glsOK、これはさまざまな空間相関構造を in / nlmewith hasine distanceで実装するオプションです。
さまざまなcorSpatialタイプのクラスには、距離メトリックが与えられた場合に、空間共変量から相関行列を構築するための機構が既に用意されています。残念ながら、distは hasersine 距離を実装しておらず、空間共変量から距離行列を計算するためにdistによって呼び出される関数です。corSpatial
距離行列の計算は で実行されgetCovariate.corSpatialます。このメソッドの修正された形式は、適切な距離を他のメソッドに渡します。メソッドの大部分は修正する必要はありません。
ここでは、新しいcorStructクラスを作成し、使用する相関関数を決定する1 つの他のメソッド ( )corHaversineのみを変更します。変更を必要としないメソッドは、同等のメソッドからコピーされます。の (新しい)引数は、対象の相関関数を持つ空間クラスの名前をとります。デフォルトでは、これは " " に設定されています。getCovariateDimcorSpatialmimiccorHaversinecorSpher
警告: このコードが球面相関関数とガウス相関関数に対して実行されることを確認する以外に、実際には多くのチェックを行っていません。
#### corHaversine - spatial correlation with haversine distance
# Calculates the geodesic distance between two points specified by radian latitude/longitude using Haversine formula.
# output in km
haversine <- function(x0, x1, y0, y1) {
a <- sin( (y1 - y0)/2 )^2 + cos(y0) * cos(y1) * sin( (x1 - x0)/2 )^2
v <- 2 * asin( min(1, sqrt(a) ) )
6371 * v
}
# function to compute geodesic haversine distance given two-column matrix of longitude/latitude
# input is assumed in form decimal degrees if radians = F
# note fields::rdist.earth is more efficient
haversineDist <- function(xy, radians = F) {
if (ncol(xy) > 2) stop("Input must have two columns (longitude and latitude)")
if (radians == F) xy <- xy * pi/180
hMat <- matrix(NA, ncol = nrow(xy), nrow = nrow(xy))
for (i in 1:nrow(xy) ) {
for (j in i:nrow(xy) ) {
hMat[j,i] <- haversine(xy[i,1], xy[j,1], xy[i,2], xy[j,2])
}
}
as.dist(hMat)
}
## for most methods, machinery from corSpatial will work without modification
Initialize.corHaversine <- nlme:::Initialize.corSpatial
recalc.corHaversine <- nlme:::recalc.corSpatial
Variogram.corHaversine <- nlme:::Variogram.corSpatial
corFactor.corHaversine <- nlme:::corFactor.corSpatial
corMatrix.corHaversine <- nlme:::corMatrix.corSpatial
coef.corHaversine <- nlme:::coef.corSpatial
"coef<-.corHaversine" <- nlme:::"coef<-.corSpatial"
## Constructor for the corHaversine class
corHaversine <- function(value = numeric(0), form = ~ 1, mimic = "corSpher", nugget = FALSE, fixed = FALSE) {
spClass <- "corHaversine"
attr(value, "formula") <- form
attr(value, "nugget") <- nugget
attr(value, "fixed") <- fixed
attr(value, "function") <- mimic
class(value) <- c(spClass, "corStruct")
value
} # end corHaversine class
environment(corHaversine) <- asNamespace("nlme")
Dim.corHaversine <- function(object, groups, ...) {
if (missing(groups)) return(attr(object, "Dim"))
val <- Dim.corStruct(object, groups)
val[["start"]] <- c(0, cumsum(val[["len"]] * (val[["len"]] - 1)/2)[-val[["M"]]])
## will use third component of Dim list for spClass
names(val)[3] <- "spClass"
val[[3]] <- match(attr(object, "function"), c("corSpher", "corExp", "corGaus", "corLin", "corRatio"), 0)
val
}
environment(Dim.corHaversine) <- asNamespace("nlme")
## getCovariate method for corHaversine class
getCovariate.corHaversine <- function(object, form = formula(object), data) {
if (is.null(covar <- attr(object, "covariate"))) { # if object lacks covariate attribute
if (missing(data)) { # if object lacks data
stop("need data to calculate covariate")
}
covForm <- getCovariateFormula(form)
if (length(all.vars(covForm)) > 0) { # if covariate present
if (attr(terms(covForm), "intercept") == 1) { # if formula includes intercept
covForm <- eval(parse(text = paste("~", deparse(covForm[[2]]),"-1",sep=""))) # remove intercept
}
# can only take covariates with correct names
if (length(all.vars(covForm)) > 2) stop("corHaversine can only take two covariates, 'lon' and 'lat'")
if ( !all(all.vars(covForm) %in% c("lon", "lat")) ) stop("covariates must be named 'lon' and 'lat'")
covar <- as.data.frame(unclass(model.matrix(covForm, model.frame(covForm, data, drop.unused.levels = TRUE) ) ) )
covar <- covar[,order(colnames(covar), decreasing = T)] # order as lon ... lat
}
else {
covar <- NULL
}
if (!is.null(getGroupsFormula(form))) { # if groups in formula extract covar by groups
grps <- getGroups(object, data = data)
if (is.null(covar)) {
covar <- lapply(split(grps, grps), function(x) as.vector(dist(1:length(x) ) ) ) # filler?
}
else {
giveDist <- function(el) {
el <- as.matrix(el)
if (nrow(el) > 1) as.vector(haversineDist(el))
else numeric(0)
}
covar <- lapply(split(covar, grps), giveDist )
}
covar <- covar[sapply(covar, length) > 0] # no 1-obs groups
}
else { # if no groups in formula extract distance
if (is.null(covar)) {
covar <- as.vector(dist(1:nrow(data) ) )
}
else {
covar <- as.vector(haversineDist(as.matrix(covar) ) )
}
}
if (any(unlist(covar) == 0)) { # check that no distances are zero
stop("cannot have zero distances in \"corHaversine\"")
}
}
covar
} # end method getCovariate
environment(getCovariate.corHaversine) <- asNamespace("nlme")
1000 の範囲パラメーターを指定して、これが実行されることをテストするには、次のようにします。
## test that corHaversine runs with spherical correlation (not testing that it WORKS ...)
library(MASS)
set.seed(1001)
sample_data <- data.frame(lon = -121:-22, lat = -50:49)
ran <- 1000 # 'range' parameter for spherical correlation
dist_matrix <- as.matrix(haversineDist(sample_data)) # haversine distance matrix
# set up correlation matrix of response
corr_matrix <- 1-1.5*(dist_matrix/ran)+0.5*(dist_matrix/ran)^3
corr_matrix[dist_matrix > ran] = 0
diag(corr_matrix) <- 1
# set up covariance matrix of response
sigma <- 2 # residual standard deviation
cov_matrix <- (diag(100)*sigma) %*% corr_matrix %*% (diag(100)*sigma) # correlated response
# generate response
sample_data$y <- mvrnorm(1, mu = rep(0, 100), Sigma = cov_matrix)
# fit model
gls_haversine <- gls(y ~ 1, correlation = corHaversine(form=~lon+lat, mimic="corSpher"), data = sample_data)
summary(gls_haversine)
# Correlation Structure: corHaversine
# Formula: ~lon + lat
# Parameter estimate(s):
# range
# 1426.818
#
# Coefficients:
# Value Std.Error t-value p-value
# (Intercept) 0.9397666 0.7471089 1.257871 0.2114
#
# Standardized residuals:
# Min Q1 Med Q3 Max
# -2.1467696 -0.4140958 0.1376988 0.5484481 1.9240042
#
# Residual standard error: 2.735971
# Degrees of freedom: 100 total; 99 residual
範囲パラメーター = 100 のガウス相関で実行されることをテストします。
## test that corHaversine runs with Gaussian correlation
ran = 100 # parameter for Gaussian correlation
corr_matrix_gauss <- exp(-(dist_matrix/ran)^2)
diag(corr_matrix_gauss) <- 1
# set up covariance matrix of response
cov_matrix_gauss <- (diag(100)*sigma) %*% corr_matrix_gauss %*% (diag(100)*sigma) # correlated response
# generate response
sample_data$y_gauss <- mvrnorm(1, mu = rep(0, 100), Sigma = cov_matrix_gauss)
# fit model
gls_haversine_gauss <- gls(y_gauss ~ 1, correlation = corHaversine(form=~lon+lat, mimic = "corGaus"), data = sample_data)
summary(gls_haversine_gauss)
とlme:
## runs with lme
# set up data with group effects
group_y <- as.vector(sapply(1:5, function(.) mvrnorm(1, mu = rep(0, 100), Sigma = cov_matrix_gauss)))
group_effect <- rep(-2:2, each = 100)
group_y = group_y + group_effect
group_name <- factor(group_effect)
lme_dat <- data.frame(y = group_y, group = group_name, lon = sample_data$lon, lat = sample_data$lat)
# fit model
lme_haversine <- lme(y ~ 1, random = ~ 1|group, correlation = corHaversine(form=~lon+lat, mimic = "corGaus"), data = lme_dat, control=lmeControl(opt = "optim") )
summary(lme_haversine)
# Correlation Structure: corHaversine
# Formula: ~lon + lat | group
# Parameter estimate(s):
# range
# 106.3482
# Fixed effects: y ~ 1
# Value Std.Error DF t-value p-value
# (Intercept) -0.0161861 0.6861328 495 -0.02359033 0.9812
#
# Standardized Within-Group Residuals:
# Min Q1 Med Q3 Max
# -3.0393708 -0.6469423 0.0348155 0.7132133 2.5921573
#
# Number of Observations: 500
# Number of Groups: 5