Title: A Tale of Two Boxes: Model Approximation Error and the Indeterminacy of Latent Variables
George Box created one of the most famous aphorisms in the statistical sciences when he quipped that “All models are wrong, but some are useful.” In this talk I will take Box’s truism seriously and suggest that—in the social sciences—all latent variable models are literally false due to the ubiquity of model approximation error. I note that this point was acknowledged by one of the first proponents of latent variable models, L. L. Thurstone (a developer of multiple factor analysis and a former instructor of geometry at the University of Minnesota), who suggested that “If the scientist takes his numerical coefficients very seriously at the exploratory stage, he may be lacking in a desirable sense of humor about the crudeness of all his tools in spite of their polished appearance” (1947, xi). Although model approximation error introduces both mathematical indeterminacy and conceptual uncertaintanty into the characterization of latent variables, false models often elucidate the underlying structure of noisy data. To illustrate this point, I summarize several models of Amazon shipping boxes to highlight what can and cannot be learned about the underlying nature of latent variables.
Niels Waller received a doctorate of psychology from the University of Minnesota in 1990 (with training in clinical psychology and psychometric methods). For the past 30 years he has been engaged in research and teaching on a wide range of topics related to psychometric methods, statistics, and individual differences. Prior to returning to the University of Minnesota in 2005, Dr. Waller chaired the quantitative methods programs at the University of California-Davis and at Vanderbilt University. His research has appeared in numerous methodology journals including Psychometrika, The American Statistician, Psychological Methods, Applied Psychological Measurement, and Multivariate Behavioral Research.