doc cleanup

DESCRIPTION

@@ -10,7 +10,7 @@ Authors@R: c(
     person("Mitzi", "Morris", role = "ctb")
   )
 Description: For Bayesian inference with spatial data, provides exploratory spatial analysis tools, multiple spatial model specifications, spatial model diagnostics, and special methods for inference with small area survey data (e.g., the America Community Survey (ACS)) and censored population health surveillance data. Models are pre-specified using the Stan programming language, a platform for Bayesian inference using Markov chain Monte Carlo (MCMC). References: Carpenter et al. (2017) <doi:10.18637/jss.v076.i01>; Donegan (2021) <doi:10.31219/osf.io/3ey65>; Donegan, Chun and Hughes (2020) <doi:10.1016/j.spasta.2020.100450>; Donegan, Chun and Griffith (2021) <doi:10.3390/ijerph18136856>; Morris et al. (2019) <doi:10.1016/j.sste.2019.100301>.
-License: GPL (>= 3) + file LICENSE
+License: GPL (>= 3)
 Encoding: UTF-8
 LazyData: true
 Roxygen: list(markdown = TRUE)

R/stan_car.R

@@ -65,35 +65,35 @@
 #' }
 #' where \eqn{I} is the identity matrix, \eqn{\rho} is a spatial dependence parameter, \eqn{C} is a spatial connectivity matrix, and \eqn{M} is a diagonal matrix of variance terms. The diagonal of \eqn{M} contains a scale parameter \eqn{\tau} multiplied by a vector of weights (often set to be proportional to the inverse of the number of neighbors assigned to each site). The CAR model owes its name to the fact that this joint distribution corresponds to a set of conditional distributions that relate the expected value of each observation to a function of neighboring values, i.e., the Markov condition holds:
 #' \deqn{
-#' E(y_i | y_1, y_2, \dots y_{i-1}, y_{i+1}, y_n) = \mu_i + \rho \sum_{j=1}^n c_{i,j} (y_j - \mu_j),
+#' E(y_i | y_1, y_2, \dots, y_{i-1}, y_{i+1}, \dots, y_n) = \mu_i + \rho \sum_{j=1}^n c_{i,j} (y_j - \mu_j),
 #' }
-#' where entries of \eqn{c_{i,j}} are non-zero only if \eqn{j \in N(i)}, and \eqn{N(i)} indexes the sites that are neighbors of the \eqn{i^{th}} site.
+#' where entries of \eqn{c_{i,j}} are non-zero only if \eqn{j \in N(i)} and \eqn{N(i)} indexes the sites that are neighbors of the \eqn{i^{th}} site.
 #' 
 #' With the Gaussian probability distribution,
 #' \deqn{
 #'  y_i | y_j: j \neq i \sim Gauss(\mu_i + \rho \sum_{j=1}^n c_{i,j} (y_j - \mu_j), \tau_i^2)
 #' }
 #' where \eqn{\tau_i} is a scale parameter and \eqn{\mu_i} may contain covariates or simply the intercept.
 #'
-#' The covariance matrix of the CAR model contains two parameters: \code{car_rho} (\eqn{\rho}), which controls the degree of spatial autocorrelation, and the scale parameter, \code{car_scale} (\eqn{\tau}). The range of permissible values for \eqn{\rho} depends on the specification of \eqn{\boldsymbol C} and \eqn{\boldsymbol M}; for specification options, see \code{\link[geostan]{prep_car_data}} and Cressie and Wikle (2011, pp. 184-188) or Donegan (2021).
+#' The covariance matrix of the CAR model contains two parameters: \eqn{\rho} (\code{car_rho}) which controls the kind (positive or negative) and degree of spatial autocorrelation, and the scale parameter \eqn{\tau} (\code{car_scale}). The range of permissible values for \eqn{\rho} depends on the specification of \eqn{\boldsymbol C} and \eqn{\boldsymbol M}; for specification options, see \link[geostan]{prep_car_data} and Cressie and Wikle (2011, pp. 184-188) or Donegan (2021).
 #' 
-#' Further details of the models and results depend on the \code{family} argument, as well as on the particular CAR specification chosen (see \link[geostan]{prep_car_data}).
+#' Further details of the models and results depend on the \code{family} argument, as well as on the particular CAR specification chosen (from \link[geostan]{prep_car_data}).
 #'
 #' ###  Auto-Gaussian
 #'
 #' When \code{family = auto_gaussian()} (the default), the CAR model is applied directly to the data as follows:
 #' \deqn{
 #'  y \sim Gauss( \mu, (I - \rho C)^{-1} M),
 #' }
-#' where \eqn{\mu} is the mean vector (with intercept, covariates, etc.), \eqn{C} is a spatial connectivity matrix, and \eqn{M} is a known diagonal matrix containing the conditional variances \eqn{\tau_i^2}. `C` and `M` are provided by \code{\link[geostan]{prep_car_data}}.
+#' where \eqn{\mu} is the mean vector (with intercept, covariates, etc.), \eqn{C} is a spatial connectivity matrix, and \eqn{M} is a known diagonal matrix containing the conditional variances \eqn{\tau_i^2}. \eqn{C} and \eqn{M} are provided by \link[geostan]{prep_car_data}.
 #'
-#' The auto-Gaussian model contains an implicit spatial trend (i.e., autocorrelation) component \eqn{\phi} which can be calculated as follows (Cressie 2015, p. 564):
+#' The auto-Gaussian model contains an implicit spatial trend (i.e. autocorrelation) component \eqn{\phi} which can be calculated as follows (Cressie 2015, p. 564):
 #' \deqn{
 #'  \phi = \rho C (y - \mu).
 #' }
-#' This term can be extracted from a fitted auto-Gaussian model using the \code{\link[geostan]{spatial}} method.
+#' This term can be extracted from a fitted auto-Gaussian model using the \link[geostan]{spatial} method.
 #'
-#' When applied to a fitted auto-Gaussian model, the \code{\link[geostan]{residuals.geostan_fit}} method returns 'de-trended' residuals \eqn{R} by default. That is,
+#' When applied to a fitted auto-Gaussian model, the \link[geostan]{residuals.geostan_fit} method returns 'de-trended' residuals \eqn{R} by default. That is,
 #' \deqn{
 #' R = y - \mu - \rho C (y - \mu).
 #' }
@@ -106,14 +106,14 @@
 #' y \sim Poisson(e^{O + \lambda}) \\
 #' \lambda \sim Gauss(\mu, (I - \rho C)^{-1} \boldsymbol M).
 #' }
-#' If the raw outcome consists of a rate \eqn{\frac{y}{p}} with observed counts \eqn{y} and denominator {p} (often this will be the size of the population at risk), then \eqn{O=log(p)} is the log of the denominator (the offset term).
+#' If the raw outcome consists of a rate \eqn{\frac{y}{p}} with observed counts \eqn{y} and denominator {p} (often this will be the size of the population at risk), then the offset term \eqn{O=log(p)} is the log of the denominator.
 #'
 #' This is often written (equivalently) as:
 #' \deqn{
 #' y \sim Poisson(e^{O + \mu + \phi}) \\
 #' \phi \sim Gauss(0, (I - \rho C)^{-1} \boldsymbol M).
 #' }
-#' For Poisson models, the \code{\link[geostan]{spatial}} method returns the parameter vector \eqn{\phi}.
+#' For Poisson models, the \link[geostan]{spatial} method returns the parameter vector \eqn{\phi}.
 #' 
 #' In the Poisson CAR model, \eqn{\phi} contains a latent spatial trend as well as additional variation around it: \eqn{\phi_i = \rho \sum_{i=1}^n c_{ij} \phi_j + \epsilon_i}, \eqn{\epsilon_i \sim Gauss(0, \tau_i^2)}. If you would like to extract the latent/implicit spatial trend from \eqn{\phi}, you can do so by calculating (following Cressie 2015, p. 564):
 #' \deqn{
@@ -127,14 +127,14 @@
 #' y \sim Binomial(N, \lambda)  \\
 #' logit(\lambda) \sim Gauss(\mu, (I - \rho C)^{-1} \boldsymbol M).
 #' }
-#' where outcome data `y` are counts, `N` is the number of trials, and `theta` is the 'success' rate. Note that the model formula should be structured as: `cbind(sucesses, failures) ~ x`, such that `trials = successes + failures`.
+#' where outcome data \eqn{y} are counts, \eqn{N} is the number of trials, and \eqn{\lambda} is the 'success' rate. Note that the model formula should be structured as: `cbind(sucesses, failures) ~ x`, such that `trials = successes + failures`.
 #'
 #' This is often written (equivalently) as:
 #' \deqn{
 #' y \sim Binomial(N, (\mu + \phi))  \\
 #' logit(\phi) \sim Gauss(0, (I - \rho C)^{-1} \boldsymbol M).
 #' }
-#' For fitted Binomial models, the \code{\link[geostan]{spatial}} method will return the parameter vector \code{phi}.
+#' For fitted Binomial models, the \link[geostan]{spatial} method will return the parameter vector \code{phi}.
 #' 
 #' As is also the case for the Poisson model, \eqn{\phi} contains a latent spatial trend as well as additional variation around it. If you would like to extract the latent/implicit spatial trend from \eqn{\phi}, you can do so by calculating:
 #' \deqn{
@@ -147,7 +147,7 @@
 #' \deqn{
 #'  y = W X \gamma + X \beta + \epsilon
 #' }
-#' where \eqn{W} is a row-standardized spatial weights matrix (see \code{\link[geostan]{shape2mat}}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
+#' where \eqn{W} is a row-standardized spatial weights matrix (see \link[geostan]{shape2mat}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
 #' ```
 #' stan_glm(y ~ x1 + x2, slx = ~ x1 + x2, \...),
 #' ```

R/stan_esf.R

@@ -75,9 +75,9 @@
 #' \tau \sim student(20, 0, 2) \\
 #' \beta_{E} \sim horseshoe(.)
 #' }
-#' The form of this model is similar to the BYM model (see \code{\link[geostan]{stan_icar}}), in the sense that it contains a spatially structured trend term (\eqn{E \beta_{E}}) and an unstructured ('random effects') term (\eqn{A}).
+#' The form of this model is similar to the BYM model (see \link[geostan]{stan_icar}), in the sense that it contains a spatially structured trend term (\eqn{E \beta_{E}}) and an unstructured ('random effects') term (\eqn{A}).
 #' 
-#' The \code{\link[geostan]{spatial.geostan_fit}} method will return \eqn{E \beta_{E}}.
+#' The \link[geostan]{spatial.geostan_fit} method will return \eqn{E \beta_{E}}.
 #'
 #' The model can also be extended to the space-time domain; see \link[geostan]{shape2mat} to specify a space-time connectivity matrix. 
 #' 
@@ -89,7 +89,7 @@
 #' \deqn{
 #'  y = W X \gamma + X \beta + \epsilon
 #' }
-#' where \eqn{W} is a row-standardized spatial weights matrix (see \code{\link[geostan]{shape2mat}}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
+#' where \eqn{W} is a row-standardized spatial weights matrix (see \link[geostan]{shape2mat}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
 #' ```
 #' stan_glm(y ~ x1 + x2, slx = ~ x1 + x2, \...),
 #' ```

R/stan_icar.R

@@ -152,7 +152,7 @@
 #' \deqn{
 #'  y = W X \gamma + X \beta + \epsilon
 #' }
-#' where \eqn{W} is a row-standardized spatial weights matrix (see \code{\link[geostan]{shape2mat}}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
+#' where \eqn{W} is a row-standardized spatial weights matrix (see \link[geostan]{shape2mat}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
 #' ```
 #' stan_glm(y ~ x1 + x2, slx = ~ x1 + x2, \...),
 #' ```

R/stan_sar.R

@@ -73,7 +73,7 @@
 #' 
 #' Most often, this model is applied directly to observations (referred to below as the auto-Gaussian model). The SAR model can also be applied to a vector of parameters inside a hierarchical model. The latter enables spatial autocorrelation to be modeled when the observations are discrete counts (e.g., disease incidence data).
 #'
-#' A note on terminology: the spatial statistics literature conceptualizes the simultaneously-specified spatial autoregressive model (SAR) in relation to the conditionally-specified spatial autoregressive model (CAR) (see \code{\link[geostan]{stan_car}}) (see Cliff and Ord 1981). The spatial econometrics literature, by contrast, refers to the simultaneously-specified spatial autoregressive (SAR) model as the spatial error model (SEM), and they contrast the SEM with the spatial lag model (which contains a spatially-lagged dependent variable on the right-hand-side of the regression equation) (see LeSage 2014). 
+#' A note on terminology: the spatial statistics literature conceptualizes the simultaneously-specified spatial autoregressive model (SAR) in relation to the conditionally-specified spatial autoregressive model (CAR) (see \link[geostan]{stan_car}) (see Cliff and Ord 1981). The spatial econometrics literature, by contrast, refers to the simultaneously-specified spatial autoregressive (SAR) model as the spatial error model (SEM), and they contrast the SEM with the spatial lag model (which contains a spatially-lagged dependent variable on the right-hand-side of the regression equation) (see LeSage 2014). 
 #' 
 #' ###  Auto-Gaussian
 #'
@@ -89,9 +89,9 @@
 #' \phi = \rho W (y - \mu)
 #' }
 #' 
-#' This term can be extracted from a fitted auto-Gaussian model using the \code{\link[geostan]{spatial}} method.
+#' This term can be extracted from a fitted auto-Gaussian model using the \link[geostan]{spatial} method.
 #'
-#' When applied to a fitted auto-Gaussian model, the \code{\link[geostan]{residuals.geostan_fit}} method returns 'de-trended' residuals \eqn{R} by default. That is,
+#' When applied to a fitted auto-Gaussian model, the \link[geostan]{residuals.geostan_fit} method returns 'de-trended' residuals \eqn{R} by default. That is,
 #' \deqn{
 #' R = y - \mu - \rho W (y - \mu).
 #' }
@@ -106,7 +106,7 @@
 #' \lambda \sim Gauss(\mu, \Sigma)   \\
 #' \Sigma = \sigma^2 (I - \rho W)^{-1}(I - \rho W')^{-1}.
 #' }
-#' If the raw outcome consists of a rate \eqn{\frac{y}{p}} with observed counts \eqn{y} and denominator {p} (often this will be the size of the population at risk), then \eqn{O=log(p)} is the log of the denominator (the offset term).
+#' If the raw outcome consists of a rate \eqn{\frac{y}{p}} with observed counts \eqn{y} and denominator {p} (often this will be the size of the population at risk), then the offset term \eqn{O=log(p)} is the log of the denominator.
 #' 
 #' This is often written (equivalently) as:
 #' \deqn{
@@ -115,7 +115,7 @@
 #' \Sigma = \sigma^2 (I - \rho W)^{-1}(I - \rho W')^{-1}
 #' }
 #'
-#' For Poisson models, the \code{\link[geostan]{spatial}} method returns the parameter vector \eqn{\phi}.
+#' For Poisson models, the \link[geostan]{spatial} method returns the parameter vector \eqn{\phi}.
 #'
 #' In the Poisson SAR model, \eqn{\phi} contains a latent spatial trend as well as additional variation around it. If you would like to extract the latent/implicit spatial trend from \eqn{\phi}, you can do so by calculating:
 #' \deqn{
@@ -130,7 +130,7 @@
 #' logit(\lambda) \sim Gauss(\mu, \Sigma)  \\
 #' \Sigma = \sigma^2 (I - \rho W)^{-1}(I - \rho W')^{-1}
 #' }
-#' where outcome data `y` are counts, `N` is the number of trials, and \eqn{\lambda} is the rate of 'success'. Note that the model formula should be structured as: `cbind(sucesses, failures) ~ 1` (for an intercept-only model), such that `trials = successes + failures`.
+#' where outcome data \eqn{y} are counts, \eqn{N} is the number of trials, and \eqn{\lambda} is the rate of 'success'. Note that the model formula should be structured as: `cbind(sucesses, failures) ~ 1` (for an intercept-only model), such that `trials = successes + failures`.
 #' 
 #' For fitted Binomial models, the \code{\link[geostan]{spatial}} method will return the parameter vector \code{phi}, equivalent to:
 #' \deqn{
@@ -147,7 +147,7 @@
 #' \deqn{
 #'  y = W X \gamma + X \beta + \epsilon
 #' }
-#' where \eqn{W} is a row-standardized spatial weights matrix (see \code{\link[geostan]{shape2mat}}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
+#' where \eqn{W} is a row-standardized spatial weights matrix (see \link[geostan]{shape2mat}), \eqn{WX} is the mean neighboring value of \eqn{X}, and \eqn{\gamma} is a coefficient vector. This specifies a regression with spatially lagged covariates. SLX terms can specified by providing a formula to the \code{slx} argument:
 #' ```
 #' stan_glm(y ~ x1 + x2, slx = ~ x1 + x2, \...),
 #' ```
@@ -200,7 +200,7 @@
 #'
 #' Internally, `geostan` will keep the index values of each censored observation, and the index value of each of the fully observed outcome values. For all observed counts, the likelihood statement will be:
 #' \deqn{
-#' p(y_i | \data, model) = poisson(y_i | \mu_i), 
+#' p(y_i | data, model) = poisson(y_i | \mu_i), 
 #' }
 #' as usual, where \eqn{\mu_i} may include whatever spatial terms are present in the model.
 #'

docs/pkgdown.yml

@@ -4,7 +4,7 @@ pkgdown_sha: ~
 articles:
   measuring-sa: measuring-sa.html
   spatial-me-models: spatial-me-models.html
-last_built: 2022-09-13T13:40Z
+last_built: 2022-09-17T23:06Z
 urls:
   reference: https://connordonegan.github.io/geostan/reference
   article: https://connordonegan.github.io/geostan/articles