Bayesian Generalized Additive Models for Location, Scale, and Shape for Zero-Inflated and Overdispersed Count Data

By N. Klein, Thomas Kneib, Stefan Lang. 2015

161 citations recorded by the source corpus.

Frequent problems in applied research preventing the application of the classical Poisson log-linear model for analyzing count data include overdispersion, an excess of zeros compared to the Poisson distribution, correlated responses, as well as complex predictor structures comprising nonlinear effects of continuous covariates, interactions or spatial effects. We propose a general class of Bayesian generalized additive models for zero-inflated and overdispersed count data within the framework of generalized additive models for location, scale, and shape where semiparametric predictors can be specified for several parameters of a count data distribution. As standard options for applied work we consider the zero-inflated Poisson, the negative binomial and the zero-inflated negative binomial distribution. The additive predictor specifications rely on basis function approximations for the different types of effects in combination with Gaussian smoothness priors. We develop Bayesian inference based on Markov chain Monte Carlo simulation techniques where suitable proposal densities are constructed based on iteratively weighted least squares approximations to the full conditionals. To ensure practicability of the inference, we consider theoretical properties like the involved question whether the joint posterior is proper. The proposed approach is evaluated in simulation studies and applied to count data arising from patent citations and claim frequencies in car insurances. For the comparison of models with respect to the distribution, we consider quantile residuals as an effective graphical device and scoring rules that allow us to quantify the predictive ability of the models. The deviance information criterion is used to select appropriate predictor specifications once a response distribution has been chosen. Supplementary materials for this article are available online.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2b2a49a0ac1a548963d602f921aeff3cb5156872

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Citations in the corpus

Bayesian Structured Additive Distributional Regression (2013, background): “In many applications, e.g. insurances [Klein et al., 2013a, Heller et al., 2006] or weather forecasts [Gneiting and Ranjan, 2011], distributions with point masses at zero are of great interest.”
Bayesian structured additive distributional regression with an application to regional income inequality in Germany (2015, methodology): “Similarly, multivariate extensions of beta regression lead to Dirichlet distributed responses representing multiple percentages that sum up to one; see Klein et al. (2015a) for a first attempt in this direction.”
Nonlife Ratemaking and Risk Management with Bayesian Additive Models for Location, Scale and Shape (2013, methodology): “Note that the performance of the DIC in count data models has been evaluated in the supplement of Klein et al. (2013a) and rated to provide valid guidance.”