如何获取model.avg生成的GLMM模型平均预测值的标准误与置信区间？

Got it, let's work through this problem together. When you're dealing with model-averaged GLMMs from model.avg, the go-to tools like predictInterval or bootMer don't play nicely with the model.avg object directly—but there are three solid workarounds to get those confidence intervals and standard errors you need:

1. Manual Calculation (Fixed-Effects Only) #

This method uses the model-averaged coefficients and their variance-covariance matrix to compute SEs and CIs, focusing only on fixed effects (it doesn't account for random effect variability).

• First, extract the model-averaged coefficients and their variance-covariance matrix:

  # Get full model-averaged coefficients (including terms with zero weight)
  avg_coef <- coef(my_model_avg, full = TRUE)
  # Get corresponding variance-covariance matrix
  avg_vcov <- vcov(my_model_avg, full = TRUE)
  

• Next, build the design matrix for your new prediction data:

  # Use the fixed-effects formula from your model.avg object
  X <- model.matrix(formula(my_model_avg, fixed.only = TRUE), newdata = your_new_data)
  

• Calculate linear predictions and their SEs, then convert to the response scale (adjust the link function for your GLMM type—e.g., plogis for logistic, exp for Poisson):

  # Linear predictions (link scale)
  lin_pred <- X %*% avg_coef
  # SE of linear predictions
  lin_se <- sqrt(diag(X %*% avg_vcov %*% t(X)))
  
  # Convert to response scale (example: logistic GLMM)
  resp_pred <- plogis(lin_pred)
  # Use delta method to get SE on response scale
  resp_se <- lin_se * plogis(lin_pred) * (1 - plogis(lin_pred))
  
  # 95% confidence intervals on response scale
  resp_ci_lower <- plogis(lin_pred - 1.96 * lin_se)
  resp_ci_upper <- plogis(lin_pred + 1.96 * lin_se)
  

2. Model-by-Model Prediction + Weighted Averaging (Includes Random Effects) #

If you need to account for random effect variability, this approach computes predictions for each candidate model individually, then averages them using the AIC weights from your model.avg object.

• First, extract your candidate models and their weights:

  candidate_models <- my_model_avg$models
  model_weights <- my_model_avg$weights
  

• Use predictInterval (from merTools) to get predictions and intervals for each model, then weight-average the results:

  library(merTools)
  library(dplyr)
  
  # Store predictions for each model
  pred_results <- list()
  for (i in seq_along(candidate_models)) {
    # Get predictions with intervals for the current model
    mod_preds <- predictInterval(
      candidate_models[[i]],
      newdata = your_new_data,
      level = 0.95,
      type = "response"
    )
    # Attach the model's weight
    mod_preds$weight <- model_weights[i]
    pred_results[[i]] <- mod_preds
  }
  
  # Combine all results and compute weighted averages
  final_preds <- do.call(rbind, pred_results) %>%
    group_by(rowid) %>% # rowid links to rows in your_new_data
    summarize(
      avg_pred = weighted.mean(fit, weight),
      avg_lower_ci = weighted.mean(lwr, weight),
      avg_upper_ci = weighted.mean(upr, weight)
    )
  

3. Custom Bootstrap (Full Uncertainty, Slow but Rigorous) #

For the most rigorous approach that accounts for both model selection uncertainty and random effect variability, use a custom bootstrap workflow:

• Bootstrap steps: sample a candidate model by its AIC weight, then sample parameters from that model, compute predictions, and repeat thousands of times.

  set.seed(123) # Reproducibility
  n_boot_samples <- 1000
  boot_pred_matrix <- matrix(NA, nrow = nrow(your_new_data), ncol = n_boot_samples)
  candidate_models <- my_model_avg$models
  model_weights <- my_model_avg$weights
  
  for (b in 1:n_boot_samples) {
    # Sample a model based on its AIC weight
    sampled_mod_idx <- sample(seq_along(candidate_models), size = 1, prob = model_weights)
    sampled_model <- candidate_models[[sampled_mod_idx]]
    
    # Use bootMer to get a single prediction sample from the model
    boot_sample <- bootMer(
      sampled_model,
      FUN = function(x) predict(x, newdata = your_new_data, type = "response"),
      nsim = 1
    )
    boot_pred_matrix[, b] <- boot_sample$t
  }
  
  # Compute final predictions and 95% CIs from bootstrap distribution
  avg_boot_pred <- rowMeans(boot_pred_matrix)
  boot_ci <- apply(boot_pred_matrix, 1, quantile, probs = c(0.025, 0.975))
  

Quick Notes on Choosing a Method #

• Use Method 1 if you only care about fixed-effect uncertainty and want a fast, simple solution.
• Use Method 2 if you need to include random effect variability and want a balance of speed and rigor.
• Use Method 3 if you need to account for both model selection and random effect uncertainty (best for small datasets or critical analyses, but computationally intensive).

内容的提问来源于stack exchange，提问作者phil.fish