# Model fit diagnostics The function `spDiag` calculates DIC, GP, GRS, and associated statistics given a `spLM`, `spMvLM`, `spGLM`, `spMvGLM`, `spMvGLM`, or `spSVC` object. ```r spDiag(sp.obj, start=1, end, thin=1, verbose=TRUE, n.report=100, ...) ``` ## Arguments - `sp.obj`: an object returned by `spLM`, `spMvLM`, `spGLM`, `spMvGLM`. For `spSVC`, `sp.obj` is an object from `spRecover`. - `start`: specifies the first sample included in the computation. The `start`, `end`, and `thin` arguments only apply to `spGLM` or `spMvGLM` objects. Sub-sampling for `spLM` and `spMvLM` is controlled using `spRecover` which must be called prior to `spDiag`. - `end`: specifies the last sample included in the computation. The default is to use all posterior samples in `sp.obj`. See `start` argument description. - `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` calculation progress is printed to the screen; otherwise, nothing is printed to the screen. - `n.report`: the interval to report progress. - `...`: currently no additional arguments. ## Returns A list with some of the following tags: - **DIC**: a matrix holding DIC and associated statistics, see Banerjee et al. (2004) for details. - **GP**: a matrix holding GP and associated statistics, see Gelfand and Ghosh (1998) for details. - **GRS**: a scoring rule, see Equation 27 in Gneiting and Raftery (2007) for details. ## 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,Fla. Finley, A.O. and S. Banerjee (2019) Efficient implementation of spatially-varying coefficients models. Gelfand A.E. and Ghosh, S.K. (1998). Model choice: a minimum posterior predictive loss approach. **Biometrika**. 85:1-11. Gneiting, T. and Raftery, A.E. (2007). Strictly proper scoring rules, prediction, and estimation. **Journal of the American Statistical Association**. 102:359-378. ## 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 <- 100 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 <- 2 tau.sq <- 0.1 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) ##too restrictive of prior on beta priors.1 <- list("beta.Norm"=list(rep(0,p), diag(1,p)), "phi.Unif"=c(3/1, 3/0.1), "sigma.sq.IG"=c(2, 2), "tau.sq.IG"=c(2, 0.1)) ##more reasonable prior for beta priors.2 <- list("beta.Norm"=list(rep(0,p), diag(1000,p)), "phi.Unif"=c(3/1, 3/0.1), "sigma.sq.IG"=c(2, 2), "tau.sq.IG"=c(2, 0.1)) cov.model <- "exponential" n.report <- 500 verbose <- TRUE m.1 <- spLM(y~X-1, coords=coords, starting=starting, tuning=tuning, priors=priors.1, cov.model=cov.model, n.samples=n.samples, verbose=verbose, n.report=n.report) m.2 <- spLM(y~X-1, coords=coords, starting=starting, tuning=tuning, priors=priors.2, cov.model=cov.model, n.samples=n.samples, verbose=verbose, n.report=n.report) ##non-spatial model m.3 <- spLM(y~X-1, n.samples=n.samples, verbose=verbose, n.report=n.report) burn.in <- 0.5*n.samples ##recover beta and spatial random effects m.1 <- spRecover(m.1, start=burn.in, verbose=FALSE) m.2 <- spRecover(m.2, start=burn.in, verbose=FALSE) ##lower is better for DIC, GPD, and GRS print(spDiag(m.1)) print(spDiag(m.2)) print(spDiag(m.3)) ## End(Not run) ```

spDiag function