求SAS中按Fish个体的随机残差模型的R等效实现方案

Got it, let's break down how to replicate your SAS GLIMMIX models in R, since your initial lmer attempt hit a syntax issue. Here are solutions using lme4 (for linear and generalized linear mixed models) and nlme (for flexible covariance structures, which matches SAS's functionality closely):

1. Replicate your first SAS model with lme4::lmer #

Your first SAS model uses random residual / subject=fish to model fish-level residual variation. In lmer, we don't use resid() in the random effect syntax—instead, we explicitly model fish-level heterogeneity with a random intercept, which captures the same individual-level residual variation as your SAS code.

library(lme4)
# Match the first SAS model: fixed effects + fish random intercept
model_lmer <- lmer(
  increment ~ age + growth_year + age:growth_year + (1 | fish),
  data = SR_data
)

This model estimates fixed effects for age, growth_year, and their interaction, plus a random intercept for each fish to account for unmeasured individual differences (exactly what your SAS random residual / subject=fish does).

2. Gamma distribution alternative with lme4::glmer #

If you want to replace the normal distribution with a gamma distribution (like a generalized linear mixed model in SAS), use glmer with the Gamma family. Note that gamma models require positive response values, so ensure increment has no zeros or negatives.

# Gamma GLMM with log link (common for positive continuous outcomes)
model_glmer_gamma <- glmer(
  increment ~ age + growth_year + age:growth_year + (1 | fish),
  data = SR_data,
  family = Gamma(link = "log")
)

You can adjust the link function (e.g., inverse) if it better fits your data's relationship.

3. Replicate both SAS models (including AR(1) structure) with nlme::lme #

The nlme package is ideal for matching SAS's complex residual covariance structures, since it lets you explicitly define how residuals correlate within groups.

First SAS model (independent residuals by fish)

library(nlme)
# Match initial SAS model: fixed effects + fish random intercept + independent residuals
model_lme_ind <- lme(
  increment ~ age + growth_year + age:growth_year,
  data = SR_data,
  random = ~1 | fish,  # Fish-level random variation
  method = "ML"  # Use REML if you want to match SAS's default, but ML works too
)

SAS model with AR(1) covariance structure

This directly replicates your second SAS code, where residuals follow an autoregressive order-1 structure within each fish:

# Match AR(1) residual structure from SAS
model_lme_ar1 <- lme(
  increment ~ age + growth_year + age:growth_year,
  data = SR_data,
  random = ~1 | fish,
  correlation = corAR1(form = ~1 | fish),  # AR(1) correlation within fish
  method = "ML"
)

Why your original lmer code failed #

The syntax (resid()|fish) isn't supported in lme4—lmer doesn't let you explicitly model residuals as random effects. Instead, random intercepts (or slopes) capture group-level variation, and the model's default residual term handles within-group variation.

内容的提问来源于stack exchange，提问作者Devon Oliver