R：GLMM（lme4）的具有连续变量和分类变量的交互图

Question

我想制作一个交互图，以直观地显示回归模型结果中分类变量（4 个水平）和标准化连续变量的交互斜率的差异或相似性。

with(GLMModel, interaction.plot(continuous.var, categorical.var, response.var)) 不是我要找的。它会生成一个绘图，其中斜率随连续变量的每个值而变化。我正在寻找一个具有恒定斜率的图，如下图所示：

有什么想法吗？

我适合fit<-glmer(resp.var ~ cont.var*cat.var + (1|rand.eff) , data = sample.data , poisson) 形式的模型 以下是一些示例数据：

structure(list(cat.var = structure(c(4L, 4L, 1L, 4L, 1L, 2L, 
1L, 1L, 1L, 1L, 4L, 1L, 1L, 3L, 2L, 4L, 1L, 1L, 1L, 2L, 1L, 2L, 
2L, 1L, 3L, 1L, 1L, 2L, 4L, 1L, 2L, 1L, 1L, 4L, 1L, 3L, 1L, 3L, 
3L, 4L, 3L, 4L, 1L, 3L, 3L, 1L, 2L, 3L, 4L, 3L, 4L, 2L, 1L, 1L, 
4L, 1L, 1L, 1L, 1L, 1L, 1L, 4L, 1L, 4L, 4L, 3L, 3L, 1L, 3L, 3L, 
3L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 4L, 1L, 3L, 4L, 1L, 1L, 4L, 
1L, 3L, 1L, 1L, 3L, 2L, 4L, 1L, 4L, 1L, 4L, 4L, 4L, 4L, 2L, 4L, 
4L, 1L, 2L, 1L, 4L, 3L, 1L, 1L, 3L, 2L, 4L, 4L, 1L, 4L, 1L, 3L, 
2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 1L, 
2L, 2L, 1L, 1L, 2L, 3L, 1L, 4L, 4L, 4L, 1L, 4L, 4L, 3L, 2L, 4L, 
1L, 3L, 1L, 1L, 4L, 4L, 2L, 4L, 1L, 1L, 3L, 4L, 2L, 1L, 3L, 3L, 
4L, 3L, 2L, 3L, 1L, 4L, 2L, 2L, 1L, 4L, 1L, 2L, 3L, 4L, 1L, 4L, 
2L, 1L, 3L, 3L, 3L, 4L, 1L, 1L, 1L, 3L, 1L, 3L, 4L, 2L, 1L, 4L, 
1L, 1L, 1L, 2L, 1L, 1L, 4L, 1L, 3L, 1L, 2L, 1L, 4L, 1L, 2L, 4L, 
1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 3L, 1L, 3L, 4L, 1L, 4L, 3L, 
3L, 3L, 4L, 1L, 3L, 1L, 1L, 4L, 4L, 4L, 4L, 2L, 1L, 1L, 3L, 2L, 
1L, 4L, 4L, 2L, 4L, 2L, 4L, 1L, 3L, 4L, 1L, 1L, 2L, 3L, 2L, 4L, 
1L, 1L, 3L, 4L, 2L, 2L, 3L, 4L, 1L, 2L, 3L, 1L, 2L, 4L, 1L, 4L, 
2L, 4L, 3L, 4L, 2L, 1L, 1L, 1L, 1L, 1L, 4L, 4L, 1L, 4L, 4L, 1L, 
4L, 2L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 3L, 3L, 2L, 2L, 1L, 1L, 4L, 
1L, 4L, 3L, 1L, 2L, 1L, 4L, 2L, 4L, 4L, 1L, 2L, 1L, 1L, 1L, 4L, 
1L, 4L, 1L, 2L, 1L, 3L, 1L, 3L, 3L, 1L, 1L, 4L, 3L, 1L, 4L, 1L, 
2L, 4L, 1L, 1L, 3L, 3L, 2L, 4L, 4L, 1L, 1L, 2L, 2L, 1L, 2L, 4L, 
3L, 4L, 4L, 4L, 4L, 1L, 3L, 1L, 2L, 2L, 2L, 4L, 2L, 3L, 4L, 1L, 
3L, 2L, 2L, 1L, 1L, 1L, 3L, 1L, 2L, 2L, 1L, 1L, 3L, 2L, 1L, 1L, 
1L, 1L, 2L, 1L, 1L, 1L, 4L, 4L, 4L, 3L, 3L, 2L, 1L, 3L, 2L, 1L, 
1L, 1L, 4L, 1L, 1L, 2L, 3L, 1L, 1L, 2L, 4L, 3L, 2L, 4L, 3L, 2L, 
1L, 3L, 1L, 3L, 1L, 4L, 3L, 1L, 4L, 4L, 2L, 4L, 1L, 1L, 2L, 4L, 
4L, 2L, 3L, 4L, 4L, 3L, 1L, 4L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L, 
1L, 1L, 1L, 3L, 4L, 1L, 4L, 4L, 2L, 2L, 2L, 2L, 3L, 4L, 4L, 1L, 
1L, 4L, 2L, 3L, 3L, 1L, 1L, 1L, 1L, 3L, 1L, 1L, 1L, 3L, 4L, 2L, 
3L, 1L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 4L, 1L, 1L, 1L, 1L), .Label = c("A", 
"B", "C", "D"), class = "factor"), cont.var = c(-0.0682900527296927, 
0.546320421837542, -0.273160210918771, -0.887770685486005, 0.136580105459385, 
0.75119058002662, 0.546320421837542, -0.273160210918771, -0.682900527296927, 
0.136580105459385, 0.75119058002662, 0.75119058002662, 0.75119058002662, 
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0.75119058002662, 0.136580105459385), resp.var = c(2L, 1L, 0L, 
1L, 0L, 0L, 0L, 0L, 0L, 1L, 3L, 1L, 0L, 1L, 0L, 1L, 2L, 0L, 1L, 
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0L, 3L, 2L, 0L, 2L, 2L, 0L, 0L, 0L, 1L, 1L, 3L, 1L, 2L, 0L, 1L, 
0L, 0L, 1L, 0L, 2L, 0L, 2L, 4L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L, 
3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 2L, 
0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 2L, 0L, 1L, 0L, 4L, 1L, 0L, 
1L, 1L, 0L, 0L, 0L, 1L, 3L, 0L, 2L, 0L, 0L, 2L, 1L, 0L, 0L, 2L, 
0L, 0L, 0L, 2L, 0L, 0L, 3L, 0L, 0L, 2L, 1L, 1L, 0L, 0L, 3L, 1L, 
1L, 2L, 0L, 2L, 0L, 2L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 2L, 2L, 1L, 0L, 0L, 1L, 
0L, 0L, 0L, 0L, 6L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 
1L, 0L, 0L, 1L, 3L, 1L, 0L, 2L, 3L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 
0L, 0L, 0L, 0L, 1L, 2L, 1L, 1L, 0L, 0L, 2L, 0L, 2L, 0L, 0L, 1L, 
1L, 0L, 0L, 2L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
0L, 1L, 0L, 2L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 
0L, 3L, 0L, 0L, 3L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
0L, 2L, 1L, 1L, 0L, 2L, 2L, 0L, 2L, 1L, 0L, 2L, 0L, 0L, 0L, 0L, 
3L, 0L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 2L, 0L, 1L, 1L, 0L, 1L, 
0L, 3L, 1L, 3L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 2L, 0L, 
2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 2L, 0L, 3L, 0L, 0L, 0L, 
0L, 1L, 0L, 0L, 3L, 1L, 1L, 2L, 0L, 0L, 3L, 0L, 0L, 0L, 1L, 1L, 
0L, 1L, 3L, 0L, 2L, 0L, 0L, 1L, 3L, 1L, 0L, 0L, 4L, 3L, 0L, 2L, 
0L, 0L, 0L, 3L, 0L, 0L, 2L, 3L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 
0L, 0L, 0L, 3L, 3L, 2L, 0L, 0L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 
0L, 0L, 0L, 1L, 0L, 2L, 0L, 0L, 1L, 0L, 0L, 1L, 2L, 0L, 1L, 0L, 
2L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 3L, 1L, 0L, 0L, 0L, 0L, 0L, 
1L, 2L, 0L, 2L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 
0L, 0L, 3L, 2L, 2L, 0L, 1L, 0L, 5L, 0L, 4L, 2L, 0L, 3L, 0L, 0L, 
1L, 1L, 0L, 0L, 0L, 2L, 0L, 1L, 0L, 3L, 0L, 2L, 0L, 0L, 0L, 2L, 
0L), rand.eff = c(37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
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37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 37L, 
37L, 37L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
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40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L)), .Names = c("cat.var", 
"cont.var", "resp.var", "rand.eff"), row.names = c(NA, 500L), class = "data.frame")

Answer 1

这是一个各种各样的答案（顺便说一下，您在上面的数据框中缺少一些引号，必须手动修复......）

拟合模型：

library(lme4)
fit <- glmer(resp.var ~ cont.var:cat.var + (1|rand.eff) ,
           data = sample.data , poisson)

（请注意，这是一个有点奇怪的模型规范——强制所有类别在 cont.var==0 处具有相同的值。您的意思是 cont.var*cat.var 吗？

library(ggplot2)
theme_update(theme_bw())  ## set white rather than gray background

快速而肮脏的线性回归：

ggplot(sample.data,aes(cont.var,resp.var,linetype=cat.var))+
    geom_smooth(method="lm",se=FALSE)

现在使用泊松 GLM（但不包含随机效应），并显示数据点：

ggplot(sample.data,aes(cont.var,resp.var,colour=cat.var))+
    stat_sum(aes(size=..n..),alpha=0.5)+
    geom_smooth(method="glm",family="poisson")

下一位需要lme4的开发（r-forge）版本，它有一个predict方法：

设置数据框进行预测：

predframe <- with(sample.data,
                  expand.grid(cat.var=levels(cat.var),
                              cont.var=seq(min(cont.var),
                              max(cont.var),length=51)))

在人口水平 (REform=NA) 的线性预测 (logit) 尺度上进行预测（这是在绘图上获得直线的唯一方法）

predframe$pred.logit <- predict(fit,newdata=predframe,REform=NA)

minmaxvals <- range(sample.data$cont.var)

ggplot(predframe,aes(cont.var,pred.logit,linetype=cat.var))+geom_line()+
    geom_point(data=subset(predframe,cont.var %in% minmaxvals),
               aes(shape=cat.var))

现在在反应量表上：

predframe$pred <- predict(fit,newdata=predframe,REform=NA,type="response")
ggplot(predframe,aes(cont.var,pred,linetype=cat.var))+geom_line()+
    geom_point(data=subset(predframe,cont.var %in% minmaxvals),
               aes(shape=cat.var))

Answer 2

jtools 包 (CRAN link) 可以使此类模型的绘图变得非常简单。我是那个包的开发者。

我们将像 Ben 在他的回答中所做的那样拟合模型：

library(lme4)
fit <- glmer(resp.var ~ cont.var:cat.var + (1 | rand.eff),
             data = sample.data, family = poisson)

对于jtools，我们只需像这样使用interact_plot 函数：

library(jtools)
interact_plot(fit, pred = cont.var, modx = cat.var)

结果：

默认情况下，它绘制在响应比例上，但您可以使用outcome.scale = "link" 参数（默认为"response"）将其绘制在线性比例上。

Answer 3

effects 包支持lme4 模型，应该可以做你想做的事。

效果：线性、广义线性和其他模型的效果显示

具有线性预测变量的各种统计模型的图形和表格效果显示，例如交互作用。

它还附带了两个稍微过时的papers（您可以将它们视为小插曲）。