# Simon Jackman’s Bayesian Model Examples in Stan

*Jeffrey B. Arnold*

*2018-05-07*

# Preface

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

## Dependencies

The R packages, Stan models, and datasets needed to run the code examples can be installed with

## Colonophon

```
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:
#> [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
#>
#> attached base packages:
#> [1] methods stats graphics grDevices utils datasets base
#>
#> loaded via a namespace (and not attached):
#> [1] Rcpp_0.12.16 knitr_1.20 magrittr_1.5
#> [4] munsell_0.4.3 colorspace_1.3-2 rlang_0.2.0
#> [7] stringr_1.3.0 plyr_1.8.4 tools_3.4.4
#> [10] parallel_3.4.4 grid_3.4.4 gtable_0.2.0
#> [13] xfun_0.1 htmltools_0.3.6 StanHeaders_2.17.2
#> [16] lazyeval_0.2.1 rprojroot_1.3-2 digest_0.6.15
#> [19] tibble_1.4.2 rstan_2.17.3 bookdown_0.7.7
#> [22] gridExtra_2.3 ggplot2_2.2.1 inline_0.3.14
#> [25] evaluate_0.10.1 rmarkdown_1.9 stringi_1.1.7
#> [28] pillar_1.2.1 compiler_3.4.4 scales_0.5.0
#> [31] backports_1.1.2 stats4_3.4.4
```