Simon Jackman’s Bayesian Model Examples in Stan
Jeffrey B. Arnold
This work contains the Bayesian model examples written by Simon Jackman and previously available on his website. These were originally written in WinBUGS or JAGS. I have translated these examples into Stan and revised or edited them as appropriate.
This work is licensed under the Creative Commons Attribution 4.0 International License
- Undervote: difference of two independent proportions; racial differences in self-reported undervoting
- Cancer: difference of two independent proportions; differences in rates of lung cancer by smoking
- Florida: learning about an unknown proportion from survey data; using survey data to update beliefs about support for Bush in Florida in the 2000 presidential election campaign
- Turnout: logit/probit models for binary response; voter turnout as a function of covariates
- Co-Sponsor: computing auxiliary quantities from MCMC output, such as residuals, goodness of fit; logit model of legislative co-sponsorship
- Reagan: linear regression with AR(1) disturbances; monthly presidential approval ratings for Ronald Reagan
- Political Sophistication: generalized latent variable modeling (item-response modeling with a mix of binary and ordinal responses); assessing levels of political knowledge among survey respondents in France
- Legislators: generalized latent variable modeling (two-parameter item-response model); estimating legislative ideal points from roll call data
- Judges: item response modeling; estimating ideological locations of Supreme Court justices via analysis of decisions
- Resistant: outlier-resistant regression via the t density; votes in U.S. Congressional elections, 1956-1994; incumbency advantage.
- House of Commons: analysis of compositional data; vote shares for candidates to the U.K. House of Commons
- Campaign: tracking a latent variable over time; support for candidates over the course of an election campaign, as revealed by polling from different survey houses.
- Aspirin: meta-analysis via hierarchical modeling of treatment effects; combining numerous experimental studies of effect of aspirin on surviving myocardial infarction (heart attack)
- Corporatism hierarchical linear regression model, normal errors; joint impact of left-wing governments and strength of trade unions in structuring the determinants of economic growth
- Bimodal: severe pattern of missingness in bivariate normal data; bimodal density over correlation coefficient
- Unidentified: the consequences of over-parameterization; contrived example from Carlin and Louis
- Engines: modeling truncated data; time to failure, engines being bench-tested at different operating temperatures
- Truncated: Example of sampling from a truncated normal distribution.
- Generalized Beetles: Generalizing link functions for binomial GLMs.
- Negative Binomial: Example of a negative binomial regression of homicides
The R packages, Stan models, and datasets needed to run the code examples can be installed with
sessionInfo() #> R version 3.4.4 (2018-03-15) #> Platform: x86_64-apple-darwin15.6.0 (64-bit) #> Running under: macOS High Sierra 10.13.3 #> #> Matrix products: default #> BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib #> LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib #> #> locale: #>  en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8 #> #> attached base packages: #>  methods stats graphics grDevices utils datasets base #> #> loaded via a namespace (and not attached): #>  Rcpp_0.12.16 knitr_1.20 magrittr_1.5 #>  munsell_0.4.3 colorspace_1.3-2 rlang_0.2.0 #>  stringr_1.3.0 plyr_1.8.4 tools_3.4.4 #>  parallel_3.4.4 grid_3.4.4 gtable_0.2.0 #>  xfun_0.1 htmltools_0.3.6 StanHeaders_2.17.2 #>  lazyeval_0.2.1 rprojroot_1.3-2 digest_0.6.15 #>  tibble_1.4.2 rstan_2.17.3 bookdown_0.7.7 #>  gridExtra_2.3 ggplot2_2.2.1 inline_0.3.14 #>  evaluate_0.10.1 rmarkdown_1.9 stringi_1.1.7 #>  pillar_1.2.1 compiler_3.4.4 scales_0.5.0 #>  backports_1.1.2 stats4_3.4.4