在R的glm中，Gamma系列的默认链接功能为inverse，identity和log。现在针对我的特定问题，我需要使用回复Y的伽玛回归和log(E(Y)-1))形式的修改链接函数。因此，我考虑修改R中的一些glm相关函数。有几个函数可能是相关的，我正在寻求任何有过这方面经验的人的帮助。
例如，函数Gamma定义为
function (link = "inverse")
{
linktemp <- substitute(link)
if (!is.character(linktemp))
linktemp <- deparse(linktemp)
okLinks <- c("inverse", "log", "identity")
if (linktemp %in% okLinks)
stats <- make.link(linktemp)
else if (is.character(link))
stats <- make.link(link)
else {
if (inherits(link, "link-glm")) {
stats <- link
if (!is.null(stats$name))
linktemp <- stats$name
}
else {
stop(gettextf("link \"%s\" not available for gamma family; available links are %s",
linktemp, paste(sQuote(okLinks), collapse = ", ")),
domain = NA)
}
}
variance <- function(mu) mu^2
validmu <- function(mu) all(mu > 0)
dev.resids <- function(y, mu, wt) -2 * wt * (log(ifelse(y ==
0, 1, y/mu)) - (y - mu)/mu)
aic <- function(y, n, mu, wt, dev) {
n <- sum(wt)
disp <- dev/n
-2 * sum(dgamma(y, 1/disp, scale = mu * disp, log = TRUE) *
wt) + 2
}
initialize <- expression({
if (any(y <= 0)) stop("non-positive values not allowed for the 'gamma' family")
n <- rep.int(1, nobs)
mustart <- y
})
simfun <- function(object, nsim) {
wts <- object$prior.weights
if (any(wts != 1))
message("using weights as shape parameters")
ftd <- fitted(object)
shape <- MASS::gamma.shape(object)$alpha * wts
rgamma(nsim * length(ftd), shape = shape, rate = shape/ftd)
}
structure(list(family = "Gamma", link = linktemp, linkfun = stats$linkfun,
linkinv = stats$linkinv, variance = variance, dev.resids = dev.resids,
aic = aic, mu.eta = stats$mu.eta, initialize = initialize,
validmu = validmu, valideta = stats$valideta, simulate = simfun),
class = "family")
}
另外，为了使用命令glm(y ~ log(mu), family = Gamma(link = MyLink))，我是否还需要修改glm.fit功能？谢谢！
更新和新问题
根据@Ben Bolker的评论，我们需要编写一个名为vlog的新链接函数（实名"log(exp(y)-1)"）。我发现make.link函数可能负责这样的修改。它被定义为
function (link)
{
switch(link, logit = {
linkfun <- function(mu) .Call(C_logit_link, mu)
linkinv <- function(eta) .Call(C_logit_linkinv, eta)
mu.eta <- function(eta) .Call(C_logit_mu_eta, eta)
valideta <- function(eta) TRUE
},
...
}, log = {
linkfun <- function(mu) log(mu)
linkinv <- function(eta) pmax(exp(eta), .Machine$double.eps)
mu.eta <- function(eta) pmax(exp(eta), .Machine$double.eps)
valideta <- function(eta) TRUE
},
...
structure(list(linkfun = linkfun, linkinv = linkinv, mu.eta = mu.eta,
valideta = valideta, name = link), class = "link-glm")
}
我的问题是：如果我们想要永久将此链接功能vlog添加到glm，那么在每个R会话中，我们可以直接使用glm(y~x,family=Gamma(link="log(exp(y)-1)"))，我们是否应该使用fix(make.link)然后将vlog的定义添加到其正文中？或fix()只能在当前的R会话中执行此操作？再次感谢！
还有一件事：我意识到可能需要修改另一个功能。它是Gamma，定义为
function (link = "inverse")
{
linktemp <- substitute(link)
if (!is.character(linktemp))
linktemp <- deparse(linktemp)
okLinks <- c("inverse", "log", "identity")
if (linktemp %in% okLinks)
stats <- make.link(linktemp)
else if (is.character(link))
stats <- make.link(link)
else {
if (inherits(link, "link-glm")) {
stats <- link
if (!is.null(stats$name))
linktemp <- stats$name
}
else {
stop(gettextf("link \"%s\" not available for gamma family; available links are %s",
linktemp, paste(sQuote(okLinks), collapse = ", ")),
domain = NA)
}
}
variance <- function(mu) mu^2
validmu <- function(mu) all(mu > 0)
dev.resids <- function(y, mu, wt) -2 * wt * (log(ifelse(y ==
0, 1, y/mu)) - (y - mu)/mu)
aic <- function(y, n, mu, wt, dev) {
n <- sum(wt)
disp <- dev/n
-2 * sum(dgamma(y, 1/disp, scale = mu * disp, log = TRUE) *
wt) + 2
}
initialize <- expression({
if (any(y <= 0)) stop("non-positive values not allowed for the 'gamma' family")
n <- rep.int(1, nobs)
mustart <- y
})
simfun <- function(object, nsim) {
wts <- object$prior.weights
if (any(wts != 1))
message("using weights as shape parameters")
ftd <- fitted(object)
shape <- MASS::gamma.shape(object)$alpha * wts
rgamma(nsim * length(ftd), shape = shape, rate = shape/ftd)
}
structure(list(family = "Gamma", link = linktemp, linkfun = stats$linkfun,
linkinv = stats$linkinv, variance = variance, dev.resids = dev.resids,
aic = aic, mu.eta = stats$mu.eta, initialize = initialize,
validmu = validmu, valideta = stats$valideta, simulate = simfun),
class = "family")
}
我认为我们还需要修改
okLinks <- c("inverse", "log", "identity")
到
okLinks <- c("inverse", "log", "identity", "log(exp(y)-1)")
答案 0 :(得分：12)
我基本上遵循?family中示例的形式，其中显示了qlogis(mu^(1/days))形式的用户指定链接。
我们需要eta = log(exp(y)-1)形式的链接（因此反向链接为y=log(exp(eta)+1)，mu.eta = dy/d(eta) = 1/(1+exp(-eta))
vlog <- function() {
## link
linkfun <- function(y) log(exp(y)-1)
## inverse link
linkinv <- function(eta) log(exp(eta)+1)
## derivative of invlink wrt eta
mu.eta <- function(eta) { 1/(exp(-eta) + 1) }
valideta <- function(eta) TRUE
link <- "log(exp(y)-1)"
structure(list(linkfun = linkfun, linkinv = linkinv,
mu.eta = mu.eta, valideta = valideta,
name = link),
class = "link-glm")
}
基本检查：
vv <- vlog()
vv$linkfun(vv$linkinv(27)) ## check invertibility
library("numDeriv")
all.equal(grad(vv$linkinv,2),vv$mu.eta(2)) ## check derivative
示例：
set.seed(101)
n <- 1000
x <- runif(n)
sh <- 2
y <- rgamma(n,scale=vv$linkinv(2+3*x)/sh,shape=sh)
glm(y~x,family=Gamma(link=vv))
##
## Call: glm(formula = y ~ x, family = Gamma(link = vv))
##
## Coefficients:
## (Intercept) x
## 1.956 3.083
##
## Degrees of Freedom: 999 Total (i.e. Null); 998 Residual
## Null Deviance: 642.2
## Residual Deviance: 581.8 AIC: 4268
##
答案 1 :(得分：2)
试试gnlm::gnlr()。使用Ben Bolker示例中的x，y，sh：
library(gnlm)
# custom link / inverse
custom_inv <- function(eta) log(exp(eta)+1)
library(gnlm)
gnlr(y=y,
distribution = "gamma",
mu = ~ custom_inv(beta0 + beta1*x),
pmu = list(beta0=0, beta1=0),
pshape=sh
)
# Location parameters:
# estimate se
# beta0 1.956 0.1334
# beta1 3.083 0.2919
#
# Shape parameters:
# estimate se
# p[1] 0.625 0.04133