Many modeling techniques that appear to be stable with realistic sample sizes in psychology often times make unrealistic assumptions such as multivariate normality or an otherwise correctly specified model. Missing responses are also a common problem in real datasets. Conversely, sometimes researchers employ planned missing data designs to reduce respondent burden, and preemptively reduce the number of careless or random responses. Our research in this area tests and develops methods for analyzing data under such suboptimal conditions. Much of this research is in the realm of multiple regression or structural equation modeling and/or overlaps with that on mediation analysis. Some research deals with small samples and model misspecification in general.