R/sfMsAbund.R

In spAbundance: Univariate and Multivariate Spatial Modeling of Species Abundance

sfMsAbund <- function(formula, data, inits, priors,
                      tuning, cov.model = 'exponential', NNGP = TRUE,
                      n.neighbors = 15, search.type = 'cb', n.factors,
                      n.batch, batch.length, accept.rate = 0.43, family = 'Poisson',
                      n.omp.threads = 1, verbose = TRUE, n.report = 100,
                      n.burn = round(.10 * n.batch * batch.length),
                      n.thin = 1, n.chains = 1, save.fitted = TRUE, ...){

  ptm <- proc.time()

  if (!(family) %in% c('Poisson', 'NB', 'Gaussian', 'zi-Gaussian')) {
    stop("family must be either 'Poisson', 'NB', 'Gaussian', or 'zi-Gaussian'")
  }
  if (family %in% c('Gaussian', 'zi-Gaussian')) {
    sfMsAbundGaussian(formula, data, inits, priors, tuning, cov.model,
		      NNGP, n.neighbors, search.type, n.factors, n.batch,
		      batch.length, accept.rate, family, n.omp.threads,
		      verbose, n.report, n.burn, n.thin, n.chains, save.fitted)
  } else {


    # Functions -----------------------------------------------------------
    logit <- function(theta, a = 0, b = 1) {log((theta-a)/(b-theta))}
    logit.inv <- function(z, a = 0, b = 1) {b-(b-a)/(1+exp(z))}
    rigamma <- function(n, a, b){
      1/rgamma(n = n, shape = a, rate = b)
    }

    # Make it look nice
    if (verbose) {
      cat("----------------------------------------\n");
      cat("\tPreparing to run the model\n");
      cat("----------------------------------------\n");
    }
    # Check for unused arguments ------------------------------------------
    formal.args <- names(formals(sys.function(sys.parent())))
    elip.args <- names(list(...))
    for(i in elip.args){
        if(! i %in% formal.args)
            warning("'",i, "' is not an argument")
    }
    # Call ----------------------------------------------------------------
    # Returns a call in which all of the specified arguments are
    # specified by their full names.
    cl <- match.call()

    # Some initial checks -------------------------------------------------
    # Only implemented for NNGP
    if (!NNGP) {
      stop("error: sfMsAbund is currently only implemented for NNGPs, not full Gaussian Processes. Please set NNGP = TRUE.")
    }
    if (missing(data)) {
      stop("error: data must be specified")
    }
    if (!is.list(data)) {
      stop("error: data must be a list")
    }
    names(data) <- tolower(names(data))
    if (!'y' %in% names(data)) {
      stop("error: count data y must be specified in data")
    }
    if (!(length(dim(data$y)) %in% c(2, 3))) {
      stop("error: count data y must be a two or three-dimensional array with dimensions corresponding to species, sites, and replicates.")
    }
    sp.names <- attr(data$y, 'dimnames')[[1]]
    if (length(dim(data$y)) == 2) {
      data$y <- array(data$y, dim = c(nrow(data$y), ncol(data$y), 1))
      dimnames(data$y)[[1]] <- sp.names
    }
    y <- data$y
    # Offset
    if ('offset' %in% names(data)) {
      offset <- data$offset
      if (length(offset) == 1) {
        offset <- matrix(offset, ncol(y), dim(y)[3])
      } else if (length(dim(offset)) == 1) { # Value for each site
        if (length(offset) != ncol(y)) {
          stop(paste0("offset must be a single value, vector of length ", ncol(y), " or a matrix with ",
                     ncol(y), " rows and ", dim(y)[3], " columns."))
        }
        offset <- matrix(offset, ncol(y), dim(y)[3])
      } else if (length(dim(offset)) == 2) { # Value for each site/obs
        if (nrow(offset) != ncol(y) | ncol(offset) != dim(y)[3]) {
          stop(paste0("offset must be a single value, vector of length ", ncol(y), " or a matrix with ",
                      ncol(y), " rows and ", dim(y)[3], " columns."))

        }
      }
    } else {
      offset <- matrix(1, ncol(y), dim(y)[3])
    }
    if (!'covs' %in% names(data)) {
      if (formula == ~ 1) {
        if (verbose) {
          message("abundance covariates (covs) not specified in data.\nAssuming intercept only abundance model.\n")
        }
        data$covs <- list(int = array(1, dim = c(dim(y)[2], dim(y)[3])))
      } else {
        stop("error: covs must be specified in data for an abundance model with covariates")
      }
    }
    if (!is.list(data$covs)) {
      stop("error: covs must be a list of matrices, data frames, and/or vectors")
    }
    if (!'coords' %in% names(data)) {
      stop("error: coords must be specified in data for a spatial abundance model.")
    }
    if (!is.matrix(data$coords) & !is.data.frame(data$coords)) {
      stop("error: coords must be a matrix or data frame")
    }
    coords <- as.matrix(data$coords)
    if (missing(n.batch)) {
      stop("error: must specify number of MCMC batches")
    }
    if (missing(batch.length)) {
      stop("error: must specify length of each MCMC batch")
    }
    n.samples <- n.batch * batch.length
    if (n.burn > n.samples) {
      stop("error: n.burn must be less than n.samples")
    }
    if (n.thin > n.samples) {
      stop("error: n.thin must be less than n.samples")
    }
    # Check if n.burn, n.thin, and n.samples result in an integer and error if otherwise.
    if (((n.samples - n.burn) / n.thin) %% 1 != 0) {
      stop("the number of posterior samples to save ((n.samples - n.burn) / n.thin) is not a whole number. Please respecify the MCMC criteria such that the number of posterior samples saved is a whole number.")
    }
    if (missing(n.factors)) {
      stop("error: n.factors must be specified for a spatial factor GLMM")
    }

    if (family == 'NB' & verbose) {
      message('**NOTE**: spatial negative binomial models can be difficult to\nestimate as they contain two forms of overdispersion. If experiencing\nvery poor mixing/convergence of MCMC chains (particularly kappa and phi),\nconsider using a spatial Poisson model or more informative\npriors on kappa or phi.\n')
    }

    # Neighbors and Ordering ----------------------------------------------
    if (NNGP) {
      u.search.type <- 2
      ## Order by x column. Could potentially allow this to be user defined.
      ord <- order(coords[,1])
      # Reorder everything to align with NN ordering
      y <- y[, ord, , drop = FALSE]
      offset <- offset[ord, , drop = FALSE]
      coords <- coords[ord, , drop = FALSE]
      # Covariates
      for (i in 1:length(data$covs)) {
        if (!is.null(dim(data$covs[[i]]))) {
          data$covs[[i]] <- data$covs[[i]][ord, , drop = FALSE]
        } else {
          data$covs[[i]] <- data$covs[[i]][ord]
        }
      }
    }
    # For later
    y.mat <- y
    offset.mat <- offset

    # First subset covariates to only use those that are included in the analysis.
    # Get occurrence covariates in proper format
    # Subset covariates to only use those that are included in the analysis
    data$covs <- data$covs[names(data$covs) %in% all.vars(formula)]
    # Null model support
    if (length(data$covs) == 0) {
      data$covs <- list(int = matrix(1, nrow = dim(y)[2], ncol = dim(y)[3]))
    }
    # Ordered by rep, then site within rep
    data$covs <- data.frame(lapply(data$covs, function(a) unlist(c(a))))
    # Check if only site-level covariates are included
    if (nrow(data$covs) == dim(y)[2]) {
      data$covs <- as.data.frame(lapply(data$covs, rep, dim(y)[3]))
    }

    # Check whether random effects are sent in as numeric, and
    # return error if they are.
    # Abundance -------------------------
    if (!is.null(findbars(formula))) {
      abund.re.names <- unique(unlist(sapply(findbars(formula), all.vars)))
      for (i in 1:length(abund.re.names)) {
        if (is(data$covs[, abund.re.names[i]], 'factor')) {
          stop(paste("error: random effect variable ", abund.re.names[i], " specified as a factor. Random effect variables must be specified as numeric.", sep = ''))
        }
        if (is(data$covs[, abund.re.names[i]], 'character')) {
          stop(paste("error: random effect variable ", abund.re.names[i], " specified as character. Random effect variables must be specified as numeric.", sep = ''))
        }
      }
    }

    # Checking missing values ---------------------------------------------
    # y -------------------------------
    y.na.test <- apply(y.mat, c(1, 2), function(a) sum(!is.na(a)))
    if (sum(y.na.test == 0) > 0) {
      stop("error: some sites in y have all missing detection histories. Remove these sites from all objects in the 'data' argument, then use 'predict' to obtain predictions at these locations if desired.")
    }
    # covs ------------------------
    for (i in 1:ncol(data$covs)) {
      # Note that this assumes the same detection history for each species.
      if (sum(is.na(data$covs[, i])) > sum(is.na(y.mat[1, , ]))) {
        stop("error: some elements in covs have missing values where there is an observed data value in y. Please either replace the NA values in covs with non-missing values (e.g., mean imputation) or set the corresponding values in y to NA where the covariate is missing.")
      }
    }
    # Misalignment between y and covs
    y.missing <- which(is.na(y[1, , ]))
    covs.missing <- lapply(data$covs, function(a) which(is.na(a)))
    for (i in 1:length(covs.missing)) {
      tmp.indx <- !(y.missing %in% covs.missing[[i]])
      if (sum(tmp.indx) > 0) {
        if (i == 1 & verbose) {
          message("There are missing values in data$y with corresponding non-missing values in data$covs.\nRemoving these site/replicate combinations for fitting the model.")
        }
        data$covs[y.missing, i] <- NA
      }
    }

    # Remove missing values from covs in order to ensure formula parsing
    # works when random slopes are provided.
    tmp <- apply(data$covs, 1, function (a) sum(is.na(a)))
    data$covs <- as.data.frame(data$covs[tmp == 0, , drop = FALSE])

    # Check save.fitted ---------------------------------------------------
    if (!(save.fitted %in% c(TRUE, FALSE))) {
      stop("save.fitted must be either TRUE or FALSE")
    }

    # Formula -------------------------------------------------------------
    # Abundance -----------------------
    if (missing(formula)) {
      stop("error: formula must be specified")
    }
    if (is(formula, 'formula')) {
      tmp <- parseFormula(formula, data$covs)
      X <- as.matrix(tmp[[1]])
      X.re <- as.matrix(tmp[[4]])
      x.re.names <- colnames(X.re)
      x.names <- tmp[[2]]
      X.random <- as.matrix(tmp[[5]])
      x.random.names <- colnames(X.random)
    } else {
      stop("error: formula is misspecified")
    }
    # Get RE level names
    re.level.names <- lapply(data$covs[, x.re.names, drop = FALSE],
        		     function (a) sort(unique(a)))
    x.re.names <- x.random.names

    # Extract data from inputs --------------------------------------------
    # Number of species
    n.sp <- dim(y)[1]
    # Number of latent factors
    q <- n.factors
    # Number of abundance parameters
    p.abund <- ncol(X)
    # Number of abundance random effect parameters
    p.abund.re <- ncol(X.re)
    # Number of latent abundance random effect values
    n.abund.re <- length(unlist(apply(X.re, 2, unique)))
    n.abund.re.long <- apply(X.re, 2, function(a) length(unique(a)))
    # Number of sites
    J <- nrow(coords)
    # Number of replicate surveys
    # Note this assumes equivalent detection histories for all species.
    # May want to change this at some point.
    n.rep <- apply(y.mat[1, , , drop = FALSE], 2, function(a) sum(!is.na(a)))
    K.max <- dim(y.mat)[3]
    # Because I like K better than n.rep
    K <- n.rep

    # Get indices to map N to y -------------------------------------------
    site.indx <- rep(1:J, dim(y.mat)[3])
    site.indx <- site.indx[!is.na(c(y.mat[1, , ]))]
    # Subtract 1 for indices in C
    site.indx <- site.indx - 1
    # y is stored in the following order: species, site, visit
    y <- c(y)
    offset <- c(offset)
    # Assumes the missing data are constant across species, which seems likely,
    # but may eventually need some updating.
    names.long <- which(!is.na(c(y.mat[1, , ])))
    # Only need to check this when there are observation level covariates.
    if (nrow(X) == length(y) / n.sp) {
      X <- X[!is.na(c(y.mat[1, , ])), , drop = FALSE]
    }
    if (nrow(X.re) == length(y) / n.sp & p.abund.re > 0) {
      X.re <- X.re[!is.na(c(y.mat[1, , ])), , drop = FALSE]
    }
    if (nrow(X.random) == length(y) / n.sp & p.abund.re > 0) {
      X.random <- X.random[!is.na(c(y.mat[1, , ])), , drop = FALSE]
    }
    y <- y[!is.na(y)]
    offset <- offset[!is.na(c(y.mat[1, , ]))]
    # Number of pseudoreplicates
    n.obs <- nrow(X)

    # Get random effect matrices all set ----------------------------------
    X.re <- X.re - 1
    if (p.abund.re > 1) {
      for (j in 2:p.abund.re) {
        X.re[, j] <- X.re[, j] + max(X.re[, j - 1]) + 1
      }
    }

    # Separate out priors -------------------------------------------------
    if (missing(priors)) {
      priors <- list()
    }
    names(priors) <- tolower(names(priors))

    # Independent beta parameters -----
    if ('independent.betas' %in% names(priors)) {
      if (priors$independent.betas == TRUE) {
        message("Beta parameters will be estimated independently\n")
        ind.betas <- TRUE
      } else if (priors$independent.betas == FALSE) {
        ind.betas <- FALSE
      }
    } else {
      ind.betas <- FALSE
    }
    # beta.comm -----------------------
    if ("beta.comm.normal" %in% names(priors)) {
      if (!is.list(priors$beta.comm.normal) | length(priors$beta.comm.normal) != 2) {
        stop("error: beta.comm.normal must be a list of length 2")
      }
      mu.beta.comm <- priors$beta.comm.normal[[1]]
      sigma.beta.comm <- priors$beta.comm.normal[[2]]
      if (length(mu.beta.comm) != p.abund & length(mu.beta.comm) != 1) {
        if (p.abund == 1) {
          stop(paste("error: beta.comm.normal[[1]] must be a vector of length ",
          	     p.abund, " with elements corresponding to beta.comms' mean", sep = ""))
        } else {
          stop(paste("error: beta.comm.normal[[1]] must be a vector of length ",
          	     p.abund, " or 1 with elements corresponding to beta.comms' mean", sep = ""))
        }
      }
      if (length(sigma.beta.comm) != p.abund & length(sigma.beta.comm) != 1) {
        if (p.abund == 1) {
          stop(paste("error: beta.comm.normal[[2]] must be a vector of length ",
        	   p.abund, " with elements corresponding to beta.comms' variance", sep = ""))
        } else {
          stop(paste("error: beta.comm.normal[[2]] must be a vector of length ",
        	   p.abund, " or 1 with elements corresponding to beta.comms' variance", sep = ""))
        }
      }
      if (length(sigma.beta.comm) != p.abund) {
        sigma.beta.comm <- rep(sigma.beta.comm, p.abund)
      }
      if (length(mu.beta.comm) != p.abund) {
        mu.beta.comm <- rep(mu.beta.comm, p.abund)
      }
      Sigma.beta.comm <- sigma.beta.comm * diag(p.abund)
    } else {
      if (verbose & !ind.betas) {
        message("No prior specified for beta.comm.normal.\nSetting prior mean to 0 and prior variance to 100\n")
      }
      mu.beta.comm <- rep(0, p.abund)
      sigma.beta.comm <- rep(100, p.abund)
      Sigma.beta.comm <- diag(p.abund) * 100
    }

    # tau.sq.beta -----------------------
    if ("tau.sq.beta.ig" %in% names(priors)) {
      if (!is.list(priors$tau.sq.beta.ig) | length(priors$tau.sq.beta.ig) != 2) {
        stop("error: tau.sq.beta.ig must be a list of length 2")
      }
      tau.sq.beta.a <- priors$tau.sq.beta.ig[[1]]
      tau.sq.beta.b <- priors$tau.sq.beta.ig[[2]]
      if (length(tau.sq.beta.a) != p.abund & length(tau.sq.beta.a) != 1) {
        if (p.abund == 1) {
          stop(paste("error: tau.sq.beta.ig[[1]] must be a vector of length ",
        	   p.abund, " with elements corresponding to tau.sq.betas' shape", sep = ""))
        } else {
          stop(paste("error: tau.sq.beta.ig[[1]] must be a vector of length ",
        	   p.abund, " or 1 with elements corresponding to tau.sq.betas' shape", sep = ""))
        }
      }
      if (length(tau.sq.beta.b) != p.abund & length(tau.sq.beta.b) != 1) {
        if (p.abund == 1) {
          stop(paste("error: tau.sq.beta.ig[[2]] must be a vector of length ",
        	   p.abund, " with elements corresponding to tau.sq.betas' scale", sep = ""))
        } else {
          stop(paste("error: tau.sq.beta.ig[[2]] must be a vector of length ",
        	   p.abund, " or 1 with elements corresponding to tau.sq.betas' scale", sep = ""))
        }
      }
      if (length(tau.sq.beta.a) != p.abund) {
        tau.sq.beta.a <- rep(tau.sq.beta.a, p.abund)
      }
      if (length(tau.sq.beta.b) != p.abund) {
        tau.sq.beta.b <- rep(tau.sq.beta.b, p.abund)
      }
    } else {
      if (verbose & !ind.betas) {
        message("No prior specified for tau.sq.beta.ig.\nSetting prior shape to 0.1 and prior scale to 0.1\n")
      }
      tau.sq.beta.a <- rep(0.1, p.abund)
      tau.sq.beta.b <- rep(0.1, p.abund)
    }
    # sigma.sq.mu --------------------
    if (p.abund.re > 0) {
      if ("sigma.sq.mu.ig" %in% names(priors)) {
        if (!is.list(priors$sigma.sq.mu.ig) | length(priors$sigma.sq.mu.ig) != 2) {
          stop("error: sigma.sq.mu.ig must be a list of length 2")
        }
        sigma.sq.mu.a <- priors$sigma.sq.mu.ig[[1]]
        sigma.sq.mu.b <- priors$sigma.sq.mu.ig[[2]]
        if (length(sigma.sq.mu.a) != p.abund.re & length(sigma.sq.mu.a) != 1) {
          if (p.abund.re == 1) {
          stop(paste("error: sigma.sq.mu.ig[[1]] must be a vector of length ",
          	   p.abund.re, " with elements corresponding to sigma.sq.mus' shape", sep = ""))
          } else {
          stop(paste("error: sigma.sq.mu.ig[[1]] must be a vector of length ",
          	   p.abund.re, " or 1 with elements corresponding to sigma.sq.mus' shape", sep = ""))
          }
        }
        if (length(sigma.sq.mu.b) != p.abund.re & length(sigma.sq.mu.b) != 1) {
          if (p.abund.re == 1) {
            stop(paste("error: sigma.sq.mu.ig[[2]] must be a vector of length ",
          	   p.abund.re, " with elements corresponding to sigma.sq.mus' scale", sep = ""))
          } else {
            stop(paste("error: sigma.sq.mu.ig[[2]] must be a vector of length ",
          	   p.abund.re, " or 1with elements corresponding to sigma.sq.mus' scale", sep = ""))
          }
        }
        if (length(sigma.sq.mu.a) != p.abund.re) {
          sigma.sq.mu.a <- rep(sigma.sq.mu.a, p.abund.re)
        }
        if (length(sigma.sq.mu.b) != p.abund.re) {
          sigma.sq.mu.b <- rep(sigma.sq.mu.b, p.abund.re)
        }
    }   else {
        if (verbose) {
          message("No prior specified for sigma.sq.mu.ig.\nSetting prior shape to 0.1 and prior scale to 0.1\n")
        }
        sigma.sq.mu.a <- rep(0.1, p.abund.re)
        sigma.sq.mu.b <- rep(0.1, p.abund.re)
      }
    } else {
      sigma.sq.mu.a <- 0
      sigma.sq.mu.b <- 0
    }
    # kappa -----------------------------
    if (family == 'NB') {
      if ("kappa.unif" %in% names(priors)) {
        if (!is.list(priors$kappa.unif) | length(priors$kappa.unif) != 2) {
          stop("error: kappa.unif must be a list of length 2")
        }
        kappa.a <- priors$kappa.unif[[1]]
        kappa.b <- priors$kappa.unif[[2]]
        if (length(kappa.a) != n.sp & length(kappa.a) != 1) {
          stop(paste("error: kappa.unif[[1]] must be a vector of length ",
          	   n.sp, " or 1 with elements corresponding to kappas' lower bound for each species", sep = ""))
        }
        if (length(kappa.b) != n.sp & length(kappa.b) != 1) {
          stop(paste("error: kappa.unif[[2]] must be a vector of length ",
          	   n.sp, " or 1 with elements corresponding to kappas' upper bound for each species", sep = ""))
        }
        if (length(kappa.a) != n.sp) {
          kappa.a <- rep(kappa.a, n.sp)
        }
        if (length(kappa.b) != n.sp) {
          kappa.b <- rep(kappa.b, n.sp)
        }
      } else {
        if (verbose) {
        message("No prior specified for kappa.unif.\nSetting uniform bounds of 0 and 100.\n")
        }
        kappa.a <- rep(0, n.sp)
        kappa.b <- rep(100, n.sp)
      }
    } else {
      kappa.a <- rep(0, n.sp)
      kappa.b <- rep(0, n.sp)
    }
    # phi -----------------------------
    # Get distance matrix which is used if priors are not specified
    if ("phi.unif" %in% names(priors)) {
      if (!is.list(priors$phi.unif) | length(priors$phi.unif) != 2) {
        stop("error: phi.unif must be a list of length 2")
      }
      phi.a <- priors$phi.unif[[1]]
      phi.b <- priors$phi.unif[[2]]
      if (length(phi.a) != q & length(phi.a) != 1) {
        stop(paste("error: phi.unif[[1]] must be a vector of length ",
        	   q, " or 1 with elements corresponding to phis' lower bound for each latent factor", sep = ""))
      }
      if (length(phi.b) != q & length(phi.b) != 1) {
        stop(paste("error: phi.unif[[2]] must be a vector of length ",
        	   q, " or 1 with elements corresponding to phis' upper bound for each latent factor", sep = ""))
      }
      if (length(phi.a) != q) {
        phi.a <- rep(phi.a, q)
      }
      if (length(phi.b) != q) {
        phi.b <- rep(phi.b, q)
      }
    } else {
      if (verbose) {
      message("No prior specified for phi.unif.\nSetting uniform bounds based on the range of observed spatial coordinates.\n")
      }
      coords.D <- iDist(coords)
      phi.a <- rep(3 / max(coords.D), q)
      phi.b <- rep(3 / sort(unique(c(coords.D)))[2], q)
    }
    # nu -----------------------------
    if (cov.model == "matern") {
      if (!"nu.unif" %in% names(priors)) {
        stop("error: nu.unif must be specified in priors value list")
      }
      nu.a <- priors$nu.unif[[1]]
      nu.b <- priors$nu.unif[[2]]
      if (!is.list(priors$nu.unif) | length(priors$nu.unif) != 2) {
        stop("error: nu.unif must be a list of length 2")
      }
      if (length(nu.a) != q & length(nu.a) != 1) {
        stop(paste("error: nu.unif[[1]] must be a vector of length ",
        	   q, " or 1 with elements corresponding to nus' lower bound for each latent factor", sep = ""))
      }
      if (length(nu.b) != q & length(nu.b) != 1) {
        stop(paste("error: nu.unif[[2]] must be a vector of length ",
        	   q, " or 1 with elements corresponding to nus' upper bound for each latent factor", sep = ""))
      }
      if (length(nu.a) != q) {
        nu.a <- rep(nu.a, q)
      }
      if (length(nu.b) != q) {
        nu.b <- rep(nu.b, q)
      }
    } else {
      nu.a <- rep(0, q)
      nu.b <- rep(0, q)
    }

    # Starting values -----------------------------------------------------
    if (missing(inits)) {
      inits <- list()
    }
    names(inits) <- tolower(names(inits))
    # beta.comm -----------------------
    if ("beta.comm" %in% names(inits)) {
      beta.comm.inits <- inits[["beta.comm"]]
      if (length(beta.comm.inits) != p.abund & length(beta.comm.inits) != 1) {
        if (p.abund == 1) {
          stop(paste("error: initial values for beta.comm must be of length ", p.abund,
        	   sep = ""))
        } else {
          stop(paste("error: initial values for beta.comm must be of length ", p.abund,
        	   , " or 1", sep = ""))
        }
      }
      if (length(beta.comm.inits) != p.abund) {
        beta.comm.inits <- rep(beta.comm.inits, p.abund)
      }
    } else {
      beta.comm.inits <- rnorm(p.abund, 0, 1)
      if (verbose) {
        message('beta.comm is not specified in initial values.\nSetting initial values to random values from a standard normal distribution\n')
      }
    }
    # tau.sq.beta ------------------------
    if ("tau.sq.beta" %in% names(inits)) {
      tau.sq.beta.inits <- inits[["tau.sq.beta"]]
      if (length(tau.sq.beta.inits) != p.abund & length(tau.sq.beta.inits) != 1) {
        if (p.abund == 1) {
          stop(paste("error: initial values for tau.sq.beta must be of length ", p.abund,
        	   sep = ""))
        } else {
          stop(paste("error: initial values for tau.sq.beta must be of length ", p.abund,
        	   " or 1", sep = ""))
        }
      }
      if (length(tau.sq.beta.inits) != p.abund) {
        tau.sq.beta.inits <- rep(tau.sq.beta.inits, p.abund)
      }
    } else {
      tau.sq.beta.inits <- runif(p.abund, 0.05, 1)
      if (verbose) {
        message('tau.sq.beta is not specified in initial values.\nSetting initial values to random values between 0.05 and 1\n')
      }
    }
    # beta ----------------------------
    if ("beta" %in% names(inits)) {
      beta.inits <- inits[["beta"]]
      if (is.matrix(beta.inits)) {
        if (ncol(beta.inits) != p.abund | nrow(beta.inits) != n.sp) {
          stop(paste("error: initial values for beta must be a matrix with dimensions ",
          	   n.sp, "x", p.abund, " or a single numeric value", sep = ""))
        }
      }
      if (!is.matrix(beta.inits) & length(beta.inits) != 1) {
        stop(paste("error: initial values for beta must be a matrix with dimensions ",
        	   n.sp, " x ", p.abund, " or a single numeric value", sep = ""))
      }
      if (length(beta.inits) == 1) {
        beta.inits <- matrix(beta.inits, n.sp, p.abund)
      }
    } else {
      beta.inits <- matrix(rnorm(n.sp * p.abund, beta.comm.inits, sqrt(tau.sq.beta.inits)), n.sp, p.abund)
      if (verbose) {
        message('beta is not specified in initial values.\nSetting initial values to random values from the community-level normal distribution\n')
      }
    }
    # sigma.sq.mu -------------------
    if (p.abund.re > 0) {
      if ("sigma.sq.mu" %in% names(inits)) {
        sigma.sq.mu.inits <- inits[["sigma.sq.mu"]]
        if (length(sigma.sq.mu.inits) != p.abund.re & length(sigma.sq.mu.inits) != 1) {
          if (p.abund.re == 1) {
            stop(paste("error: initial values for sigma.sq.mu must be of length ", p.abund.re,
        	     sep = ""))
          } else {
            stop(paste("error: initial values for sigma.sq.mu must be of length ", p.abund.re,
        	     " or 1", sep = ""))
          }
        }
        if (length(sigma.sq.mu.inits) != p.abund.re) {
          sigma.sq.mu.inits <- rep(sigma.sq.mu.inits, p.abund.re)
        }
      } else {
        sigma.sq.mu.inits <- runif(p.abund.re, 0.05, 1)
        if (verbose) {
          message("sigma.sq.mu is not specified in initial values.\nSetting initial values to random values between 0.05 and 1\n")
        }
      }
      beta.star.indx <- rep(0:(p.abund.re - 1), n.abund.re.long)
      beta.star.inits <- rnorm(n.abund.re, 0, sqrt(sigma.sq.mu.inits[beta.star.indx + 1]))
      # Starting values for all species
      beta.star.inits <- rep(beta.star.inits, n.sp)
    } else {
      sigma.sq.mu.inits <- 0
      beta.star.indx <- 0
      beta.star.inits <- 0
    }
    # kappa -----------------------------
    # ORDER: a length n.sp vector ordered by species in the detection-nondetection data.
    if (family == 'NB') {
      if ("kappa" %in% names(inits)) {
        kappa.inits <- inits[["kappa"]]
        if (length(kappa.inits) != n.sp & length(kappa.inits) != 1) {
          stop(paste("error: initial values for kappa must be of length ", n.sp, " or 1",
          	   sep = ""))
        }
        if (length(kappa.inits) != n.sp) {
          kappa.inits <- rep(kappa.inits, n.sp)
        }
      } else {
        kappa.inits <- runif(n.sp, kappa.a, kappa.b)
        if (verbose) {
          message("kappa is not specified in initial values.\nSetting initial value to random values from the prior distribution\n")
        }
      }
    } else {
      kappa.inits <- rep(0, n.sp)
    }
    # phi -----------------------------
    # ORDER: a length N vector ordered by species in the detection-nondetection data.
    if ("phi" %in% names(inits)) {
      phi.inits <- inits[["phi"]]
      if (length(phi.inits) != q & length(phi.inits) != 1) {
        stop(paste("error: initial values for phi must be of length ", q, " or 1",
        	   sep = ""))
      }
      if (length(phi.inits) != q) {
        phi.inits <- rep(phi.inits, q)
      }
    } else {
      phi.inits <- runif(q, phi.a, phi.b)
      if (verbose) {
        message("phi is not specified in initial values.\nSetting initial value to random values from the prior distribution\n")
      }
    }
    # nu ------------------------
    if ("nu" %in% names(inits)) {
      nu.inits <- inits[["nu"]]
      if (length(nu.inits) != q & length(nu.inits) != 1) {
        stop(paste("error: initial values for nu must be of length ", q,  " or 1",
        	   sep = ""))
      }
      if (length(nu.inits) != q) {
        nu.inits <- rep(nu.inits, q)
      }
    } else {
      if (cov.model == 'matern') {
        if (verbose) {
          message("nu is not specified in initial values.\nSetting initial values to random values from the prior distribution\n")
        }
        nu.inits <- runif(q, nu.a, nu.b)
      } else {
        nu.inits <- rep(0, q)
      }
    }
    # lambda ----------------------------
    # ORDER: an n.sp x q matrix sent in as a column-major vector, which is ordered by
    #        factor, then species within factor.
    if ("lambda" %in% names(inits)) {
      lambda.inits <- inits[["lambda"]]
      if (!is.matrix(lambda.inits)) {
        stop(paste("error: initial values for lambda must be a matrix with dimensions ",
          	 n.sp, " x ", q, sep = ""))
      }
      if (nrow(lambda.inits) != n.sp | ncol(lambda.inits) != q) {
        stop(paste("error: initial values for lambda must be a matrix with dimensions ",
          	 n.sp, " x ", q, sep = ""))
      }
      if (!all.equal(diag(lambda.inits), rep(1, q))) {
        stop("error: diagonal of inits$lambda matrix must be all 1s")
      }
      if (sum(lambda.inits[upper.tri(lambda.inits)]) != 0) {
        stop("error: upper triangle of inits$lambda must be all 0s")
      }
    } else {
      lambda.inits <- matrix(0, n.sp, q)
      diag(lambda.inits) <- 1
      lambda.inits[lower.tri(lambda.inits)] <- 0
      if (verbose) {
        message("lambda is not specified in initial values.\nSetting initial values of the lower triangle to 0\n")
      }
      # lambda.inits are organized by factor, then by species. This is necessary for working
      # with dgemv.
      lambda.inits <- c(lambda.inits)
    }
    # w -----------------------------
    if ("w" %in% names(inits)) {
      w.inits <- inits[["w"]]
      if (!is.matrix(w.inits)) {
        stop(paste("error: initial values for w must be a matrix with dimensions ",
        	   q, " x ", J, sep = ""))
      }
      if (nrow(w.inits) != q | ncol(w.inits) != J) {
        stop(paste("error: initial values for w must be a matrix with dimensions ",
        	   q, " x ", J, sep = ""))
      }
      if (NNGP) {
        w.inits <- w.inits[, ord]
      }
    } else {
      w.inits <- matrix(0, q, J)
      if (verbose) {
        message("w is not specified in initial values.\nSetting initial value to 0\n")
      }
    }
    # Should initial values be fixed --
    if ("fix" %in% names(inits)) {
      fix.inits <- inits[["fix"]]
      if ((fix.inits != TRUE) & (fix.inits != FALSE)) {
        stop(paste("error: inits$fix must take value TRUE or FALSE"))
      }
    } else {
      fix.inits <- FALSE
    }
    if (verbose & fix.inits & (n.chains > 1)) {
      message("Fixing initial values across all chains\n")
    }
    # Covariance Model ----------------------------------------------------
    # Order must match util.cpp spCor.
    cov.model.names <- c("exponential", "spherical", "matern", "gaussian")
    if(! cov.model %in% cov.model.names){
      stop("error: specified cov.model '",cov.model,"' is not a valid option; choose from ",
           paste(cov.model.names, collapse=", ", sep="") ,".")}
    # Obo for cov model lookup on c side
    cov.model.indx <- which(cov.model == cov.model.names) - 1

    # Get tuning values ---------------------------------------------------
    # Keep this in there just for consistency
    sigma.sq.tuning <- rep(0, q)
    if (missing(tuning)) {
      beta.tuning <- rep(1, p.abund * n.sp)
      beta.star.tuning <- rep(1, n.abund.re * n.sp)
      kappa.tuning <- rep(1, n.sp)
      phi.tuning <- rep(1, q)
      if (cov.model == 'matern') {
        nu.tuning <- rep(1, q)
      } else {
        nu.tuning <- NULL
      }
      w.tuning <- rep(1, J * q)
      lambda.tuning <- rep(1, n.sp * q)
    } else {
      names(tuning) <- tolower(names(tuning))
      # beta ---------------------------
      if(!"beta" %in% names(tuning)) {
        stop("error: beta must be specified in tuning value list")
      }
      beta.tuning <- tuning$beta
      if (length(beta.tuning) != 1 & length(beta.tuning) != p.abund * n.sp) {
        stop(paste("error: beta tuning must be a single value or a vector of length ",
          	 p.abund * n.sp, sep = ''))
      }
      if (length(beta.tuning) == 1) {
        beta.tuning <- rep(beta.tuning, p.abund * n.sp)
      }
      if (p.abund.re > 0) {
        # beta.star ---------------------------
        if(!"beta.star" %in% names(tuning)) {
          stop("error: beta.star must be specified in tuning value list")
        }
        beta.star.tuning <- tuning$beta.star
        if (length(beta.star.tuning) != 1) {
          stop("error: beta.star tuning must be a single value")
        }
        beta.star.tuning <- rep(beta.star.tuning, n.abund.re * n.sp)
      } else {
        beta.star.tuning <- NULL
      }
      # kappa ---------------------------
      if (family == 'NB') {
        if(!"kappa" %in% names(tuning)) {
          stop("error: kappa must be specified in tuning value list")
        }
        kappa.tuning <- tuning$kappa
        if (length(kappa.tuning) == 1) {
          kappa.tuning <- rep(tuning$kappa, n.sp)
        } else if (length(kappa.tuning) != n.sp) {
          stop(paste("error: kappa tuning must be either a single value or a vector of length ",
          	   n.sp, sep = ""))
        }
      } else {
        kappa.tuning <- NULL
      }
      # phi ---------------------------
      if(!"phi" %in% names(tuning)) {
        stop("error: phi must be specified in tuning value list")
      }
      phi.tuning <- tuning$phi
      if (length(phi.tuning) == 1) {
        phi.tuning <- rep(tuning$phi, q)
      } else if (length(phi.tuning) != q) {
        stop(paste("error: phi tuning must be either a single value or a vector of length ",
        	   q, sep = ""))
      }
      if (cov.model == 'matern') {
        # nu --------------------------
        if(!"nu" %in% names(tuning)) {
          stop("error: nu must be specified in tuning value list")
        }
        nu.tuning <- tuning$nu
        if (length(nu.tuning) == 1) {
          nu.tuning <- rep(tuning$nu, q)
        } else if (length(nu.tuning) != q) {
          stop(paste("error: nu tuning must be either a single value or a vector of length ",
          	   q, sep = ""))
        }
      } else {
        nu.tuning <- NULL
      }
      # w ---------------------------
      if(!"w" %in% names(tuning)) {
        stop("error: w must be specified in tuning value list")
      }
      w.tuning <- tuning$w
      if (length(w.tuning) != 1 & length(w.tuning) != J * q) {
        stop(paste("error: w tuning must be a single value or a vector of length ",
          	 J * q, sep = ''))
      }
      if (length(w.tuning) == 1) {
        w.tuning <- rep(w.tuning, J * q)
      }
      # lambda ---------------------------
      if(!"lambda" %in% names(tuning)) {
        stop("error: lambda must be specified in tuning value list")
      }
      lambda.tuning <- tuning$lambda
      if (length(lambda.tuning) != 1 & length(lambda.tuning) != n.sp * q) {
        stop(paste("error: lambda tuning must be a single value or a vector of length ",
          	 n.sp * q, sep = ''))
      }
      if (length(lambda.tuning) == 1) {
        lambda.tuning <- rep(lambda.tuning, n.sp * q)
      }
    }
    tuning.c <- log(c(beta.tuning, sigma.sq.tuning, phi.tuning, nu.tuning, lambda.tuning,
          	    w.tuning, beta.star.tuning, kappa.tuning))

    # Other miscellaneous ---------------------------------------------------
    # For prediction with random slopes
    re.cols <- list()
    if (p.abund.re > 0) {
      split.names <- strsplit(x.re.names, "[-]")
      for (j in 1:p.abund.re) {
        re.cols[[j]] <- split.names[[j]][1]
        names(re.cols)[j] <- split.names[[j]][2]
      }
    }

    curr.chain <- 1
    if (!NNGP)  {
      stop("error: sfMsAbund is currently only implemented for NNGPs, not full Gaussian Processes. Please set NNGP = TRUE.")

    } else {
      # Nearest Neighbor Search ---------------------------------------------
      if(verbose){
        cat("----------------------------------------\n");
        cat("\tBuilding the neighbor list\n");
        cat("----------------------------------------\n");
      }

      search.type.names <- c("brute", "cb")

      if(!search.type %in% search.type.names){
        stop("error: specified search.type '",search.type,
             "' is not a valid option; choose from ",
             paste(search.type.names, collapse=", ", sep="") ,".")
      }

      ## Indexes
      if(search.type == "brute"){
        indx <- mkNNIndx(coords, n.neighbors, n.omp.threads)
      } else{
        indx <- mkNNIndxCB(coords, n.neighbors, n.omp.threads)
      }

      nn.indx <- indx$nnIndx
      nn.indx.lu <- indx$nnIndxLU
      nn.indx.run.time <- indx$run.time

      if(verbose){
        cat("----------------------------------------\n");
        cat("Building the neighbors of neighbors list\n");
        cat("----------------------------------------\n");
      }

      indx <- mkUIndx(J, n.neighbors, nn.indx, nn.indx.lu, u.search.type)

      u.indx <- indx$u.indx
      u.indx.lu <- indx$u.indx.lu
      ui.indx <- indx$ui.indx
      u.indx.run.time <- indx$run.time

      # Set storage for all variables ---------------------------------------
      storage.mode(y) <- "double"
      storage.mode(X) <- "double"
      storage.mode(coords) <- "double"
      storage.mode(offset) <- 'double'
      consts <- c(n.sp, J, n.obs, p.abund, p.abund.re, n.abund.re, q, ind.betas, save.fitted)
      storage.mode(consts) <- "integer"
      storage.mode(beta.inits) <- "double"
      storage.mode(kappa.inits) <- "double"
      storage.mode(beta.comm.inits) <- "double"
      storage.mode(tau.sq.beta.inits) <- "double"
      storage.mode(lambda.inits) <- "double"
      storage.mode(w.inits) <- "double"
      storage.mode(phi.inits) <- "double"
      storage.mode(nu.inits) <- "double"
      storage.mode(site.indx) <- "integer"
      storage.mode(mu.beta.comm) <- "double"
      storage.mode(Sigma.beta.comm) <- "double"
      storage.mode(kappa.a) <- "double"
      storage.mode(kappa.b) <- "double"
      storage.mode(tau.sq.beta.a) <- "double"
      storage.mode(tau.sq.beta.b) <- "double"
      storage.mode(phi.a) <- "double"
      storage.mode(phi.b) <- "double"
      storage.mode(nu.a) <- "double"
      storage.mode(nu.b) <- "double"
      storage.mode(n.batch) <- "integer"
      storage.mode(batch.length) <- "integer"
      storage.mode(accept.rate) <- "double"
      storage.mode(tuning.c) <- "double"
      storage.mode(n.omp.threads) <- "integer"
      storage.mode(verbose) <- "integer"
      storage.mode(n.report) <- "integer"
      storage.mode(nn.indx) <- "integer"
      storage.mode(nn.indx.lu) <- "integer"
      storage.mode(u.indx) <- "integer"
      storage.mode(u.indx.lu) <- "integer"
      storage.mode(ui.indx) <- "integer"
      storage.mode(n.neighbors) <- "integer"
      storage.mode(cov.model.indx) <- "integer"
      chain.info <- c(curr.chain, n.chains)
      storage.mode(chain.info) <- "integer"
      n.post.samples <- length(seq(from = n.burn + 1,
          			 to = n.samples,
          			 by = as.integer(n.thin)))
      # samples.info order: burn-in, thinning rate, number of posterior samples
      samples.info <- c(n.burn, n.thin, n.post.samples)
      storage.mode(samples.info) <- "integer"
      # For abundance random effects
      storage.mode(X.re) <- "integer"
      storage.mode(X.random) <- "double"
      beta.level.indx <- sort(unique(c(X.re)))
      storage.mode(beta.level.indx) <- "integer"
      storage.mode(sigma.sq.mu.inits) <- "double"
      storage.mode(sigma.sq.mu.a) <- "double"
      storage.mode(sigma.sq.mu.b) <- "double"
      storage.mode(beta.star.inits) <- "double"
      storage.mode(beta.star.indx) <- "integer"
      # NB = 1, Poisson = 0
      family.c <- ifelse(family == 'NB', 1, 0)
      storage.mode(family.c) <- "integer"

      # Fit the model -------------------------------------------------------
      out.tmp <- list()
      out <- list()
      for (i in 1:n.chains) {
        # Change initial values if i > 1
        if ((i > 1) & (!fix.inits)) {
          if (!ind.betas) {
            beta.comm.inits <- rnorm(p.abund, 0, 1)
            tau.sq.beta.inits <- runif(p.abund, 0.05, 1)
	  }
          beta.inits <- matrix(rnorm(n.sp * p.abund, beta.comm.inits,
                		     sqrt(tau.sq.beta.inits)), n.sp, p.abund)
          if (family == 'NB') {
            kappa.inits <- runif(n.sp, kappa.a, kappa.b)
          }
          lambda.inits <- matrix(0, n.sp, q)
          diag(lambda.inits) <- 1
          lambda.inits[lower.tri(lambda.inits)] <- rnorm(sum(lower.tri(lambda.inits)))
          lambda.inits <- c(lambda.inits)
          phi.inits <- runif(q, phi.a, phi.b)
          if (cov.model == 'matern') {
            nu.inits <- runif(q, nu.a, nu.b)
          }
          if (p.abund.re > 0) {
            sigma.sq.mu.inits <- runif(p.abund.re, 0.05, 1)
            beta.star.inits <- rnorm(n.abund.re, 0, sqrt(sigma.sq.mu.inits[beta.star.indx + 1]))
            beta.star.inits <- rep(beta.star.inits, n.sp)
          }
        }

        storage.mode(chain.info) <- "integer"
        out.tmp[[i]] <- .Call("sfMsAbundNNGP", y, X, coords, X.re, X.random,
        		      consts, n.abund.re.long,
          	              n.neighbors, nn.indx, nn.indx.lu, u.indx, u.indx.lu, ui.indx,
          		      beta.inits, kappa.inits, beta.comm.inits,
          	              tau.sq.beta.inits,
          		      phi.inits, lambda.inits, nu.inits, w.inits,
          		      sigma.sq.mu.inits, beta.star.inits,site.indx,
          		      beta.star.indx, beta.level.indx,
          		      mu.beta.comm, Sigma.beta.comm, kappa.a,
            		      kappa.b, tau.sq.beta.a, tau.sq.beta.b,
          	              phi.a, phi.b, nu.a, nu.b,
          		      sigma.sq.mu.a, sigma.sq.mu.b, tuning.c, cov.model.indx,
          		      n.batch, batch.length, accept.rate, n.omp.threads,
        	              verbose, n.report, samples.info, chain.info, family.c, offset)
        chain.info[1] <- chain.info[1] + 1
      }
      # Calculate R-Hat ---------------
      out <- list()
      out$rhat <- list()
      if (n.chains > 1) {
        # as.vector removes the "Upper CI" when there is only 1 variable.
        if (!ind.betas) {
        out$rhat$beta.comm <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
        					      mcmc(t(a$beta.comm.samples)))),
        			     autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
        out$rhat$tau.sq.beta <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
        					      mcmc(t(a$tau.sq.beta.samples)))),
        			     autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
	} else {
          out$rhat$beta.comm <- rep(NA, p.abund)
	  out$rhat$tau.sq.beta <- rep(NA, p.abund)
	}
        out$rhat$beta <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
        					         mcmc(t(a$beta.samples)))),
        			     autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
        if (family == 'NB') {
          out$rhat$kappa <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
        					      mcmc(t(a$kappa.samples)))),
        			     autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
        }
        out$rhat$theta <- gelman.diag(mcmc.list(lapply(out.tmp, function(a)
        					      mcmc(t(a$theta.samples)))),
        			      autoburnin = FALSE, multivariate = FALSE)$psrf[, 2]
        lambda.mat <- matrix(lambda.inits, n.sp, q)
        out$rhat$lambda.lower.tri <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
          					       mcmc(t(a$lambda.samples[c(lower.tri(lambda.mat)), ])))),
          					       autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
        if (p.abund.re > 0) {
          out$rhat$sigma.sq.mu <- as.vector(gelman.diag(mcmc.list(lapply(out.tmp, function(a)
          					      mcmc(t(a$sigma.sq.mu.samples)))),
          			     autoburnin = FALSE, multivariate = FALSE)$psrf[, 2])
        }
      } else {
        out$rhat$beta.comm <- rep(NA, p.abund)
        out$rhat$tau.sq.beta <- rep(NA, p.abund)
        out$rhat$beta <- rep(NA, p.abund * n.sp)
        out$rhat$theta <- rep(NA, ifelse(cov.model == 'matern', 2 * q, q))
        out$rhat$kappa <- rep(NA, n.sp)
        if (p.abund.re > 0) {
          out$rhat$sigma.sq.mu <- rep(NA, p.abund.re)
        }
      }
      # Put everything into MCMC objects
      out$beta.comm.samples <- mcmc(do.call(rbind, lapply(out.tmp, function(a) t(a$beta.comm.samples))))
      colnames(out$beta.comm.samples) <- x.names
      out$tau.sq.beta.samples <- mcmc(do.call(rbind,
        				lapply(out.tmp, function(a) t(a$tau.sq.beta.samples))))
      colnames(out$tau.sq.beta.samples) <- x.names

      if (is.null(sp.names)) {
        sp.names <- paste('sp', 1:n.sp, sep = '')
      }
      coef.names <- paste(rep(x.names, each = n.sp), sp.names, sep = '-')
      out$beta.samples <- mcmc(do.call(rbind, lapply(out.tmp, function(a) t(a$beta.samples))))
      colnames(out$beta.samples) <- coef.names
      if (family == 'NB') {
        out$kappa.samples <- mcmc(do.call(rbind, lapply(out.tmp, function(a) t(a$kappa.samples))))
        colnames(out$kappa.samples) <- paste('kappa', sp.names, sep = '-')
      }
      loadings.names <- paste(rep(sp.names, times = n.factors), rep(1:n.factors, each = n.sp), sep = '-')
      out$lambda.samples <- mcmc(do.call(rbind, lapply(out.tmp, function(a) t(a$lambda.samples))))
      colnames(out$lambda.samples) <- loadings.names
      out$theta.samples <- mcmc(do.call(rbind, lapply(out.tmp, function(a) t(a$theta.samples))))
      if (cov.model != 'matern') {
        theta.names <- paste(rep(c('phi'), each = q), 1:q, sep = '-')
      } else {
        theta.names <- paste(rep(c('phi', 'nu'), each = q), 1:q, sep = '-')
      }
      colnames(out$theta.samples) <- theta.names
      y.non.miss.indx <- which(!is.na(y.mat), arr.ind = TRUE)
      if (save.fitted) {
        out$y.rep.samples <- do.call(abind, lapply(out.tmp, function(a) array(a$y.rep.samples,
          								dim = c(n.sp * n.obs, n.post.samples))))
        tmp <- array(NA, dim = c(n.post.samples * n.chains, n.sp, J, K.max))
        for (j in 1:(n.obs * n.sp)) {
          curr.indx <- y.non.miss.indx[j, ]
          tmp[, curr.indx[1], curr.indx[2], curr.indx[3]] <- out$y.rep.samples[j, ]
        }
        out$y.rep.samples <- tmp[, , order(ord), , drop = FALSE]
        out$mu.samples <- do.call(abind, lapply(out.tmp, function(a) array(a$mu.samples,
          								dim = c(n.sp * n.obs, n.post.samples))))
        tmp <- array(NA, dim = c(n.post.samples * n.chains, n.sp, J, K.max))
        for (j in 1:(n.obs * n.sp)) {
          curr.indx <- y.non.miss.indx[j, ]
          tmp[, curr.indx[1], curr.indx[2], curr.indx[3]] <- out$mu.samples[j, ]
        }
        out$mu.samples <- tmp[, , order(ord), , drop = FALSE]
        out$like.samples <- do.call(abind, lapply(out.tmp, function(a) array(a$like.samples,
          								dim = c(n.sp * n.obs, n.post.samples))))
        tmp <- array(NA, dim = c(n.post.samples * n.chains, n.sp, J, K.max))
        for (j in 1:(n.obs * n.sp)) {
          curr.indx <- y.non.miss.indx[j, ]
          tmp[, curr.indx[1], curr.indx[2], curr.indx[3]] <- out$like.samples[j, ]
        }
        out$like.samples <- tmp[, , order(ord), , drop = FALSE]
      }
      out$w.samples <- do.call(abind, lapply(out.tmp, function(a) array(a$w.samples,
        								dim = c(q, J, n.post.samples))))
      out$w.samples <- out$w.samples[, order(ord), , drop = FALSE]
      out$w.samples <- aperm(out$w.samples, c(3, 1, 2))
      if (p.abund.re > 0) {
        out$sigma.sq.mu.samples <- mcmc(
          do.call(rbind, lapply(out.tmp, function(a) t(a$sigma.sq.mu.samples))))
        colnames(out$sigma.sq.mu.samples) <- x.re.names
        out$beta.star.samples <- mcmc(
          do.call(rbind, lapply(out.tmp, function(a) t(a$beta.star.samples))))
        tmp.names <- unlist(re.level.names)
        beta.star.names <- paste(rep(x.re.names, n.abund.re.long), tmp.names, sep = '-')
        beta.star.names <- paste(beta.star.names, rep(sp.names, each = n.abund.re), sep = '-')
        colnames(out$beta.star.samples) <- beta.star.names
        out$re.level.names <- re.level.names
      }
      # Calculate effective sample sizes
      out$ESS <- list()
      out$ESS$beta.comm <- effectiveSize(out$beta.comm.samples)
      out$ESS$tau.sq.beta <- effectiveSize(out$tau.sq.beta.samples)
      out$ESS$beta <- effectiveSize(out$beta.samples)
      if (family == 'NB') {
        out$ESS$kappa <- effectiveSize(out$kappa.samples)
      }
      out$ESS$theta <- effectiveSize(out$theta.samples)
      out$ESS$lambda <- effectiveSize(out$lambda.samples)
      if (p.abund.re > 0) {
        out$ESS$sigma.sq.mu <- effectiveSize(out$sigma.sq.mu.samples)
      }
      tmp <- matrix(NA, J * K.max, p.abund)
      tmp[names.long, ] <- X
      tmp <- array(tmp, dim = c(J, K.max, p.abund))
      tmp <- tmp[order(ord), , , drop = FALSE]
      out$X <- tmp
      dimnames(out$X)[[3]] <- x.names
      tmp <- matrix(NA, J * K.max, p.abund.re)
      tmp[names.long, ] <- X.re
      tmp <- array(tmp, dim = c(J, K.max, p.abund.re))
      tmp <- tmp[order(ord), , , drop = FALSE]
      out$X.re <- tmp
      dimnames(out$X.re)[[3]] <- colnames(X.re)
      tmp <- matrix(NA, J * K.max, p.abund.re)
      tmp[names.long, ] <- X.random
      tmp <- array(tmp, dim = c(J, K.max, p.abund.re))
      tmp <- tmp[order(ord), , , drop = FALSE]
      out$X.random <- tmp
      dimnames(out$X.random)[[3]] <- x.random.names
      out$y <- y.mat[, order(ord), , drop = FALSE]
      out$offset <- offset.mat[order(ord), , drop = FALSE]
      out$call <- cl
      out$n.samples <- n.samples
      out$x.names <- x.names
      out$sp.names <- sp.names
      out$n.post <- n.post.samples
      out$n.thin <- n.thin
      out$n.burn <- n.burn
      out$n.chains <- n.chains
      out$theta.names <- theta.names
      out$type <- "NNGP"
      out$coords <- coords[order(ord), ]
      out$cov.model.indx <- cov.model.indx
      out$n.neighbors <- n.neighbors
      out$dist <- family
      out$re.cols <- re.cols
      out$q <- q
      if (p.abund.re > 0) {
        out$muRE <- TRUE
      } else {
        out$muRE <- FALSE
      }
    } # NNGP
    class(out) <- "sfMsAbund"
    out$run.time <- proc.time() - ptm
    out
  }
}