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Response styles introduce construct-irrelevant variance as a result of respondents systematically responding to Likert-type items regardless of content. Methods to account for response styles through data analysis as well as approaches to mitigating the effects of response styles during data collection have been well-documented. Recent approaches to modeling Likert responses, such as the IRTree model, rely on the response process individuals take when answering item responses. In this study, we advocate for the use of IRTrees to analyze Likert items in addition to using the hypothesized response process to design new items. Combining these two approaches facilitates answering Likert item design questions that have plagued researchers. These include the interpretation of a middle response option, the optimal number of response options, and how to label the response options. We present 7 research questions that could be answered using this new approach, outline methods of data collection and analysis for each, and present results from an empirical example to address one of these seven questions.

Data simulation and Monte Carlo simulation studies are important skills for researchers and practitioners of educational and psychological measurement, but there are few resources on the topic specific to item response theory. Even fewer resources exist on the statistical software techniques to implement simulation studies. This article presents an introduction to the questions that simulation studies can, and cannot answer, along with the primary steps of the simulation study. We primarily focus on the parts of the simulation for which statistical software is used, presenting syntax for simulating 2PL data, and discuss how to extend the basic syntax to more complex models. We focus on SAS software in the article to build upon an existing syntax base, as most universities have SAS licenses. Two small simulations serve as didactic illustrations and to demonstrate parameter recovery of the SAS IRT procedure and an evaluation of the procedure's item-fit options.

Bayesian item response theory (IRT) modeling stages include (a) specifying the IRT likelihood model, (b) specifying the parameter prior distributions, (c) obtaining the posterior distribution, and (d) making appropriate inferences. The latter stage, and the focus of this research, includes model criticism. Choice of priors with the posterior predictive checks (PPC) model-checking method requires more attention. The objective of this research is to investigate the extent of the effect of prior specification on the conclusions drawn from the PPC method. Findings indicated that the choice of discrepancy measure is an important factor in the overall success of the method, and that different discrepancy measures are affected more than others by prior specification. The use of percent correct as a discrepancy statistic was ineffective regardless of prior specification or type of misfit. Recommendations and suggestions for future research are provided.

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing environments, including R, Python, MATLAB, Stata, and Mathematica. Programs written in Stan are portable across these interfaces, encouraging collaboration and transparency. These benefits, and others, offer several advantages for measurement practitioners; this review uses a simple example of Stan for a two-parameter logistic IRT model to illustrate the utility of Stan and its relevant features.