如何预测和绘制lmer或glmer中的非线性变化斜率？

Question

我的目标是使用R中lme4包的lmer和glmer函数，从变截距，变斜率多级模型计算预测值。并且清楚，我在这里展示了一个玩具示例，其中包括＆＃34; mtcars＆＃34;数据集：

以下是我通常如何通过变截距，变斜率多级模型创建预测值（此代码应该可以正常工作）：

# loading in-built cars dataset
data(mtcars)

# the "gear" column will be the group-level factor, so we'll have cars nested 
# within "gear" type
mtcars$gear <- as.factor(mtcars$gear)

# fitting varying-slope, varying-intercept model
m <- lmer(mpg ~ 1 + wt + hp + (1 + wt|gear), data=mtcars)

# creating the prediction frame
newdata <- with(mtcars, expand.grid(wt=unique(wt),
                              gear=unique(gear),
                              hp=mean(hp)))

# calculating predictions
newdata$pred <- predict(m, newdata, re.form=~(1 + wt|gear))

# quick ggplot2 graph
p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear))
p + geom_line() + ggtitle("Varying Slopes")

上面的R代码应该可以工作，但是如果我想从非线性变量截距，变化斜率创建和绘制预测，那么它显然会失败。为了简单和可重复，这里是使用＆＃34; mtcars＆＃34;的绊脚石。数据集：

# key question: how to create predictions if I want to examine a non-linear 
# varying slope?

# creating a squared term for a non-linear relationship
# NB: usually I use the `poly` function
mtcars$wtsq <- (mtcars$wt)^2

# fitting varying-slope, varying-intercept model with a non-linear trend
m <- lmer(mpg ~ 1 + wt + wtsq + hp + (1 + wt + wtsq|gear), data=mtcars)

# creating the prediction frame
newdata <- with(mtcars, expand.grid(wt=unique(wt),
                                wtsq=unique(wtsq),
                                gear=unique(gear),
                                hp=mean(hp)))

# calculating predictions
newdata$pred <- predict(m, newdata, re.form=~(1 + wt + wtsq|gear))

# quick ggplot2 graph 
# clearly not correct (see the graph below)
p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear))
p + geom_line() + ggtitle("Varying Slopes")

显然，预测帧未正确设置。在R中拟合非线性变截距，变斜率多级模型时，如何创建和绘制预测值的任何想法？谢谢！

Answer 1

问题是，当expand.grid与wt同时使用wt^2时，您会创建wt和wt^2的所有可能组合。您对代码的修改有效：

newdata <- with(mtcars, expand.grid(wt=unique(wt),
                                gear=unique(gear),
                                hp=mean(hp)))
newdata$wtsq <- newdata$wt^2

newdata$pred <- predict(m, newdata)

p <- ggplot(newdata, aes(x=wt, y=pred, colour=gear, group=gear))
p + geom_line() + ggtitle("Varying Slopes")