −1.00 to +1.00 scale.
In Figure 12.12, you can see that both attitude and subjective norm were significant predictors of intention to consume alcohol. However, the predicted relationship between behavioral control and intention was not significant (therefore, the path is depicted as a dashed line). Intention was strongly related to actual behavior. Note also that behavioral control had a direct path to behavior; this indicates that difficulty in controlling alcohol consumption is directly related to actual consumption.
Structural model based on data from Huchting, Lac, and LaBrie (2008)
Besides illustrating how variables are related, a final application of SEM in the Huchting et al. study was to evaluate how closely the obtained data fit the specified model. The researchers concluded that the model did in fact closely fit the data. The lack of a path from behavioral control to intention is puzzling and will lead to further research.
There are many other applications of SEM. For example, researchers can compare two competing models in terms of how well each fits obtained data. Researchers can also examine much more complex models that contain many more variables. These techniques allow us to study nonexperimental data in more complex ways. This type of research leads to a better understanding of the complex networks of relationships among variables.
In the next chapter we turn from description of data to making decisions about statistical significance. These two topics are of course related. The topic of effect size that was described in this chapter is also very important when evaluating statistical significance.