Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

The latent growth model (LGM) is a popular tool in the social and behavioral sciences to study development processes of continuous and discrete outcome variables. A special case are frequency measurements of behaviors or events, such as doctor visits per month or crimes committed per year. Probability distributions for such outcomes include the…

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for…

What is the processing cost of being garden-pathed by a temporary syntactic ambiguity? We argue that comparing average reading times in garden-path versus non-garden-path sentences is not enough to answer this question. Trial-level contaminants such as inattention, the fact that garden pathing may occur non-deterministically in the ambiguous…

Standard meta-analysis methods are vulnerable to bias from incomplete reporting of results (both publication and outcome reporting bias) and poor study quality. Several alternative methods have been proposed as being less vulnerable to such biases. To evaluate these claims independently we simulated study results under a broad range of conditions…

The COVID-19 pandemic is arguably the worst crisis the world has faced, so far, in this new century. We haven't seen a pandemic like this since the "1918 Flu" at the beginning of the last century, and, as of this writing, there appears to be no end in sight. What those of us who're focused on quantitative methods have noticed, in…

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). A multilevel mediation model is used as an illustrative example to compare different types of DIC and WAIC. More specifically, the study compares the…

Pearson's product-moment correlation can be explained by means of the probability of concordant pairs of observations on two continuous variables (ie, the order of the observations from two randomly selected individuals is the same between the two variables). The probability of concordant pairs features relatively easy computation and offers an…

When constructed-response items are administered for a second time, it is necessary to evaluate whether the current Time B administration's raters have drifted from the scoring of the original administration at Time A. To study this, Time A papers are sampled and rescored by Time B scorers. Commonly the scores are compared using the proportion of…

The topic of Bayesian updating is explored using standard and non-standard dice as an intuitive and motivating model. Details of calculating posterior probabilities for a discrete distribution are provided, offering a different view to P-values. This article also includes the stars and bars counting technique, a powerful method of counting that is…

An interval estimation procedure is discussed that can be used to evaluate the probability of a particular response for a binary or binary scored item at a pre-specified point along an underlying latent continuum. The item is assumed to: (a) be part of a unidimensional multi-component measuring instrument that may contain also polytomous items,…

Doubly robust (DR) estimators that combine regression adjustments and inverse probability weighting (IPW) are widely used in causal inference with observational data because they are claimed to be consistent when either the outcome or the treatment selection model is correctly specified (Scharfstein et al., 1999). This property of "double…

This tutorial uses publicly available data from drug makers and the Food and Drug Administration to guide learners to estimate the confidence intervals of COVID-19 vaccine efficacy rates with a Bayesian framework. Under the classical approach, there is no probability associated with a parameter, and the meaning of confidence intervals can be…

One common score reported from diagnostic classification assessments is the vector of posterior means of the skill mastery indicators. As with any assessment, it is important to derive and report estimates of the reliability of the reported scores. After reviewing a reliability measure suggested by Templin and Bradshaw, this article suggests three…

The "Borel" board game consists of a series of experiments involving dice rolls, coin flips, or drawing colored balls from bags. Before each experiment is conducted, each player bets for or bets against a statement regarding the random outcome. We suggest that the collection of "Borel" experiments be used as a resource to…