无需构建双模型及ANOVA，如何比较同一回归的标准化β系数？

Great question! You absolutely don't need to fit two separate models or run an ANOVA to compare standardized β coefficients from the same multiple regression model. There are much simpler, single-function approaches to do this directly with your existing model. Let's walk through the most practical methods using your example:

Method 1: Use linearHypothesis() from the car package #

This is a robust, widely-used approach that leverages linear hypothesis testing to compare the standardized coefficients. Since standardized β = unstandardized β * (SD of predictor / SD of outcome), we can frame the test as checking if the scaled unstandardized coefficients are equal.

Here's how to apply it to your model:

# Load required packages
library(car)
library(lm.beta)

# Fit your original unstandardized model (needed for hypothesis testing)
fit1 <- lm(Umint_gesamt ~ Alter + Geschlecht_Dummy + SE_gesamt + CE_gesamt + EmoP_gesamt + Emp_gesamt + IN_gesamt + DN_gesamt + SozID_gesamt, data=dataset)

# Calculate standard deviations for scaling
sd_se <- sd(dataset$SE_gesamt, na.rm = TRUE)
sd_ce <- sd(dataset$CE_gesamt, na.rm = TRUE)

# Test the hypothesis that standardized β_SE = standardized β_CE
# The outcome SD cancels out, so we simplify to comparing scaled unstandardized coefficients
hypothesis_test <- linearHypothesis(fit1, paste0("SE_gesamt * ", sd_se, " = CE_gesamt * ", sd_ce))

# View results
print(hypothesis_test)

Interpretation: Check the Pr(>F) value. If it falls below your significance threshold (e.g., 0.05), you can conclude the two standardized β coefficients are significantly different.

Method 2: Use beta_compare() from the reghelper package #

For an even more streamlined workflow, the reghelper package has a dedicated function that handles all the scaling and testing automatically—no manual calculations needed:

# Install the package first if you haven't
# install.packages("reghelper")
library(reghelper)

# Fit your original model
fit1 <- lm(Umint_gesamt ~ Alter + Geschlecht_Dummy + SE_gesamt + CE_gesamt + EmoP_gesamt + Emp_gesamt + IN_gesamt + DN_gesamt + SozID_gesamt, data=dataset)

# Compare the two standardized coefficients directly
beta_compare(fit1, c("SE_gesamt", "CE_gesamt"))

This function outputs the difference between the standardized βs, its standard error, a t-statistic, and a p-value for the test that the difference equals zero. It’s a one-step solution tailored exactly for this use case.

Why two models/ANOVA aren't necessary #

ANOVA is designed to compare overall fits of nested models, but here we’re testing a specific parameter constraint within a single model. Linear hypothesis testing targets this constraint directly, eliminating the need to refit models and making the process far more efficient.

内容的提问来源于stack exchange，提问作者Karen H