Assessment of Model Fit Sample Clauses

Assessment of Model Fit. There are a variety of methods to assess model fit in Bayesian analysis. These meth- ods can fall into the category of model fit, model comparison, and model checking [96]. In order to compare the fit of models between naive and more informative mod- els, we focus on the deviance information criterion (DIC). As models with increased complexity generally provide a better fit, this Bayesian information criterion adds a penalty for increased model complexity. The DIC estimates the effective number of parameters in a Bayesian hierarchical model in order to appropriately penalize for additional model complexity. pD = D(θ) − Dˆ(θ) = E[D(θ)|y] − D[E(θ)|y] (4.16) DIC = D(θ) + pD = D(θ) + D(θ) − Dˆ(θ) = 2D(θ) − Dˆ(θ) = 2E[D(θ)|y] − D[E(θ)|y] (4.17) The deviance, D(θ), is an overall measure of model fit and is calculated by twice the negative log likelihood of the model. pD is the estimate of the effective number of parameters and represents the model’s complexity. DIC is the difference in twice the posterior mean of the deviance and the deviance evaluated at the posterior mean of the parameters. Generally, if two models differ in DIC by more than 3, the model with the smaller DIC provides a better fit [114]. WinBUGS does not provide an estimate of DIC for models such as those presented in this research. While an estimate of the deviance, D(θ), is provided by XxxXXXX, Dˆ(θ) is not. This can be calculated in R by evaluating the deviance at the posterior mean of the random variables. For this work, we calculate the observed deviance (and hence the observed DIC) based on the observed data likelihood presented in equations 4.13 and 4.14.
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