Sar*_*rah 2 statistics r distance correlation mixed-models
我正在尝试创建一个线性混合模型（lmm），它允许点之间的空间相关性（每个点都有纬度/经度）。我希望空间相关性基于点之间的大圆距离。
\n\n该包ramps包含一个相关结构，用于计算 \xe2\x80\x98havesine\xe2\x80\x99 距离 \xe2\x80\x93 尽管我在实现它时遇到了麻烦。我以前使用过其他相关结构（corGaus，corExp）并且没有遇到任何困难。我假设corRGaus“haversine”指标可以以相同的方式实现。
我能够使用该lme函数成功创建一个具有在平面距离上计算的空间相关性的 lmm。
我还能够创建一个线性模型（未混合），并使用大圆距离计算空间相关性，尽管使用该gls命令的相关结构存在错误。
当尝试使用gls具有大圆距离的线性模型的命令时，我遇到以下错误：
x = runif(20, 1,50)\ny = runif(20, 1,50)\ngls(x ~ y, cor = corRGaus(form = ~ x + y))\n\nGeneralized least squares fit by REML\n Model: x ~ y \n Data: NULL \nLog-restricted-likelihood: -78.44925\n\nCoefficients:\n (Intercept) y \n24.762656602 0.007822469 \n\nCorrelation Structure: corRGaus\n Formula: ~x + y \n Parameter estimate(s):\nError in attr(object, "fixed") && unconstrained : \n invalid \'x\' type in \'x && y\'\n当我增加数据大小时，会出现内存分配错误（仍然是一个非常小的数据集）：
\n\nx = runif(100, 1, 50)\ny = runif(100, 1, 50)\nlat = runif(100, -90, 90)\nlong = runif(100, -180, 180)\ngls(x ~ y, cor = corRGaus(form = ~ x + y))\n\nError in glsEstimate(glsSt, control = glsEstControl) : \n\'Calloc\' could not allocate memory (18446744073709551616 of 8 bytes)\nlme当尝试使用命令和包corRGaus中的命令运行混合模型时，ramps结果如下：
x = runif(100, 1, 50)\ny = runif(100, 1, 50)\nLC = c(rep(1, 50) , rep(2, 50))\nlat = runif(100, -90, 90)\nlong = runif(100, -180, 180)\n\nlme(x ~ y,random = ~ y|LC, cor = corRGaus(form = ~ long + lat))\n\nError in `coef<-.corSpatial`(`*tmp*`, value = value[parMap[, i]]) : \n NA/NaN/Inf in foreign function call (arg 1)\nIn addition: Warning messages:\n1: In nlminb(c(coef(lmeSt)), function(lmePars) -logLik(lmeSt, lmePars), :\n NA/NaN function evaluation\n2: In nlminb(c(coef(lmeSt)), function(lmePars) -logLik(lmeSt, lmePars), :\n NA/NaN function evaluation\n我不确定如何继续使用此方法。我想用“haversine”函数来完成我的模型，但我在实现它们时遇到了困难。关于这个包的问题很少ramps，而且我看到的实现也很少。任何帮助将不胜感激。
我之前曾尝试修改该nlme软件包，但未能成功。我发布了一个关于此的问题，建议我使用该ramps包。
我在 Windows 8 计算机上使用 R 3.0.0。
\n好的，这里有一个选项，可以在半正弦距离中实现各种空间相关gls结构nlme。
各种类型corSpatial的类已经有了适当的机制，可以在给定距离度量的情况下从空间协变量构建相关矩阵。不幸的是，dist它没有实现半正矢距离，并且是由空间协变量计算距离矩阵dist所调用的函数。corSpatial
距离矩阵计算在 中执行getCovariate.corSpatial。此方法的修改形式会将适当的距离传递给其他方法，并且大多数方法不需要修改。
在这里，我创建一个新corStruct类 ，corHaversine并仅修改getCovariate另一个方法 ( Dim) 来确定使用哪个相关函数。那些不需要修改的方法是从等效corSpatial方法复制的。中的（新）mimic参数corHaversine采用具有感兴趣的相关函数的空间类的名称：默认情况下，它设置为“ corSpher”。
警告：除了确保该代码适用于球形和高斯相关函数之外，我还没有真正进行大量检查。
#### 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")
为了测试它是否运行，给定范围参数 1000：
## 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$y <- mvrnorm(1, mu = rep(0, 100), Sigma = cov_matrix)
# fit model
gls_haversine <- gls(y ~ 1, correlation = corHaversine(form=~lon+lat, mimic="corSpher"), data = sample_data)
summary(gls_haversine)
# Correlation Structure: corHaversine
# Formula: ~lon + lat
# Parameter estimate(s):
# range
# 1426.818
#
# Coefficients:
# Value Std.Error t-value p-value
# (Intercept) 0.9397666 0.7471089 1.257871 0.2114
#
# Standardized residuals:
# Min Q1 Med Q3 Max
# -2.1467696 -0.4140958 0.1376988 0.5484481 1.9240042
#
# Residual standard error: 2.735971
# Degrees of freedom: 100 total; 99 residual
测试它是否以高斯相关运行，范围参数 = 100：
## test that corHaversine runs with Gaussian correlation
ran = 100 # parameter for Gaussian correlation
corr_matrix_gauss <- exp(-(dist_matrix/ran)^2)
diag(corr_matrix_gauss) <- 1
# set up covariance matrix of response
cov_matrix_gauss <- (diag(100)*sigma) %*% corr_matrix_gauss %*% (diag(100)*sigma) # correlated response
# generate response
sample_data$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)
和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