## Testing Small Variance Priors Using Prior-Posterior Predictive P-values

Muthen and Asparouhov (2012) propose to evaluate model fit in structural equation models based on approximate (using small variance priors) instead of exact equality of (combinations of) parameters to zero. This is an important development that adequately addresses Cohen’s (1994) “The earth is round (p < .05)”, which stresses that point null-hypotheses are so precise that small and irrelevant differences from the null-hypothesis may lead to their rejection.

## Measurement Invariance (book)

Multi-item surveys are frequently used to study scores on latent factors, like human values, attitudes and behavior. Such studies often include a comparison, between specific groups of individuals, either at one or multiple points in time.

## “Is the Hypothesis Correct” or “Is it Not”: Bayesian Evaluation of One Informative Hypothesis for ANOVA

Researchers in the behavioral and social sciences often have one informative hypothesis with respect to the state of affairs in the population from which they sampled their data. The question they would like an answer to is “Is the Hypothesis Correct” or “Is it Not.”

## Bayesian Evaluation of Inequality-Constrained Hypotheses in SEM Models using Mplus

Researchers in the behavioral and social sciences often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model resulting in an informative hypothesis. The questions they would like an answer to are “Is the hypothesis Correct” or “Is the hypothesis incorrect”?

## One Size Does Not Fit All: proposal for a prior-adapted BIC

This paper presents a refinement of the Bayesian Information Criterion (BIC). While the original BIC selects models on the basis of complexity and fit, the so-called prior-adapted BIC allows us to choose among statistical models that differ on three scores: fit, complexity, and model size.

## A prior predictive loss function for the evaluation of inequality constrained hypotheses

In many types of statistical modeling, inequality constraints are imposed between the parameters of interest. As we will show in this paper, the DIC (i.e., posterior Deviance Information Criterium as proposed as a Bayesian model selection tool by Spiegelhalter, Best, Carlin, & Van Der Linde, 2002) fails when comparing inequality constrained hypotheses.

## Informative hypotheses: How to move beyond classical null hypothesis testing

Almost all researchers in psychology have specific expectations about their theories in the form of hypothesized order constraints between statistical parameters. For example: the mean of group 1 is larger than the mean of group 2 which in turn is larger than the mean of group 3.

## Testing inequality constrained hypotheses in SEM Models

Researchers often have expectations that can be expressed in the form of inequality constraints among the parameters of a structural equation model. It is currently not possible to test these so-called informative hypotheses in structural equation modeling software.

## Bayesian model selection of informative hypotheses for repeated measurements

When analyzing repeated measurements data, researchers often have expectations about the relations between the measurement means. The expectations can often be formalized using equality and inequality constraints between (i) the measurement means over time, (ii) the measurement means between groups,