Sensitivity analysis in Bayesian generalized linear mixed models for binary data

By Malgorzata Roos, Leonhard Held. 2011

151 citations recorded by the source corpus.

Generalized linear mixed models (GLMMs) enjoy increasing popularity because of their ability to model correlated observations. Integrated nested Laplace approximations (INLAs) provide a fast implementation of the Bayesian approach to GLMMs. However, sensitivity to prior assumptions on the random effects precision parameters is a potential problem. To quantify the sensitivity to prior assumptions, we develop a general sensitivity measure based on the Hellinger distance to assess sensitivity of the posterior distributions with respect to changes in the prior distributions for the precision parameters. In addition, for model selection we suggest several cross-validatory techniques for Bayesian GLMMs with a dichotomous outcome. Although the proposed methodology holds in greater generality, we make use of the developed methods in the particular context of the well-known salamander mating data. We arrive at various new findings with respect to the best fitting model and the sensitivity of the estimates of the model components.

Subfields: Artificial Intelligence, Genetics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/060021c051ba86a9f5c096d3c270e7e267eb4a3c

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Citations in the corpus

Spatial and spatio-temporal models with R-INLA. (2013, unknown): “For this reason, INLA can be successfully used in a great variety of applications (e.g. Li et al., 2012; Riebler et al., 2012; Ruiz-Cárdenas et al., 2012; Martino et al., 2011; Roos and Held, 2011; Schrödle and Held, 2011a,b; Schrödle et al., 2011; Paul et al., 2010), also thanks to the availability”
Spatial and spatio-temporal models with R-INLA. (2013, background): “…successfully used in a great variety of applications (e.g. Li et al., 2012; Riebler et al., 2012; Ruiz-C´ardenas et al., 2012; Martino et al., 2011; Roos and Held, 2011; Schr¨o-dle and Held, 2011a,b; Schr¨odle et al., 2011; Paul et al., 2010), also thanks to the availability of an R package named…”
Bayesian Computing with INLA: A Review (2016, methodology): “Besides others we plan to integrate automatic tests for prior sensitivity, following the work of Roos and Held (2011); Roos et al. (2015a).”
Bayesian analysis of measurement error models using integrated nested Laplace approximations (2015, methodology): “Models can be fitted in short time making prior sensitivity analysis (Roos and Held, 2011) and even bootstrap studies (see Section 5.”
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors (2014, methodology): “er¨ and Wagner (2011) demonstrate overﬁtting due to Gamma-priors and suggest using a (half) Gaussian prior for the standard deviation to overcome this problem, as suggested by Gelman (2006); See also Roos and Held (2011) and the discussion of Lunn et al. (2009). Using (approximate) parameter orthogo”
Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations (2012, background): “…(in simulated data sets not shown) that posterior inferences can be sensitive to prior assumptions on the variance components in Poisson models where many of the counts are close to zero or in binary data where the cluster size is small (see Browne and Draper ( 2006) and Roos and Held (2011)).”
Estimation and prediction of the spatial occurrence of fish species using Bayesian latent Gaussian models (2013, background): “response, measuring the degree to which the fitted probabilities of fish presence at location i coincide with the observed binary outcomes Zi (Roos and Held 2011).”