Bayesian Estimation of Repeated Measures Model Using MCMC

Document Type

Presentation

Publication Date

4-10-2014

Faculty Mentor

Daniel Coster

Abstract

We analyze the annual proportion of audit fees to assets for 1947 companies from 2002 through 2009 as functions of company size and degree of industry regulation. Bayesian models with different variance-covariance structures across the 8 years of repeated measures are used and model fits are compared and contrasted with traditional parametric mixed models fitted using likelihood methods. Markov Chain Monte Carlo (MCMC) methods are used for the simulations as they provide estimates of the posterior distributions for model parameters which are not dependent on parametric assumptions such as normality or constant variance and are generally robust to choices of priors, most especially non-informative priors. In cases where an analytic representation of the posterior distribution is not tractable, an additional Metropolis-Hastings (MH) step is incorporated at the expense of greater computational complexity. Within the fitted model structures, we compare mean responses between large companies and small companies and regulated and non-regulated industries and analyze the trend in mean audit fee ratios across the eight years of observed data. Of greater importance in these analyses is any trend(s), before and after regulatory requirements changed at year 2004, in variability in audit-fee ratios and the degree of dependence between adjacent years, as these are measures of changing economic volatility in company audit expenses.

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