关于R语言lme4包多层模型随机效应置信区间的疑问

Hey Simon, great call on your initial guess—you’re totally right about sd_(Intercept)|id! Let’s unpack each of these random effect confidence interval terms from your lme4 output clearly:

What Each Term Means #

• sd_(Intercept)|id: As you suspected, this is the 95% confidence interval for the standard deviation of the random intercepts grouped by id. In multilevel modeling, we assume every id group has its own intercept that deviates from the overall fixed-effect intercept. This interval quantifies the plausible range of how much those group-specific intercepts vary, with 95% statistical confidence.
• sd_fd|id: This represents the 95% confidence interval for the standard deviation of the random slopes for the fd variable across id groups. If your model includes a random slope for fd (like specifying (fd | id) in your formula), this tells you how much the effect of fd differs from group to group—and the range that variation is likely to fall into.
• cor_fd.(Intercept)|id: This is the 95% confidence interval for the correlation between the random intercepts and random slopes for fd within id groups. For example, a positive correlation here would mean groups with higher-than-average intercepts tend to also have stronger (higher) slopes for fd, while a negative correlation would mean the opposite. The interval shows where the true population correlation is likely to lie.

A quick note: These intervals are typically calculated using profile likelihood or bootstrapping in lme4 (depending on which method you used with confint()), so they reflect uncertainty around the estimated random effect variance/covariance parameters.

内容的提问来源于stack exchange，提问作者Simon