Working with imperfect models

Since the early years of psychological research, investigators in psychology have made use of mathematical models of psychological phenomena. Models are now routinely used to represent and study cognitive processes, the structure of psychological measurements, the structure of correlational relationships among variables, the nature of change over time, and many other topics and phenomena of interest. All of these models, in their attempt to provide a parsimonious representation of psychological phenomena, are wrong to some degree and are thus implausible if taken literally. Such models simply cannot fully represent the complexities of the phenomena of interest and at best provide an approximation of the real world. This imperfection has implications for how we specify, estimate, and evaluate models, and how we interpret results of fitting models to data. Using factor analysis and structural equation models as a context, I examine some implications of model imperfection for our use of models, focusing on formal specification of models; the nature of parameters and parameter estimates; the relevance of discrepancy functions; the issue of sample size; the evaluation, development, and selection of models; and the conduct of simulation studies. The overall perspective is that our use and study of models should be guided by an understanding that our models are imperfect and cannot be made to be exactly correct.