R语言lme4包glmer函数能否纳入相关结构及默认设置咨询

Hey there! Let's break down your questions about using glmer() from the lme4 package for your Bernoulli longitudinal data, using your code as context.

1. Can glmer() include Mc1/MC2 correlation structures? #

Short answer: No, you can't directly specify Mc1/MC2 (or other explicit correlation structures like autoregressive or unstructured) in glmer().

The lme4 package’s mixed models (including glmer() for generalized linear mixed models) rely on a random effects framework to handle clustering/longitudinal dependence. Instead of defining explicit correlation structures (like those used in the bild package or nlme’s corAR1), lme4 captures dependence by estimating the covariance matrix of random effects.

For example, your model uses (1 | School) to add a random intercept for each school—this assumes observations from the same school share a common unmeasured effect, and the covariance between any two observations from the same school is determined by the variance of this random intercept.

2. What's the default correlation structure in glmer()? #

When you fit a model like your mm2 (with a random intercept (1 | School)), the marginal correlation structure (correlation between observations without conditioning on random effects) is Compound Symmetry (CS). Here’s what that means:

• Any two observations from the same school have the same correlation coefficient (calculated as σ_b² / (σ_b² + σ_e²), where σ_b² is the random intercept variance and σ_e² is the residual variance).
• Observations from different schools have zero correlation.

When conditioning on the random effects (i.e., once you account for the school-level intercept), the model assumes residual errors are independent and identically distributed (i.i.d.).

Alternative Packages for Explicit Correlation Structures #

If you need to use structures like Mc1/MC2 (or other flexible correlation structures) for your Bernoulli longitudinal data, consider these packages:

• glmmTMB: Supports both random effects and explicit correlation structures for generalized linear mixed models.
• brms: Uses Bayesian methods and allows for a wide range of correlation structures via its intuitive syntax.
• gee: Fits marginal models (instead of mixed models) with various correlation structures, though it doesn’t include random effects.

Your Formatted R Code Example #

library(dplyr)
n = 300
xx<-c("r1","r2","r3","r4","r5")
xxx<-c("e1","e2","e3")
p=0.3

df1 <- data_frame(
  xx1 = runif(n, min = 0, max = 10),
  xx2 = runif(n, min = 0, max = 10),
  xx3 = runif(n, min = 0, max = 10),
  School = factor(sample(xxx, n,re=TRUE)),
  yx = as.factor(rbinom(n, size = 1, prob = p))
)

library(lme4)
mm2 <- glmer(yx ~ xx1 + xx2 + xx3 + (1 | School), 
             data = df1, 
             family = "binomial",
             control = glmerControl(calc.derivs = FALSE))

内容的提问来源于stack exchange，提问作者Cleber Iack