Bounded continuous data are encountered in many applications of item response theory, including the measurement of mood, personality, and response times and in the analyses of summed item scores. Although different item response theory models exist to analyze such bounded continuous data, most models assume the data to be in an open interval and…

With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex…

In causal matching designs, some control subjects are often left unmatched, and some covariates are often left unmodeled. This article introduces "rebar," a method using high-dimensional modeling to incorporate these commonly discarded data without sacrificing the integrity of the matching design. After constructing a match, a researcher…

Multiple imputation (MI) can be used to address missing data at Level 2 in multilevel research. In this article, we compare joint modeling (JM) and the fully conditional specification (FCS) of MI as well as different strategies for including auxiliary variables at Level 1 using either their manifest or their latent cluster means. We show with…

Ecological momentary assessment (EMA) is a popular assessment method in psychology that aims to capture events, emotions, and cognitions in real time, usually repeatedly throughout the day. Because EMA typically involves more intensive monitoring than traditional assessment methods, missing data are commonly an issue and this missingness may bias…

It is well known that dichotomizing continuous data has the effect to decrease statistical power when the goal is to test for a statistical association between two variables. Modern researchers however are focusing not only on statistical significance but also on an estimation of the "effect size" (i.e., the strength of association…

A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a…

Mixed models are used for the analysis of data measured over time to study population-level change and individual differences in change characteristics. Linear and nonlinear functions may be used to describe a longitudinal response, individuals need not be observed at the same time points, and missing data, assumed to be missing at random (MAR),…

A promising "underlying bivariate normal" approach was proposed by Jöreskog and Moustaki for use in the factor analysis of ordinal data. This was a limited information approach that involved the maximization of a composite likelihood function. Its advantage over full-information maximum likelihood was that very much less computation was…

Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and…

Outliers in questionnaire data are unusual observations, which may bias statistical results, and outlier statistics may be used to detect such outliers. The authors investigated the effect outliers have on the specificity and the sensitivity of each of six different outlier statistics. The Mahalanobis distance and the item-pair based outlier…

In the case of trials with nested data, the optimal allocation of units depends on the budget, the costs, and the intracluster correlation coefficient. In general, the intracluster correlation coefficient is unknown in advance and an initial guess has to be made based on published values or subject matter knowledge. This initial estimate is likely…

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Test administrators often face the challenge of detecting differential item functioning (DIF) with samples of size smaller than that recommended by experts. A Bayesian approach can incorporate, in the form of a prior distribution, existing information on the inference problem at hand, which yields more stable estimation, especially for small…

The generalized linear latent and mixed modeling (GLLAMM framework) includes many models such as hierarchical and structural equation models. However, GLLAMM cannot currently accommodate some models because it does not allow some parameters to be random. GLLAMM is extended to overcome the limitation by adding a submodel that specifies a…