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. Author manuscript; available in PMC: 2014 Oct 27.
Published in final edited form as: Chapman Hall CRC Handb Mod Stat Methods. 2010;2010:541–558. doi: 10.1201/9781420072884-c30

Table 30.1.

Association between asthma hospitalization and log PM2.5 (β̂1) and elevation (β̂2). The four models above the line are fitted using maximum and quasi-maximum likelihood estimation, the two below are Bayesian hierarchical models (and assume a Poisson likelihood). The “Log-Linear Model” refers to model (30.1) while the “Aggregate Exposure Model” refers to model (30.15) using modeled exposures. “Convolution” refers to the model with non-spatial and spatial random effects modeled via an ICAR model.

Mean Model Estimation Model β̂1 Std. Err. β̂2 Std. Err.
Log-linear Model Poisson 0.306 0.013 −0.017 0.007
Log-linear Model Quasi-Likelihood 0.306 0.128 −0.017 0.064
Log-linear Model Negaive Binomial 0.227 0.171 −0.143 0.045
Aggregate Exposure Model Quasi-Likelihood 0.261 0.092 0.011 0.058
Log-linear Model Hierarchical Non-Spatial 0.240 0.177 −0.146 0.047
Log-linear Model Hierarchical Convolution 0.230 0.217 −0.146 0.048