Summary
The question revolves around calculating predicted values for a mixed linear model averaged over random effects and computing differences between levels for factor variable groups. The user is seeking an R package to simplify these calculations, including the computation of standard errors (SEs) and 95% confidence intervals (CIs).
Root Cause
The root cause of the issue is the complexity of dealing with mixed effects models and the desire for a straightforward method to calculate predicted values averaged over random effects and to perform difference-in-differences analyses.
Why This Happens in Real Systems
This occurs in real systems due to the inherent complexity of mixed effects models, which account for both fixed and random effects. Calculating predicted values and performing comparisons between groups while averaging over random effects requires careful consideration of the model’s structure and the variability introduced by random effects.
Real-World Impact
In real-world applications, particularly in fields like biomedical research, psychology, and social sciences, understanding the effects of different factors (while controlling for the variability introduced by random effects) is crucial. Accurate calculation of predicted values and differences between groups can inform policy decisions, treatment strategies, and further research directions.
Example or Code
library(lme4)
library(emmeans)
# Mixed linear model
m <- lmer(log(distance) ~ age * Sex + (1|Subject), data = Orthodont)
# Predicted values for the fixed effects part of the model
p_log <- predict(m, re.form = NA)
# Convert to response scale
p_distance <- exp(p_log)
# Merge predicted values with original data
pred_data <- cbind(Orthodont, p_distance)
# Use emmeans for average predictions and comparisons
em_m <- emmeans(m, ~ age * Sex)
# Average predictions
summary(em_m)
# Pairwise comparisons including SEs and 95% CIs
pairs(em_m)How Senior Engineers Fix It
Senior engineers typically approach this problem by leveraging specialized R packages like emmeans, which provides a straightforward interface for calculating marginal means (predictors) and performing pairwise comparisons, including the computation of SEs and 95% CIs. They recognize the importance of accounting for the model's random effects structure in these calculations.
Why Juniors Miss It
Juniors may miss this solution because they are less familiar with the specialized packages available for mixed effects models or may not fully understand the nuances of calculating predicted values in the context of random effects. The complexity of mixed models and the variety of R packages available can make it difficult for less experienced engineers to identify the most appropriate tools and methods for their specific needs.