geostan_fit-methods.R

#' print or plot a fitted geostan model
#'
#' @description Print a summary of model results to the R console, or plot posterior distributions of model parameters.
#'
#' @param x A fitted model object of class \code{geostan_fit}.
#' @param digits number of digits to print
#' @param probs Argument passed to \code{quantile}; which quantiles to calculate and print.
#' 
#' @param pars parameters to include; a character string (or vector) of parameter names.
#' @param plotfun Argument passed to \code{rstan::plot}. Options include histograms ("hist"), MCMC traceplots ("trace"), and density plots ("dens"). Diagnostic plots are also available such as Rhat statistics ("rhat"), effective sample size ("ess"), and MCMC autocorrelation ("ac").
#' 
#' @param fill fill color for histograms and density plots.
#'
#' @param ... additional arguments to `rstan::plot` or `rstan::print.stanfit`.
#' 
#' @examples
#' data(georgia)
#' georgia$income <- georgia$income/1e3
#' 
#' fit <- stan_glm(deaths.male ~ offset(log(pop.at.risk.male)) + log(income),
#'                 centerx = TRUE,
#'                 data = georgia,
#'                 family = poisson(),
#'                 chains = 2, iter = 600) # for speed only
#'
#' 
#' # print and plot results
#' print(fit)
#' plot(fit)
#' @export
#' @md
#' @method print geostan_fit
#' @rdname print_geostan_fit
print.geostan_fit <- function(x,
                              probs = c(0.025, 0.2, 0.5, 0.8, 0.975),
                              digits = 3,
                              pars = NULL, ...) {
  pars <- c(pars, "intercept")
  cat("Spatial Model Results \n")
  cat("Formula: ")
  print(x$formula)
  if (inherits(x$slx, "formula")) {
   cat("SLX: ")
   print(x$slx)
   pars <- c(pars, "gamma")
  }
  x.pars <- c("beta", "nu", "sigma")
  if (any(x.pars %in% names(x$priors))) pars <- c(pars, names(x$priors)[grep(paste0(x.pars, collapse="$|"), names(x$priors))])   
  if(inherits(x$re$formula, "formula")) {
    cat("Partial pooling (varying intercept): ")
    print(x$re$formula)
    pars <- c(pars, "alpha_tau")
  }
  cat("Spatial method (outcome): ", as.character(x$spatial$method), "\n")
  if (x$spatial$method == "CAR") pars <- c(pars, "car_rho", "car_scale")
  if (x$spatial$method == "SAR") pars <- c(pars, "sar_rho", "sar_scale")  
  if (x$spatial$method == "BYM2") pars <- c(pars, "rho", "spatial_scale")
  if (x$spatial$method == "BYM") pars <- c(pars, "spatial_scale", "theta_scale")
  if (x$spatial$method == "ICAR") pars <- c(pars, "spatial_scale")  
  cat("Likelihood function: ", x$family$family, "\n")
  cat("Link function: ", x$family$link, "\n")
  cat("Residual Moran Coefficient: ", x$diagnostic["Residual_MC"], "\n")
  if (!is.na(x$diagnostic["WAIC"])) cat("WAIC: ", x$diagnostic["WAIC"], "\n")
  cat("Observations: ", x$N, "\n")  
  cat("Data models (ME): ")
  if (x$ME$has_me) {
      cat(paste(names(x$ME$se), sep = ", ")) 
      if (x$ME$spatial_me) {
          cat("\n Data model (ME prior): CAR (auto Gaussian)")
      } else {
          cat("\nData model (ME prior): Student's t")
      }
  } else {
      cat("none")
  }
  if (x$spatial$method == "HS") {
    cat("\nHorseshoe global shrinkage prior: ", round(x$priors$beta_ev$global_scale, 2), "\n")
  }
  cat("\n")
  print(x$stanfit, pars = pars, digits = digits, probs = probs, ...)
}


#' @export
#' @import graphics
#' @importFrom signs signs
#' @rdname print_geostan_fit
#' @method plot geostan_fit
plot.geostan_fit <- function(x,
                             pars,
                             plotfun = "hist",
                             fill = "steelblue4",
                             ...) {
  if(missing(pars)) {
      pars <- "intercept"
      if (inherits(x$slx, "formula")) pars <- c(pars, "gamma")      
      x.pars <- c("beta", "nu", "sigma", "alpha_tau")
      if (any(x.pars %in% names(x$priors))) pars <- c(pars, names(x$priors)[grep(paste0(x.pars, collapse="|"), names(x$priors))])
      if (x$spatial$method == "SAR") pars <- c(pars, "sar_rho", "sar_scale")  
      if (x$spatial$method == "CAR") pars <- c(pars, "car_rho", "car_scale")
      if (x$spatial$method == "BYM2") pars <- c(pars, "rho", "spatial_scale")
      if (x$spatial$method == "BYM") pars <- c(pars, "spatial_scale", "theta_scale")
      if (x$spatial$method == "ICAR") pars <- c(pars, "spatial_scale")
  }
  rstan::plot(x$stanfit, pars = pars, fill = fill, plotfun = plotfun, ...) +
      scale_x_continuous(labels = signs::signs) +
      scale_y_continuous(labels = signs::signs)
}




#' Extract residuals, fitted values, or the spatial trend 
#'
#' @description Extract model residuals, fitted values, or spatial trend from a fitted \code{geostan_fit} model. 
#'
#' @param object A fitted model object of class \code{geostan_fit}.
#' 
#' @param summary Logical; should the values be summarized by their mean, standard deviation, and quantiles (\code{probs = c(.025, .2, .5, .8, .975)}) for each observation? Otherwise, a matrix containing samples from the posterior distributions is returned.
#'
#' @param rates For Poisson and Binomial models, should the fitted values be returned as rates, as opposed to raw counts? Defaults to `TRUE`; see the `Details` section for more information.
#' 
#' @param detrend For auto-normal models (CAR and SAR models with Gaussian likelihood only); if `detrend = TRUE`, the implicit spatial trend will be removed from the residuals. The implicit spatial trend is `Trend = rho * C %*% (Y - Mu)` (see \link[geostan]{stan_car} or \link[geostan]{stan_sar}). I.e., `resid = Y - (Mu + Trend)`.
#' 
#' @param trend For auto-normal models (CAR and SAR models with Gaussian likelihood only); if `trend = TRUE`, the fitted values will include the implicit spatial trend term. The implicit spatial trend is `Trend = rho * C %*% (Y - Mu)` (see \link[geostan]{stan_car} or \link[geostan]{stan_sar}). I.e., if `trend = TRUE`, `fitted = Mu + Trend`.
#' 
#' @param ... Not used
#'
#' @details
#'
#' When \code{rates = FALSE} and the model is Poisson or Binomial, the fitted values returned by the \code{fitted} method are the expected value of the response variable. The \code{rates} argument is used to translate count outcomes to rates by dividing by the appropriate denominator. The behavior of the `rates` argument depends on the model specification. Consider a Poisson model of disease incidence, such as the following intercept-only case:
#' ```
#' fit <- stan_glm(y ~ offset(log(E)),
#'                data = data,
#'                family = poisson())
#' ```
#' If the fitted values are extracted using `rates = FALSE`, then \code{fitted(fit)} will return the expectation of \eqn{y}. If `rates = TRUE` (the default), then \code{fitted(fit)} will return the expected value of the rate \eqn{\frac{y}{E}}.
#'
#' If a binomial model is used instead of the Poisson, then using `rates = TRUE` will return the expectation of \eqn{\frac{y}{N}} where \eqn{N} is the sum of the number of 'successes' and 'failures', as in:
#' ```
#' fit <- stan_glm(cbind(successes, failures) ~ 1,
#'                data = data,
#'                family = binomial())
#' ```
#' 
#' @examples
#' \donttest{
#' data(georgia)
#' A <- shape2mat(georgia, "B")
#' 
#' fit <- stan_esf(deaths.male ~ offset(log(pop.at.risk.male)),
#'                 C = A,
#'                 data = georgia,
#'                 family = poisson(),
#'                 chains = 1, iter = 600) # for speed only
#'
#' 
#' # Residuals
#' r <- resid(fit)
#' moran_plot(r$mean, A)
#' head(r)
#' 
#' # Fitted values
#' f <- fitted(fit)
#'
#' # Fitted values, unstandardized
#' f <- fitted(fit, rates = FALSE)
#' head(f)
#'
#' # Spatial trend
#' esf <- spatial(fit)
#' head(esf)
#' }
#' @export
#' @md
#' @method residuals geostan_fit
#' @rdname resid_geostan_fit
#' @export
residuals.geostan_fit <- function(object,
                                  summary = TRUE,
                                  rates = TRUE,
                                  detrend = TRUE,
                                  ...) {
    y <- object$data[,1]
    fits <- fitted(object, summary = FALSE, rates = rates, trend = detrend)
    if (rates && object$family$family == "binomial") { y <- y / (y + object$data[,2]) }
    if (rates && object$family$family == "poisson" && "offset" %in% c(colnames(object$data))) {
        log.at.risk <- object$data[, "offset"]
        at.risk <- exp( log.at.risk )
        y <- y / at.risk     
    }
    R = sweep(fits, MARGIN = 2, STATS = as.array(y), FUN = .resid)
    colnames(R) <- gsub("fitted", "residual", colnames(R))
    if (summary) return( post_summary(R) )
    return (R)  
}


#' @noRd
.resid <- function(yhat, y) y - yhat

#' @export
#' 
#' @import stats
#' @method fitted geostan_fit
#' @rdname resid_geostan_fit
fitted.geostan_fit <- function(object,
                               summary = TRUE,
                               rates = TRUE,
                               trend = TRUE,
                               ...) {
    fits <- as.matrix(object$stanfit, pars = "fitted")
    if (object$family$family == "auto_gaussian" && trend == TRUE) {
        spatial_samples <- spatial(object, summary = FALSE)
        fits <- fits + spatial_samples
    }
    if (!rates && object$family$family == "binomial") {        
        trials <- object$data[,1] + object$data[,2]
        fits <- sweep(fits, MARGIN = 2, STATS = as.array(trials), FUN = "*")
    }
    if (rates && object$family$family == "poisson" && "offset" %in% c(colnames(object$data))) {
        log.at.risk <- object$data[, "offset"]
        at.risk <- exp( log.at.risk )
        fits <- sweep(fits, MARGIN = 2, STATS = as.array(at.risk), FUN = "/")
    }
    if (summary) return( post_summary(fits) )
    return (fits)          
}

#' Extract spatial component from a fitted geostan model
#' @export
#' @rdname resid_geostan_fit
spatial <- function(object,
                    summary = TRUE,
                    ...) {
    UseMethod("spatial", object)
}

#' @export
#' @method spatial geostan_fit
#' @rdname resid_geostan_fit
spatial.geostan_fit <- function(object,
                                summary = TRUE,
                                ...) {
    if (is.na(object$spatial$par)) stop("This model does not have a spatial trend component to extract.")
    if (object$spatial$method %in% c("CAR", "SAR")) {
        spatial.samples <- extract_autoGauss_trend(object)
    } else {
        par <- as.character(object$spatial$par)
        spatial.samples <- as.matrix(object, pars = par, ...)
    }
  if (summary) {
    return ( post_summary(spatial.samples) )
  } else {
      return( spatial.samples )
  }
}

extract_autoGauss_trend <- function(object) {
    if (object$spatial$method == "CAR") rho_name <- "car_rho"
    if (object$spatial$method == "SAR") rho_name <- "sar_rho"
    if (object$family$family == "auto_gaussian") {
        C <- object$C
        y <- object$data[,1]
        rho <- as.matrix(object, pars = rho_name)
        fits <- as.matrix(object$stanfit, pars = "fitted")
        R = sweep(fits, MARGIN = 2, STATS = as.array(y), FUN = .resid)
        spatial.samples <- t(sapply(1:nrow(rho), function(i) {
            as.numeric( rho[i] * C %*% R[i,] )
        }))         
      } else {
          log_lambda_mu <- as.matrix(object, pars = "log_lambda_mu")
          log_lambda <- log( fitted(object, summary = FALSE, rates = TRUE) )
          spatial.samples <- log_lambda - log_lambda_mu
      }
    return (spatial.samples)
}



#' Extract samples from a fitted model
#'
#' @description Extract samples from the joint posterior distribution of parameters.
#'
#' @param x A fitted model object of class \code{geostan_fit}.
#'
#' @param ... Further arguments passed to \code{rstan} methods for for `as.data.frame`, `as.matrix`, or `as.array`
#'
#' @return
#'
#' A matrix, data frame, or array of MCMC samples is returned.
#' 
#' @examples
#' data(georgia)
#' A <- shape2mat(georgia, "B")
#' 
#' fit <- stan_glm(deaths.male ~ offset(log(pop.at.risk.male)),
#'                 C = A,
#'                 data = georgia,
#'                 family = poisson(),
#'                 chains = 1, iter = 600) # for speed only
#'
#' 
#' s <- as.matrix(fit)
#' dim(s)
#'
#' a <- as.matrix(fit, pars = "intercept")
#' dim(a)
#'
#' # Or extract the stanfit object
#' S <- fit$stanfit
#' print(S, pars = "intercept")
#' samples <- as.matrix(S)
#' dim(samples)
#' @md
#' @export
#' @rdname samples_geostan_fit
#' @method as.matrix geostan_fit
as.matrix.geostan_fit <- function(x, ...) {
  as.matrix(x$stanfit, ...)
}

#' @export
#' @rdname samples_geostan_fit
#' @method as.data.frame geostan_fit
as.data.frame.geostan_fit <- function(x, ...) {
    as.data.frame(x$stanfit, ...)
}

#' @export
#' @rdname samples_geostan_fit
#' @method as.array geostan_fit
as.array.geostan_fit <- function(x, ...){
    as.array(x$stanfit, ...)
}


#' Predict method for `geostan_fit` models
#'
#' @description Obtain predicted values from a fitted model by providing new covariate values.
#' 
#' @param object A fitted model object of class \code{geostan_fit}.
#' 
#' @param newdata A data frame in which to look for variables with which to predict, presumably for the purpose of viewing marginal effects. Note that if the model formula includes an offset term, `newdata` must contain the offset. Note also that any spatially-lagged covariate terms will be ignored if they were provided using the `slx` argument. If covariates in the model were centered using the `centerx` argument, the `predict.geostan_fit` method will automatically center the predictors in `newdata` using the values stored in `object$x_center`. If `newdata` is missing, the fitted values of the model will be returned.
#' 
#' @param alpha A single numeric value or a numeric vector with length equal to `nrow(newdata)`; `alpha` serves as the intercept in the linear predictor. The default is to use the posterior mean of the intercept. Even if \code{type = "response"}, this needs to be provided on the scale of the linear predictor. 
#'
#' @param center May be a vector of numeric values or a logical scalar to pass to \code{\link[base]{scale}}. Defaults to using `object$x_center`. If the model was fit using `centerx = TRUE`, then covariates were centered and their mean values are stored in `object$x_center` and the `predict` method will use them to automatically center `newdata`; if the model was fit with `centerx = FALSE`, then `object$x_center = FALSE` and `newdata` will not be centered.
#'
#' @param summary Logical; should the values be summarized with the mean, standard deviation and quantiles (\code{probs = c(.025, .2, .5, .8, .975)}) for each observation? Otherwise a matrix containing samples from the posterior distribution at each observation is returned.
#' 
#' @param type By default, results from `predict` are on the scale of the linear predictor (`type = "link")`). The alternative (`type = "response"`) is on the scale of the response variable. For example, the default return values for a Poisson model on the log scale, and using `type = "response"` will return the original scale of the outcome variable (by exponentiating the log values).
#'
#' @param ... Not used
#'
#' @details
#'
#' The purpose of the predict method is to explore marginal effects of (combinations of) covariates. The method sets the intercept equal to its posterior mean (i.e., `alpha = mean(as.matrix(object, pars = "intercept"))`); the only source of uncertainty in the results is the posterior distribution of the coefficients, which can be obtained using `Beta = as.matrix(object, pars = "beta")`.
#'
#' The model formula will be taken from `object$formula`, and then a model matrix will be created by passing `newdata` to the \link[stats]{model.frame} function (as in: \code{model.frame(newdata, object$formula}). 
#' 
#' Be aware that in generalized linear models (such as Poisson and Binomial models) marginal effects of each covariate are sensitive to the level of other covariates in the model. If the model includes any spatially-lagged covariates (introduced using the `slx` argument) or a spatial autocorrelation term (for example, you used a spatial CAR, SAR, or ESF model), these terms will essentially be fixed at zero for the purposes of calculating marginal effects. If you want to change this, you can introduce spatial trend values by specifying a varying intercept using the `alpha` argument.
#' 
#' @return
#'
#' If `summary = FALSE`, a matrix of samples is returned. If `summary = TRUE` (the default), a data frame is returned.
#' 
#' @examples
#' data(georgia)
#' georgia$income <- georgia$income / 1e3
#' 
#' fit <- stan_glm(deaths.male ~ offset(log(pop.at.risk.male)) + log(income),
#'                data = georgia,
#'                centerx = TRUE,
#'                family = poisson(),
#'                chains = 2, iter = 600) # for speed only
#'
#' # note: pop.at.risk.male=1 leads to log(pop.at.risk.male)=0
#' # so that the predicted values are rates
#' newdata <- data.frame(
#'              income = seq(min(georgia$income),
#'                           max(georgia$income),
#'                            length.out = 100),
#'              pop.at.risk.male = 1)
#'
#' preds <- predict(fit, newdata, type = "response")
#' head(preds)
#' plot(preds$income,
#'      preds$mean * 10e3,
#'      type = "l",
#'      ylab = "Deaths per 10,000",
#'      xlab = "Income ($1,000s)")
#'
#' # here the predictions are rates per 10,000
#' newdata$pop.at.risk.male <- 10e3
#' preds <- predict(fit, newdata, type = "response")
#' head(preds)
#' plot(preds$income,
#'     preds$mean,
#'     type = "l",
#'     ylab = "Deaths per 10,000",
#'     xlab = "Income ($1,000s)")
#' @export 
predict.geostan_fit <- function(object,
                                newdata,
                                alpha = mean(as.matrix(object, pars = "intercept")),
                                center = object$x_center,
                                summary = TRUE,
                                type = c("link", "response"),
                                ...) {
    type <- match.arg(type)
    if (missing(newdata)) return (fitted(object, summary = summary, ...))
    f <- object$formula[-2]
    X <- as.matrix(model.matrix(f, newdata)[,-1])    
    X <- scale(X, center = center, scale = FALSE)
    O <- model.offset( model.frame(f, newdata) )
    O <- ifelse(is.null(O), 0, O)
    B <- as.matrix(object, pars = "beta") 
    M <- nrow(B)
    N <- nrow(X)
    P <- matrix(NA, nrow = M, ncol = N)
    for (m in 1:M) P[m,] <- O + alpha + X %*% B[m,] 
    if (type == "response") {
        if (object$family$link == "log") P <- exp(P)
        if (object$family$link == "logit") P <- inv_logit(P)
    }
    if (summary) {
        P <- post_summary(P)
        P <- cbind(newdata, alpha = alpha, P)
    }
    return (P)
}