The **geostan** R package supports a complete spatial analysis workflow with Bayesian models for areal data, including a suite of functions for visualizing spatial data and model results. **geostan** models were built using **Stan**, a state-of-the-art platform for Bayesian modeling. The package is designed partly for public health research with spatial data, for which it complements the **surveil** R package for time series analysis of public health surveillance data.

Features include:

**Disease mapping and spatial regression**Statistical models for data recorded across areal units like states, counties, or census tracts.**Spatial analysis tools**Tools for visualizing and measuring spatial autocorrelation and map patterns, for exploratory analysis and model diagnostics.

**Observational uncertainty**Incorporate information on data reliability, such as standard errors of American Community Survey estimates, into any**geostan**model.**Missing and Censored observations**Vital statistics and disease surveillance systems like CDC Wonder censor case counts that fall below a threshold number;**geostan**can model disease or mortality risk for small areas with censored observations or with missing observations.**The RStan ecosystem**Interfaces easily with many high-quality R packages for Bayesian modeling.**Custom spatial models**Tools for building custom spatial models in Stan.

Using your R console, you can install **geostan** from CRAN:

You can install the latest version from the package github repository:

```
if (!require('devtools')) install.packages('devtools')
devtools::install_github("connordonegan/geostan")
```

If you are using Windows, you may need to install Rtools first. To install Rtools:

- Visit the Rtools site: https://cran.r-project.org/bin/windows/Rtools/
- Select the version that corresponds to the version of R that you have installed (e.g., R 4.3).
- After selecting the correct version, look for the “Install Rtools” section (just below the introductory text) and click on the “installer” to download it. For example, for Rtools43 (for R version 4.3), click on “Rtools43 installer.”
- Go to the
`.exe`

file you just downloaded and double-click to begin installation of Rtools.

All functions and methods are documented (with examples) on the website reference page. See the package vignettes for more on exploratory spatial analysis, spatial measurement error models, spatial regression with raster layers, and building custom spatial model in Stan.

To ask questions, report a bug, or discuss ideas for improvements or new features please visit the issues page, start a discussion, or submit a pull request.

Load the package and the `georgia`

county mortality data set:

This has county population and mortality data by sex for ages 55-64, and for the period 2014-2018. As is common for public access data, some of the observations missing because the CDC has censored them.

The `sp_diag`

function provides visual summaries of spatial data, including a histogram, Moran scatter plot, and map. Here is a visual summary of crude female mortality rates (as deaths per 10,000):

```
A <- shape2mat(georgia, style = "B")
mortality_rate <- georgia$rate.female * 10e3
sp_diag(mortality_rate, georgia, w = A)
#> 3 NA values found in x will be dropped from data x and matrix w
#> Warning: Removed 3 rows containing non-finite outside the scale range
#> (`stat_bin()`).
```

The following code fits a spatial conditional autoregressive (CAR) model to female county mortality data. These models are used for estimating disease risk in small areas like counties, and for analyzing covariation of health outcomes with other area qualities. The R syntax for fitting the models is similar to using `lm`

or `glm`

. We provide the population at risk (the denominator for mortality rates) as an offset term, using the log-transform. In this case, three of the observations are missing because they have been censored; per CDC criteria, this means that there were 9 or fewer deaths in those counties. By using the `censor_point`

argument and setting it to `censor_point = 9`

, the model will account for the censoring process when providing estimates of the mortality rates:

```
cars <- prep_car_data(A)
#> Range of permissible rho values: -1.661134 1
fit <- stan_car(deaths.female ~ offset(log(pop.at.risk.female)),
censor_point = 9,
data = georgia,
car_parts = cars,
family = poisson(),
cores = 4, # for multi-core processing
refresh = 0) # to silence some printing
#> 3 NA values identified in the outcome variable
#> Found in rows: 55, 126, 157
#>
#> *Setting prior parameters for intercept
#> Distribution: normal
#> location scale
#> 1 -4.7 5
#>
#> *Setting prior for CAR scale parameter (car_scale)
#> Distribution: student_t
#> df location scale
#> 1 10 0 3
#>
#> *Setting prior for CAR spatial autocorrelation parameter (car_rho)
#> Distribution: uniform
#> lower upper
#> 1 -1.7 1
```

Passing a fitted model to the `sp_diag`

function will return a set of diagnostics for spatial models:

```
sp_diag(fit, georgia, w = A)
#> Using sp_diag(y, shape, rates = TRUE, ...). To examine data as (unstandardized) counts, use rates = FALSE.
#> 3 NA values found in x will be dropped from data x and matrix w
#> Warning: Removed 3 rows containing missing values or values outside the scale
#> range (`geom_pointrange()`).
```

The `print`

method returns a summary of the probability distributions for model parameters, as well as Markov chain Monte Carlo (MCMC) diagnostics from Stan (Monte Carlo standard errors of the mean `se_mean`

, effective sample size `n_eff`

, and the R-hat statistic `Rhat`

):

```
print(fit)
#> Spatial Model Results
#> Formula: deaths.female ~ offset(log(pop.at.risk.female))
#> Spatial method (outcome): CAR
#> Likelihood function: poisson
#> Link function: log
#> Residual Moran Coefficient: 0.002382
#> WAIC: 1228.61
#> Observations: 156
#> Data models (ME): none
#> Inference for Stan model: foundation.
#> 4 chains, each with iter=2000; warmup=1000; thin=1;
#> post-warmup draws per chain=1000, total post-warmup draws=4000.
#>
#> mean se_mean sd 2.5% 20% 50% 80% 97.5% n_eff Rhat
#> intercept -4.677 0.003 0.099 -4.855 -4.734 -4.676 -4.615 -4.498 1384 1.002
#> car_rho 0.926 0.001 0.057 0.781 0.886 0.940 0.974 0.996 2921 1.001
#> car_scale 0.457 0.001 0.034 0.395 0.428 0.455 0.485 0.526 3929 1.000
#>
#> Samples were drawn using NUTS(diag_e) at Tue Apr 16 08:16:01 2024.
#> For each parameter, n_eff is a crude measure of effective sample size,
#> and Rhat is the potential scale reduction factor on split chains (at
#> convergence, Rhat=1).
```

Applying the `fitted`

method to the fitted model will return the fitted values from the model - in this case, the fitted values are the estimates of the county mortality rates. Multiplying them by 10,000 gives mortality rate per 10,000 at risk:

```
mortality_est <- fitted(fit) * 10e3
county_name <- georgia$NAME
head( cbind(county_name, mortality_est) )
#> county_name mean sd 2.5% 20% 50%
#> fitted[1] Crisp 101.70572 9.498562 83.97063 93.70448 101.24639
#> fitted[2] Candler 137.39050 16.606716 106.86044 123.51343 136.32448
#> fitted[3] Barrow 94.24360 6.351406 82.25888 88.85746 94.05780
#> fitted[4] DeKalb 59.76307 1.544278 56.72223 58.42850 59.78620
#> fitted[5] Columbia 53.31970 3.321858 47.13175 50.44742 53.30227
#> fitted[6] Cobb 54.12199 1.467704 51.33636 52.85897 54.10105
#> 80% 97.5%
#> fitted[1] 109.56469 121.40981
#> fitted[2] 150.82533 173.49393
#> fitted[3] 99.61073 107.25586
#> fitted[4] 61.08625 62.79658
#> fitted[5] 56.12651 59.92468
#> fitted[6] 55.34254 57.02782
```

The mortality estimates are stored in the column named “mean”, and the limits of the 95% credible interval are found in the columns “2.5%” and “97.5%”.

Details and demonstrations can be found in the package help pages and vignettes.

If you use geostan in published work, please include a citation.

Donegan, Connor (2022) “geostan: An R package for Bayesian spatial analysis” *The Journal of Open Source Software*. 7, no. 79: 4716. https://doi.org/10.21105/joss.04716.

```
@Article{,
title = {{geostan}: An {R} package for {B}ayesian spatial analysis},
author = {Connor Donegan},
journal = {The Journal of Open Source Software},
year = {2022},
volume = {7},
number = {79},
pages = {4716},
doi = {10.21105/joss.04716},
}
```