Chapter 7: Structural Equation Models of Latent Interaction and Quadratic Effects

Estimating interaction effects is an important concern in psychology and the social sciences more generally. In educational psychology, for example, it is often hypothesized that the effect of an instructional technique will interact with characteristics of individual students in determining learning outcomes (e.g., a special remediation program developed for slow learners might not be an effective instructional strategy for bright students). Developmental psychologists are frequently interested in how the effects of a given variable vary with age in longitudinal or cross-sectional studies. Furthermore, many psychological theories explicitly hypothesize interaction effects. For example, some forms of expectancy-value theory (Nagengast, Marsh, et al., 2011) hypothesize that resultant motivation is determined by the interaction between expectancy of success and the value placed on the outcome by the individual (e.g., motivation is high only if both probability of success and the value placed on the outcome are high). In self-concept theory following William James (Marsh, 2008), the relation between an individual component of self-concept (e.g., academic, social, physical) and global self-esteem is hypothesized to interact with the importance placed on a specific component of self-concept (e.g., if a person places no importance on physical accomplishments, then these physical accomplishments—substantial or minimal—are not expected to be substantially correlated with self-esteem). More generally, a variety of weighted-average models posit—at least implicitly—that the effects of a given set of variables will depend on the weight assigned to each variable in the set (i.e., the weight assigned to a given variable interacts with the variable to determine the contribution of that variable to the total effect).