Ordinal variables, although extremely common in psychology, are almost exclusively analyzed with statistical models that falsely assume them to be metric. This practice can lead to distorted effect-size estimates, inflated error rates, and other problems. We argue for the application of ordinal models that make appropriate assumptions about the variables under study. In this Tutorial, we first explain the three major classes of ordinal models: the cumulative, sequential, and adjacent-category models. We then show how to fit ordinal models in a fully Bayesian framework with the R package brms, using data sets on opinions about stem-cell research and time courses of marriage. The appendices provide detailed mathematical derivations of the models and a discussion of censored ordinal models. Compared with metric models, ordinal models provide better theoretical interpretation and numerical inference from ordinal data, and we recommend their widespread adoption in psychology.

One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future predictive accuracy, for instance, for the purpose of model comparison or selection. Exact cross-validation for Bayesian models is often computationally expensive, but approximate cross-validation methods have been developed, most notably methods for leave-one-out cross-validation (LOO-CV). If the actual prediction task is to predict the future given the past, LOO-CV provides an overly optimistic estimate because the information from future observations is available to influence predictions of the past. To properly account for the time series structure, we can use leave-future-out cross-validation (LFO-CV). Like exact LOO-CV, exact LFO-CV requires refitting the model many times to different subsets of the data. Using Pareto smoothed importance sampling, we propose a method for approximating exact LFO-CV that drastically reduces the computational costs while also providing informative diagnostics about the quality of the approximation.

Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose between hypotheses. While Bayes factors provide an immediate approach to hypothesis testing, they are highly sensitive to details of the data/model assumptions and it's unclear whether the details of the computational implementation (such as bridge sampling) are unbiased for complex analyses. Here, we study how Bayes factors misbehave under different conditions. This includes a study of errors in the estimation of Bayes factors; the first-ever use of simulation-based calibration to test the accuracy and bias of Bayes factor estimates using bridge sampling; a study of the stability of Bayes factors against different MCMC draws and sampling variation in the data; and a look at the variability of decisions based on Bayes factors using a utility function. We outline a Bayes factor workflow that researchers can use to study whether Bayes factors are robust for their individual analysis. (PsycInfo Database Record (c) 2022 APA, all rights reserved).