如何预测和绘制非线性变化的斜率？

Question

我的目标是使用R中的lmer和glmer包的lme4函数，从一个可变截距、变斜率的多级模型中计算预测值。为了使这个具体和清晰，我在这里给出一个带有“mtcar”数据集的玩具示例：

下面是我通常如何从一个变化的截距，变斜率的多级模型中创建预测值(这段代码应该工作得很好)：

# 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")

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上面的R代码应该可以工作，但是如果我想从一个非线性的变化截距，变斜率中创建和绘制预测，那么它显然失败了。为了简单和可重复性，下面是使用“mtcar”数据集的绊脚石：

# 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")

​

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显然，预测框架没有正确设置。对于如何在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有任何想法吗？谢谢!

Answer 1

问题是，当您将expand.grid与wt和wt^2同时使用时，您将创建wt和wt^2的所有可能组合。对代码的这种修改是有效的：

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")