# Cross validation, n-fold and leave-one-out for the hybrid methods of generalised linear models ('glm'), 'kriging' and inverse distance weighted ('IDW'). This function is a cross validation function for 38 hybrid methods of 'glm', 'kriging' and 'IDW', including the average of 'glmkrige' and 'glmidw' ('glmkrigeglmidw') and the average of 'glm', 'glmkrige' and 'glmidw' ('glmglmkrigeglmidw'), where 'kriging' methods include ordinary kriging ('OK'), simple kriging ('SK'), block 'OK' ('BOK') and block 'SK'('BSK') and 'IDW' also covers 'NN' and 'KNN' (for details, see reference #1). This function can also be sued for 38 hybrid methods of 'lm', 'kriging' and 'IDW'. ```r glmkrigeidwcv( 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, idp = 2, nmaxidw = 12, hybrid.parameter = 2, lambda = 1, 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 for 'krige'; 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. - `idp`: a numeric number specifying the inverse distance weighting power. - `nmaxidw`: 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. - `hybrid.parameter`: the default is 2 that is for 'glmkrigeglmidw'; for 'glmglmkrigeglmidw', it needs to be 3. - `lambda,`: ranging from 0 to 2; the default is 1 for 'glmkrigeglmidw' and 'glmglmkrigeglmidw'; and if it is < 1, more weight is placed on 'krige', otherwise more weight is placed on 'idw'; and if it is 0, 'idw' is not considered and the resultant methods is 'glmkrige' when the default 'hybrid.parameter' is used; and if it is 2, then the resultant method is 'glmidw' when the default 'hybrid.parameter' is 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', 'krige' and 'gstat'. ## 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) # glmokglidw 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) glmkrigeglmidwcv1 <- glmkrigeidwcv(formula.glm = model, longlat = longlat, trainxy = gravel, y = y, transformation = "none", formula.krige = res1 ~ 1, vgm.args = "Sph", nmaxkrige = 12, idp = 2, nmaxidw = 12, validation = "CV", predacc = "ALL") glmkrigeglmidwcv1 # Since the default 'family' is used, actually a 'lm' model is used. # glmokglmidw data(spongelonglat) longlat <- spongelonglat[, 7:8] model <- sponge ~ long + I(long^2) y = spongelonglat[, 1] set.seed(1234) glmkrigeglmidwcv1 <- glmkrigeidwcv(formula.glm = model, longlat = longlat, trainxy = spongelonglat, y = y, family = poisson, transformation = "arcsine", formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, idp = 2, nmaxidw = 12, validation = "CV", predacc = "ALL") glmkrigeglmidwcv1 # glmglmokglmidw data(spongelonglat) longlat <- spongelonglat[, 7:8] model <- sponge ~ long + I(long^2) y = spongelonglat[, 1] set.seed(1234) glmglmkrigeglmidwcv1 <- glmkrigeidwcv(formula.glm = model, longlat = longlat, trainxy = spongelonglat, y = y, family = poisson, transformation = "arcsine", formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, idp = 2, nmaxidw = 12, hybrid.parameter = 3, validation = "CV", predacc = "ALL") glmglmkrigeglmidwcv1 # glmokglidw 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) { glmkrigeglmidwcv1 <- glmkrigeidwcv(formula.glm = model, longlat = longlat, trainxy = spongelonglat, y = y, family = poisson, formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, idp = 2, nmaxidw = 12, validation = "CV", predacc = "VEcv") VEcv [i] <- glmkrigeglmidwcv1 } 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) # glmokglmidw 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) { glmkrigeglmidwcv1 <- glmkrigeidwcv(formula.glm = model, longlat = longlat, trainxy = gravel, y = gravel[, 7] / 100, family = binomial(link=logit), formula.krige = res1 ~ 1, vgm.args = ("Sph"), nmaxkrige = 12, idp = 2, nmaxidw = 12, validation = "CV", predacc = "VEcv") VEcv [i] <- glmkrigeglmidwcv1 } 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. (2022). Spatial Predictive Modeling with R. Boca Raton, Chapman and Hall/CRC. 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. A. Liaw and M. Wiener (2002). Classification and Regression by randomForest. R News 2(3), 18-22. Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers & Geosciences, 30: 683-691. ## Author(s) Jin Li

glmkrigeidwcv function