r - 使用 R 中的斜坡包指定线性混合模型的相关结构

Question

我正在尝试创建一个线性混合模型 (lmm)，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。

ramps 包包含一个计算“haversine”距离的相关结构——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。我假设可以用相同的方式实现带有“haversine”指标的 corRGaus。

我能够使用 lme 函数成功创建具有根据平面距离计算的空间相关性的 lmm。

尽管使用 gls 命令的相关结构存在错误，但我还能够创建一个线性模型(未混合)，其中使用大圆距离计算空间相关性。

当尝试对具有大圆距离的线性模型使用 gls 命令时，出现以下错误:

x = runif(20, 1,50)
y = runif(20, 1,50)
gls(x ~ y, cor = corRGaus(form = ~ x + y))

Generalized least squares fit by REML
 Model: x ~ y 
 Data: NULL 
Log-restricted-likelihood: -78.44925

Coefficients:
 (Intercept)            y 
24.762656602  0.007822469 

Correlation Structure: corRGaus
 Formula: ~x + y 
 Parameter estimate(s):
Error in attr(object, "fixed") && unconstrained : 
 invalid 'x' type in 'x && y'

当我增加数据大小时出现内存分配错误(仍然是一个非常小的数据集):

x = runif(100, 1, 50)
y = runif(100, 1, 50)
lat = runif(100, -90, 90)
long = runif(100, -180, 180)
gls(x ~ y, cor = corRGaus(form = ~ x + y))

Error in glsEstimate(glsSt, control = glsEstControl) : 
'Calloc' could not allocate memory (18446744073709551616 of 8 bytes)

当尝试使用 lme 命令和来自 ramps 的 corRGaus 运行混合模型时，结果如下:

x = runif(100, 1, 50)
y = runif(100, 1, 50)
LC = c(rep(1, 50) , rep(2, 50))
lat = runif(100, -90, 90)
long = runif(100, -180, 180)

lme(x ~ y,random = ~ y|LC, cor = corRGaus(form = ~ long + lat))

Error in `coef<-.corSpatial`(`*tmp*`, value = value[parMap[, i]]) : 
  NA/NaN/Inf in foreign function call (arg 1)
In addition: Warning messages:
1: In nlminb(c(coef(lmeSt)), function(lmePars) -logLik(lmeSt, lmePars),  :
  NA/NaN function evaluation
2: In nlminb(c(coef(lmeSt)), function(lmePars) -logLik(lmeSt, lmePars),  :
  NA/NaN function evaluation

我不确定如何继续使用此方法。 “haversine”函数是我想用来完成我的模型的函数，但我在实现它们时遇到了麻烦。关于 ramps 包的问题很少，而且我看到的实现也很少。任何帮助将不胜感激。

我以前曾尝试修改 nlme 包，但未能成功。我发布了一个关于 this 的问题，我被推荐使用 ramps 包。

我在 Windows 8 计算机上使用 R 3.0.0。

Answer 1

好的，这里有一个选项可以在gls中实现各种空间关联结构。/nlme与 haversine 距离。

各种corSpatial给定距离度量，-type 类已经具有从空间协变量构建相关矩阵的机制。不幸的是，dist不实现半正弦距离，dist是corSpatial调用的函数从空间协变量计算距离矩阵。

距离矩阵计算在 getCovariate.corSpatial 中执行.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，我创建了一个新的 corStruct类，corHaversine , 并且只修改 getCovariate和另一种方法 ( Dim ) 确定使用哪个相关函数。那些不需要修改的方法，是从等效的corSpatial中复制的方法。 (新)mimic corHaversine 中的参数采用具有相关相关函数的空间类的名称:默认情况下，它设置为“corSpher”。

警告:除了确保此代码针对球形和高斯相关函数运行外，我还没有真正做很多检查。

#### 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")

要测试此运行，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)

与 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