# Function for recovering regression coefficients and spatial random effects for `spLM`, `spMvLM`, `spMisalignLM`, `spSVC` using composition sampling Function for recovering regression coefficients and spatial random effects for `spLM`, `spMvLM`, and `spMisalignLM` using composition sampling. ```r spRecover(sp.obj, get.beta=TRUE, get.w=TRUE, start=1, end, thin=1, verbose=TRUE, n.report=100, n.omp.threads=1, ...) ``` ## Arguments - `sp.obj`: an object returned by `spLM`, `spMvLM`, `spMisalignLM`, or `spSVC`. - `get.beta`: if `TRUE`, regression coefficients will be recovered. - `get.w`: if `TRUE`, spatial random effects will be recovered. - `start`: specifies the first sample included in the composition sampling. - `end`: specifies the last sample included in the composition. The default is to use all posterior samples in `sp.obj`. - `thin`: a sample thinning factor. The default of 1 considers all samples between `start` and `end`. For example, if `thin = 10` then 1 in 10 samples are considered between `start` and `end`. - `verbose`: if `TRUE`, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen. - `n.report`: the interval to report sampling progress. - `n.omp.threads`: a positive integer indicating the number of threads to use for SMP parallel processing. The package must be compiled for OpenMP support. For most Intel-based machines, we recommend setting `n.omp.threads` up to the number of hyperthreaded cores. This argument is only implemented for `spSVC`. - `...`: currently no additional arguments. ## Returns The input `sp.obj` with posterior samples of regression coefficients and/or spatial random effects appended. tags: - **p.theta.recover.samples**: those `p.theta.samples` used in the composition sampling. - **p.beta.recover.samples**: a `coda` object of regression coefficients posterior samples. - **p.w.recover.samples**: a `coda` object of spatial random effects posterior samples. Rows correspond to locations' random effects and columns are posterior samples. Given $q$ responses, the `p.w.recover.samples` matrix for `spMvLM` has $qn$ rows. The recovered random effects for locations are held in rows c("$1:q, (q+1):2q, \\ldots,\n$", "$ ((n*-1)q+1):qn$") (i.e., the samples for the first location's $q$ response variables are in rows 1:q, second location in rows $(q+1):2q$, etc.). For `spSVC` given the $r$ space-varying coefficients, `p.w.recover.samples` has $rn$ rows. The recovered random effects for locations are held in rows c("$1:r, (r+1):2r, \\ldots,\n$", "$ ((n-1)r+1):rn$") (i.e., the samples for the first location's $r$ regression coefficients are in rows 1:r, second location in rows $(r+1):2r$, etc.). - **p.w.recover.samples.list**: only returned for `spSVC`. This provides `p.w.recover.samples` in a different (more convenient form). Elements in this list hold samples for each of the $r$ coefficients. List element names indicate either the coefficient index or name specified in `spSVC`'s `svc.cols` argument. The sample matrices are $n$ rows and predictive samples along the columns. - **p.tilde.beta.recover.samples.list**: only returned for `spSVC`. Like `p.w.recover.samples.list` but with the addition of the corresponding $beta$ posterior samples (i.e., $beta+w(s)$). - **p.y.samples**: only returned for `spSVC`. These posterior are the fitted values with locations on the rows and samples on the columns. For a given sample the fitted value for the $i-th$ location is c("$N(x(s_i)beta +\n$", "$ z(s_i)w(s_i), tau^2)$"). ## References Banerjee, S., Carlin, B.P., and Gelfand, A.E. (2004). Hierarchical modeling and analysis for spatial data. Chapman and Hall/CRC Press, Boca Raton, FL. Finley, A.O., S. Banerjee, and A.E. Gelfand. (2015) spBayes for large univariate and multivariate point-referenced spatio-temporal data models. **Journal of Statistical Software**, 63:1--28. [https://www.jstatsoft.org/article/view/v063i13](https://www.jstatsoft.org/article/view/v063i13). Finley, A.O. and S. Banerjee (2019) Bayesian spatially varying coefficient models in the spBayes R package. [https://arxiv.org/abs/1903.03028](https://arxiv.org/abs/1903.03028). ## Author(s) Andrew O. Finley finleya@msu.edu , Sudipto Banerjee sudipto@ucla.edu ## Examples ```r ## Not run: rmvn <- function(n, mu=0, V = matrix(1)){ p <- length(mu) if(any(is.na(match(dim(V),p)))) stop("Dimension problem!") D <- chol(V) t(matrix(rnorm(n*p), ncol=p)%*%D + rep(mu,rep(n,p))) } set.seed(1) n <- 50 coords <- cbind(runif(n,0,1), runif(n,0,1)) X <- as.matrix(cbind(1, rnorm(n))) B <- as.matrix(c(1,5)) p <- length(B) sigma.sq <- 10 tau.sq <- 0.01 phi <- 3/0.5 D <- as.matrix(dist(coords)) R <- exp(-phi*D) w <- rmvn(1, rep(0,n), sigma.sq*R) y <- rnorm(n, X%*%B + w, sqrt(tau.sq)) n.samples <- 1000 starting <- list("phi"=3/0.5, "sigma.sq"=50, "tau.sq"=1) tuning <- list("phi"=0.1, "sigma.sq"=0.1, "tau.sq"=0.1) priors <- list("beta.Flat", "phi.Unif"=c(3/1, 3/0.1), "sigma.sq.IG"=c(2, 5), "tau.sq.IG"=c(2, 0.01)) cov.model <- "exponential" m.1 <- spLM(y~X-1, coords=coords, starting=starting, tuning=tuning, priors=priors, cov.model=cov.model, n.samples=n.samples) m.1 <- spRecover(m.1, start=0.5*n.samples, thin=2) summary(window(m.1$p.beta.recover.samples)) w.hat <- apply(m.1$p.w.recover.samples, 1, mean) plot(w, w.hat, xlab="Observed w", ylab="Fitted w") ## End(Not run) ```

spRecover function