Evaluating Informative Hypotheses with Equality and Inequality Constraints: A Tutorial Using the Bayes Factor via the Encompassing Prior Approach

When conducting a study, researchers usually have expectations based on hypotheses or theoretical perspectives they want to evaluate. Equality and inequality constraints on the model parameters are used to formalize researchers' expectations or theoretical perspectives into the so-called informative hypotheses. However, traditional statistical approaches, such as the Null Hypothesis Significance Testing (NHST) or the model comparison using information criteria (e.g., AIC and BIC), are unsuitable for testing complex informative hypotheses. An alternative approach is to use the Bayes factor. In particular, the Bayes factor based on the encompassing prior approach allows researchers to easily evaluate complex informative hypotheses in a wide range of statistical models (e.g., generalized linear). This paper provides a detailed introduction to the Bayes factor with encompassing prior. First, all steps and elements involved in the formalization of informative hypotheses and the computation of the Bayes factor with encompassing prior are described. Next, we apply this method to a real case scenario, considering the attachment theory. Specifically, we analyzed the relative influence of maternal and paternal attachment on children's social-emotional development by comparing the various theoretical perspectives debated in the literature.