**Date: **Tuesday 06 June 2017

**Time: **12:45 - 13:30 (Lunch available from 12:35)

**Room:** RA 2502 (Ravelijn)

## Title: Bayesian Modeling of Large-Scale Survey Data: Issues in Statistical Computing and Hypothesis Testing

** Abstract:**

*(Background)* When administering a survey to different groups, it is important to be able to compare scores across members of those groups. In order to make meaningful comparisons between groups, obtained scores must be measured on a common scale. To accomplish a common scale analysis, differences between groups should be taken into account. In current (Bayesian) statistical models, random effects are used to model group differences, where the random effect variances are tested to make inferences about group differences. A zero variance is a null hypothesis of specific interest but difficult to evaluate, since the value is located on the boundary of the parameter space, which also complicates the specification of a prior distribution.

A Bayesian marginal modeling approach is discussed by integrating out the random effects, and directly modeling the implied covariance structure. This leads to a generalized multivariate Probit model, where the covariance parameters represent the random effect variances. To make inferences about the dependency structure, interest is focused on the covariance parameters. It is shown that after an orthogonal transformation of the observations, the posterior distribution of the covariance parameters can be obtained in closed form. This result is used to define (fractional) Bayes factors to test the dependency structure.

Attention is also focused on the developed Markov chain Monte Carlo algorithm to estimate simultaneously all model parameters. Furthermore, an importance sampling method is discussed to compute Bayes factors for more complex situations. The method is applied to empirical data using data from the European Social Survey (ESS).