我正在使用lme4软件包运行glmer logit模型。我对两种和三种方式的交互作用及其解释感兴趣。为简化起见,我只关注固定效应系数。
我设法提出了一个代码,以在logit尺度上计算和绘制这些影响,但是我很难将它们转换为预测的概率尺度。最终,我想复制effects
包的输出。
该示例依赖于UCLA's data on cancer patients。
library(lme4)
library(ggplot2)
library(plyr)
getmode <- function(v) {
uniqv <- unique(v)
uniqv[which.max(tabulate(match(v, uniqv)))]
}
facmin <- function(n) {
min(as.numeric(levels(n)))
}
facmax <- function(x) {
max(as.numeric(levels(x)))
}
hdp <- read.csv("http://www.ats.ucla.edu/stat/data/hdp.csv")
head(hdp)
hdp <- hdp[complete.cases(hdp),]
hdp <- within(hdp, {
Married <- factor(Married, levels = 0:1, labels = c("no", "yes"))
DID <- factor(DID)
HID <- factor(HID)
CancerStage <- revalue(hdp$CancerStage, c("I"="1", "II"="2", "III"="3", "IV"="4"))
})
到这里为止都是我需要的所有数据管理,功能和软件包。
m <- glmer(remission ~ CancerStage*LengthofStay + Experience +
(1 | DID), data = hdp, family = binomial(link="logit"))
summary(m)
这就是模型。它需要一分钟,并且会与以下警告融合:
Warning message:
In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
Model failed to converge with max|grad| = 0.0417259 (tol = 0.001, component 1)
即使我不太确定是否应该担心该警告,我还是使用估计来绘制兴趣交互的平均边际效应。首先,我准备要输入
predict
函数的数据集,然后使用固定效果参数计算边际效果以及置信区间。newdat <- expand.grid(
remission = getmode(hdp$remission),
CancerStage = as.factor(seq(facmin(hdp$CancerStage), facmax(hdp$CancerStage),1)),
LengthofStay = seq(min(hdp$LengthofStay, na.rm=T),max(hdp$LengthofStay, na.rm=T),1),
Experience = mean(hdp$Experience, na.rm=T))
mm <- model.matrix(terms(m), newdat)
newdat$remission <- predict(m, newdat, re.form = NA)
pvar1 <- diag(mm %*% tcrossprod(vcov(m), mm))
cmult <- 1.96
## lower and upper CI
newdat <- data.frame(
newdat, plo = newdat$remission - cmult*sqrt(pvar1),
phi = newdat$remission + cmult*sqrt(pvar1))
我相当有信心这些是对数刻度的正确估计,但也许我错了。无论如何,这是情节:
plot_remission <- ggplot(newdat, aes(LengthofStay,
fill=factor(CancerStage), color=factor(CancerStage))) +
geom_ribbon(aes(ymin = plo, ymax = phi), colour=NA, alpha=0.2) +
geom_line(aes(y = remission), size=1.2) +
xlab("Length of Stay") + xlim(c(2, 10)) +
ylab("Probability of Remission") + ylim(c(0.0, 0.5)) +
labs(colour="Cancer Stage", fill="Cancer Stage") +
theme_minimal()
plot_remission
我认为现在OY量表是按logit量表测量的,但要理解这一点,我想将其转换为预测的概率。基于wikipedia,诸如
exp(value)/(exp(value)+1)
之类的方法可以解决所需的预测概率。虽然我可以做到newdat$remission <- exp(newdat$remission)/(exp(newdat$remission)+1)
,但我不确定如何在置信区间内做到这一点?最终,我想了解
effects
包生成的图。那是:eff.m <- effect("CancerStage*LengthofStay", m, KR=T)
eff.m <- as.data.frame(eff.m)
plot_remission2 <- ggplot(eff.m, aes(LengthofStay,
fill=factor(CancerStage), color=factor(CancerStage))) +
geom_ribbon(aes(ymin = lower, ymax = upper), colour=NA, alpha=0.2) +
geom_line(aes(y = fit), size=1.2) +
xlab("Length of Stay") + xlim(c(2, 10)) +
ylab("Probability of Remission") + ylim(c(0.0, 0.5)) +
labs(colour="Cancer Stage", fill="Cancer Stage") +
theme_minimal()
plot_remission2
即使我可以只使用
effects
包,但不幸的是,它无法与我必须为自己的工作运行的许多模型一起编译:Error in model.matrix(mod2) %*% mod2$coefficients :
non-conformable arguments
In addition: Warning message:
In vcov.merMod(mod) :
variance-covariance matrix computed from finite-difference Hessian is
not positive definite or contains NA values: falling back to var-cov estimated from RX
要解决此问题,需要调整估算程序,此刻我想避免。另外,我也很好奇
effects
在这里实际做什么。我将非常感谢您提供有关如何调整初始语法以达到预测概率的建议!
最佳答案
要获得与问题中提供的effect
函数相似的结果,只需使用提供的转换将预测值和置信区间的边界从对数刻度转换为原始刻度即可:exp(x)/(1+exp(x))
。
可以使用plogis
函数在base R中完成此转换:
> a <- 1:5
> plogis(a)
[1] 0.7310586 0.8807971 0.9525741 0.9820138 0.9933071
> exp(a)/(1+exp(a))
[1] 0.7310586 0.8807971 0.9525741 0.9820138 0.9933071
因此,使用@ eipi10的建议,使用丝带作为置信带,而不是虚线(我也觉得此演示文稿更具可读性):
ggplot(newdat, aes(LengthofStay, fill=factor(CancerStage), color=factor(CancerStage))) +
geom_ribbon(aes(ymin = plogis(plo), ymax = plogis(phi)), colour=NA, alpha=0.2) +
geom_line(aes(y = plogis(remission)), size=1.2) +
xlab("Length of Stay") + xlim(c(2, 10)) +
ylab("Probability of Remission") + ylim(c(0.0, 0.5)) +
labs(colour="Cancer Stage", fill="Cancer Stage") +
theme_minimal()
结果是相同的(使用
effects_3.1-2
和lme4_1.1-13
):> compare <- merge(newdat, eff.m)
> compare[, c("remission", "plo", "phi")] <-
+ sapply(compare[, c("remission", "plo", "phi")], plogis)
> head(compare)
CancerStage LengthofStay remission Experience plo phi fit se lower upper
1 1 10 0.20657613 17.64129 0.12473504 0.3223392 0.20657613 0.3074726 0.12473625 0.3223368
2 1 2 0.35920425 17.64129 0.27570456 0.4522040 0.35920425 0.1974744 0.27570598 0.4522022
3 1 4 0.31636299 17.64129 0.26572506 0.3717650 0.31636299 0.1254513 0.26572595 0.3717639
4 1 6 0.27642711 17.64129 0.22800277 0.3307300 0.27642711 0.1313108 0.22800360 0.3307290
5 1 8 0.23976445 17.64129 0.17324422 0.3218821 0.23976445 0.2085896 0.17324530 0.3218805
6 2 10 0.09957493 17.64129 0.06218598 0.1557113 0.09957493 0.2609519 0.06218653 0.1557101
> compare$remission-compare$fit
[1] 8.604228e-16 1.221245e-15 1.165734e-15 1.054712e-15 9.714451e-16 4.718448e-16 1.221245e-15 1.054712e-15 8.326673e-16
[10] 6.383782e-16 4.163336e-16 7.494005e-16 6.383782e-16 5.689893e-16 4.857226e-16 2.567391e-16 1.075529e-16 1.318390e-16
[19] 1.665335e-16 2.081668e-16
置信边界之间的差异较高,但仍然很小:
> compare$plo-compare$lower
[1] -1.208997e-06 -1.420235e-06 -8.815678e-07 -8.324261e-07 -1.076016e-06 -5.481007e-07 -1.429258e-06 -8.133438e-07 -5.648821e-07
[10] -5.806940e-07 -5.364281e-07 -1.004792e-06 -6.314904e-07 -4.007381e-07 -4.847205e-07 -3.474783e-07 -1.398476e-07 -1.679746e-07
[19] -1.476577e-07 -2.332091e-07
但是,如果我使用正态分布
cmult <- qnorm(0.975)
的实际分位数而不是cmult <- 1.96
,那么对于这些边界,我也会获得非常小的差异:> compare$plo-compare$lower
[1] 5.828671e-16 9.992007e-16 9.992007e-16 9.436896e-16 7.771561e-16 3.053113e-16 9.992007e-16 8.604228e-16 6.938894e-16
[10] 5.134781e-16 2.289835e-16 4.718448e-16 4.857226e-16 4.440892e-16 3.469447e-16 1.006140e-16 3.382711e-17 6.765422e-17
[19] 1.214306e-16 1.283695e-16