Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

The hierarchical model of van der Linden is the most popular model for responses and response times in tests. It is composed of two separate submodels--one for the responses and one for the response times--that are joined at a higher level. The submodel for the response times is based on the lognormal distribution. The lognormal distribution is a…

The number of articles showing dissatisfaction with the null hypothesis statistical testing (NHST) framework has been progressively increasing over the years. Alternatives to NHST have been proposed and the Bayesian approach seems to have achieved the highest amount of visibility. In this last part of the special issue, a few alternative…

Factor score regression (FSR) is a popular alternative for structural equation modeling. Naively applying FSR induces bias for the estimators of the regression coefficients. Croon proposed a method to correct for this bias. Next to estimating effects without bias, interest often lies in inference of regression coefficients or in the fit of the…

P values have been critiqued on several grounds but remain entrenched as the dominant inferential method in the empirical sciences. In this article, we elaborate on the fact that in many statistical models, the one-sided "P" value has a direct Bayesian interpretation as the approximate posterior mass for values lower than zero. The…

An alternative to null hypothesis significance testing is presented and discussed. This approach, referred to as observation-oriented modeling, is centered on model building in an effort to explicate the structures and processes believed to generate a set of observations. In terms of analysis, this novel approach complements traditional methods…

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This…

Methods to assess the significance of mediated effects in education and the social sciences are well studied and fall into two categories: single sample methods and computer-intensive methods. A popular single sample method to detect the significance of the mediated effect is the test of joint significance, and a popular computer-intensive method…

A large number of approaches have been proposed for estimating and testing the significance of indirect effects in mediation models. In this study, four sets of Monte Carlo simulations involving full latent variable structural equation models were run in order to contrast the effectiveness of the currently popular bias-corrected bootstrapping…

Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…

Methods by which structural models correct for the effects of attenuation due to measurement error are reviewed, and implications of such disattenuation for interpreting the results of structural equation models are considered. Recommendations are made for improving the practice of disattenuation, and caution is urged in drawing inferences based…

The distinction between Type 1 and Type 12 sampling in connection with measurement data is discussed, and a method is presented for simulating data arising from Type 12 sampling. A Monte Carlo study is described that shows conditions under which precise confidence level control under Type 12 sampling is maintained. (SLD)

This paper makes the point that descriptive and inferential measures of nonnormality and graphic displays of the frequency distribution of important variables should be routine in research reporting. This point is particularly true for research involving measures with nonarbitrary metrics where the distribution shape is unaffected by measurement…

A Bayesian alternative to interpretations based on classical reliability theory is presented. Procedures are detailed for calculation of a posterior score and credible interval with joint consideration of item sample and occasion error. (Author/SLD)