This paper is a systematic review of the methodology for person fit research targeted specifically at methodologists in training. I analyze the ways in which researchers in the area of person fit have conducted simulation studies for parametric and nonparametric unidimensional IRT models since the seminal review paper by Meijer and Sijtsma (2001). I specifically review how researchers have operationalized different types of aberrant responding for particular testing conditions in order to compare these simulation design characteristics with features of the real-life testing situations for which person fit analyses are officially reported. I discuss the alignment between the theoretical and practical work and the implications for future simulation work and guidelines for best practice.
Key words: Person fit, systematic review, aberrant responding, item response theory, simulation study, generalizability, experimental design.
This paper is situated in the conceptual space of research on person fit, which is one aspect of the comprehensive enterprise of critiquing the alignment of the structure of a particular statistical model with a particular data set using residual-based statistics (Engelhard Jr., 2009). I first analyze the ways in which researchers in the area of person fit have conducted simulation studies in non-parametric (e.g., Sijtsma & Molenaar, 2002; van der Aark, Hemker, & Sijtsma, 2002) and parametric unidimensional item response theory (IRT) (e.g., DeAyala, 2009; Yen & Fitzpatrick, 2006) since the seminal review paper by Meijer and Sijtsma (2001). I then discuss the alignment between the theoretical and practical work and the implications for future simulation work and guidelines for best practice.
This paper is primarily intended for methodologists in training but should also prove useful for practitioners who are curious about the statistical foundations for proposed guidelines of best practice. The information in this paper may be of less interest for the relatively few specialists who are already conducting advanced simulation studies in this area. However, it should provide some useful insight into the ways these researchers conduct their work for the many other researchers and practitioners who want to be critical consumers of this work.
Simulation studies are designed statistical experiments that can provide reliable scientific evidence about the performance of statistical methods. As noted concisely by Cook and Teo (2011):
In evaluating methodologies, simulation studies: (i) provide a cost-effective way to quantify potential performance for a large range of scenarios, spanning different combinations of sample sizes and underlying parameters, (ii) allow average performance to be estimated under repeat Monte Carlo sampling and (Hi) facilitate comparison of estimates against the "true " system underlying the simulations, none of which is really achievable via genuine applications, as gratifying as those are. (p. 1)
In the context of person fit research, simulation studies are most commonly used to quantify the frequency of type-I and type-II errors and associated power rates under a variety of test design and model misspecification conditions.
Researchers who publish in this area clearly make some concerted and thoughtful efforts to summarize findings from simulation studies, especially when they are trying to situate their particular theoretical work within a relevant part of the literature. Thus, I initially started out writing this paper as a more "traditional" review paper that focused on what researchers had learned about person fit in roughly the last 10 years. However, while reviewing the recent body of work it became quickly clear that there is perhaps a more urgent need to discuss the methodology of simulation research with more scrutiny in order to help methodologists in training understand the kinds of generalizations that can and cannot be made based on this work. …