# Cross validation, n-fold and leave-one-out for the hybrid method of generalised linear models ('glm') and 'krige' ('glmkrige') This function is a cross validation function for the hybrid method of 'glm' and 'krige' (glmkrige), where 'krige' methods include ordinary kriging ('OK'), simple kriging ('SK'), block 'OK' ('BOK') and block 'SK'('BSK') (see reference #1 for further info). ```r glmkrigecv( formula.glm = NULL, longlat, trainxy, y, family = "gaussian", transformation = "none", delta = 1, formula.krige = res1 ~ 1, vgm.args = c("Sph"), anis = c(0, 1), alpha = 0, block = 0, beta, nmaxkrige = 12, validation = "CV", cv.fold = 10, predacc = "VEcv", ... ) ``` ## Arguments - `formula.glm`: a formula defining the response variable and predictive variables for 'glm'. - `longlat`: a dataframe contains longitude and latitude of point samples. - `trainxy`: a dataframe contains longitude (long), latitude (lat), predictive variables and the response variable of point samples. - `y`: a vector of the response variable in the formula, that is, the left part of the formula. - `family`: a description of the error distribution and link function to be used in the model. See '?glm' for details. - `transformation`: transform the residuals of 'glm' to normalise the data; can be "sqrt" for square root, "arcsine" for arcsine, "log" or "none" for non transformation. By default, "none" is used. - `delta`: numeric; to avoid log(0) in the log transformation. The default is 1. - `formula.krige`: formula defining the response vector and (possible) regressor. an object (i.e., 'variogram.formula') for 'variogram' or a formula for 'krige'. see 'variogram' and 'krige' in 'gstat' for details. - `vgm.args`: arguments for 'vgm', e.g. variogram model of response variable and anisotropy parameters. see 'vgm' in 'gstat' for details. By default, "Sph" is used. - `anis`: anisotropy parameters: see notes 'vgm' in 'gstat' for details. - `alpha`: direction in plane (x,y). see variogram in 'gstat' for details. - `block`: block size. see 'krige' in 'gstat' for details. - `beta`: for simple kriging. see 'krige' in 'gstat' for details. - `nmaxkrige`: for a local predicting: the number of nearest observations that should be used for a prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, 12 observations are used. - `validation`: validation methods, include 'LOO': leave-one-out, and 'CV': cross-validation. - `cv.fold`: integer; number of folds in the cross-validation. if > 1, then apply n-fold cross validation; the default is 10, i.e., 10-fold cross validation that is recommended. - `predacc`: can be either "VEcv" for vecv or "ALL" for all measures in function pred.acc. - `...`: other arguments passed on to 'glm' and 'krige'. ## Returns A list with the following components: me, rme, mae, rmae, mse, rmse, rrmse, vecv and e1; or vecv only ## Note This function is largely based on 'rfcv' in 'randomForest', 'krigecv' in 'spm2'and 'glm' in 'stats'. ## Examples ```r library(spm) data(petrel) gravel <- petrel[, c(1, 2, 6:9, 5)] longlat <- petrel[, c(1, 2)] model <- log(gravel + 1) ~ lat + bathy + I(long^3) + I(lat^2) + I(lat^3) y <- log(gravel[, 7] +1) set.seed(1234) glmkrigecv1 <- glmkrigecv(formula.glm = model, longlat = longlat, trainxy = gravel, y = y, transformation = "none", formula.krige = res1 ~ 1, vgm.args = "Sph", nmaxkrige = 12, validation = "CV", predacc = "ALL") glmkrigecv1 # Since the default 'family' is used, actually a 'lm' model is used. data(spongelonglat) longlat <- spongelonglat[, 7:8] model <- sponge ~ long + I(long^2) y = spongelonglat[, 1] set.seed(1234) glmkrigecv1 <- glmkrigecv(formula.glm = model, longlat = longlat, trainxy = spongelonglat, y = y, family = poisson, transformation = "arcsine", formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, validation = "CV", predacc = "ALL") glmkrigecv1 # glmok for count data data(spongelonglat) longlat <- spongelonglat[, 7:8] model <- sponge ~ . # use all predictive variables in the dataset y = spongelonglat[, 1] set.seed(1234) n <- 20 # number of iterations,60 to 100 is recommended. VEcv <- NULL for (i in 1:n) { glmkrigecv1 <- glmkrigecv(formula.glm = model, longlat = longlat, trainxy = spongelonglat, y = y, family = poisson, formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, validation = "CV", predacc = "VEcv") VEcv [i] <- glmkrigecv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for GLM", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) # glmok for percentage data longlat <- petrel[, c(1, 2)] model <- gravel / 100 ~ lat + bathy + I(long^3) + I(lat^2) + I(lat^3) set.seed(1234) n <- 20 # number of iterations,60 to 100 is recommended. VEcv <- NULL for (i in 1:n) { glmkrigecv1 <- glmkrigecv(formula.glm = model, longlat = longlat, trainxy = gravel, y = gravel[, 7] / 100, family = binomial(link=logit), formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, validation = "CV", predacc = "VEcv") VEcv [i] <- glmkrigecv1 } plot(VEcv ~ c(1:n), xlab = "Iteration for GLM", ylab = "VEcv (%)") points(cumsum(VEcv) / c(1:n) ~ c(1:n), col = 2) abline(h = mean(VEcv), col = 'blue', lwd = 2) ``` ## References Li, J., Alvarez, B., Siwabessy, J., Tran, M., Huang, Z., Przeslawski, R., Radke, L., Howard, F. and Nichol, S. (2017). "Application of random forest, generalised linear model and their hybrid methods with geostatistical techniques to count data: Predicting sponge species richness." Environmental Modelling & Software 97: 112-129. Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691. ## Author(s) Jin Li

glmkrigecv function