如何计算广义线性混合模型中缺失的变量个体输出值？

Hey there, let's work through how to calculate those missing individual values for your GLMM. First, let's lay out your model details clearly to make sure we're aligned:

Your GLMM Overview #

• Model Type: Generalized Linear Mixed Model (GLMM), fit via Maximum Likelihood (Laplace Approximation) — object class: glmerMod
• Family/Link: Binomial with logit link
• Formula: active ~ tair * breeding + (1 | id/family)
• Dataset: adata_sc

Fit Statistics

• AIC: 1948.6
• BIC: 2000.1
• logLik: -966.3
• Deviance: 1932.6
• Residual Degrees of Freedom: 4584

Scaled Residuals

Min 1Q Median 3Q Max
-24.1182 0.0720 0.1422 ...

Calculating Individual Values for tair & breeding #

Since you mentioned "individual values", I'll cover the most common use cases (predicting response values per observation, and extracting variable-specific effects) using R code (since you're using glmer from the lme4 package):

1. Predict Individual-Level Response Probabilities

If you want the predicted probability of active for each observation (accounting for both fixed effects and your random id/family grouping), use the predict() function:

# Replace `your_model` with the name of your glmer object
adata_sc$predicted_active <- predict(your_model, newdata = adata_sc, type = "response", re.form = NULL)

• type = "response" gives probabilities (instead of logit-scale values)
• re.form = NULL includes random effects to get individual-specific predictions; use re.form = ~0 if you want population-average predictions (ignoring random effects)

2. Extract Fixed Effect Contributions for Each Variable

Your model includes an interaction between tair (continuous) and breeding (3-level factor), so we can break down their effects per observation:
First, extract the fixed effect coefficients:

fixed_coefs <- fixef(your_model)

Your coefficients will look something like this (matching your breeding level names):

• (Intercept): Logit value when tair = 0 and breeding is at its reference level
• tair: Slope of tair for the reference breeding level
• breeding[Level2]: Difference in intercept for Level2 vs reference
• breeding[Level3]: Difference in intercept for Level3 vs reference
• tair:breeding[Level2]: Difference in tair slope for Level2 vs reference
• tair:breeding[Level3]: Difference in tair slope for Level3 vs reference

Then calculate the logit-scale linear predictor for each observation, and convert to probability:

# Calculate logit-scale prediction
adata_sc$linear_pred <- with(adata_sc,
  fixed_coefs["(Intercept)"] +
  fixed_coefs["tair"] * tair +
  fixed_coefs[paste0("breeding", breeding)] +  # Match your breeding level labels
  fixed_coefs[paste0("tair:breeding", breeding)] * tair
)

# Convert to probability scale
adata_sc$prob_pred <- plogis(adata_sc$linear_pred)

3. Get Marginal Effects (Simpler Interpretation)

For a more intuitive view of how tair acts across each breeding level (or vice versa), use the emmeans package:

library(emmeans)

# Get the slope of tair for each breeding level (logit scale)
tair_trends <- emtrends(your_model, ~ breeding, var = "tair")
# Convert to probability-scale effects
tair_trends_prob <- regrid(tair_trends, transform = "response")

# Or predict probabilities for specific tair values across breeding levels
breeding_preds <- emmeans(your_model, ~ breeding, at = list(tair = seq(min(adata_sc$tair), max(adata_sc$tair), length.out = 5)))
breeding_preds_prob <- regrid(breeding_preds, transform = "response")

内容的提问来源于stack exchange，提问作者Krista Oswald