Average Marginal Effects

marginal_effects() computes average marginal effects (AMEs) for a fitted logistic_regression model — the Stata margins, dydx(*) workhorse. AMEs translate logit coefficients into the language reports actually use: percentage-point changes in the predicted probability.

For each continuous predictor, the AME is the derivative of the predicted probability with respect to that predictor, averaged over the observed sample. For each factor level, it is the average discrete change in predicted probability compared to the reference level.

Usage

marginal_effects(model, conf.level = 0.95, ...)

Arguments

model: A fitted model object. Currently implemented for logistic_regression results (ungrouped or grouped).
conf.level: Confidence level for the AME intervals (default 0.95).
...: Additional arguments (not used).

Value

An object of class "marginal_effects" whose $results tibble holds one row per predictor term (and group combination) with:

Term: Predictor name; factor rows read "var: level vs. ref"
Type: "dydx" (continuous derivative) or "discrete" (factor-level contrast)
AME: Average marginal effect on the probability scale
SE: Delta-method standard error
z, p_value: Wald test of the AME
CI_lower, CI_upper: Confidence interval at conf.level

Details

Understanding the Output

An AME of 0.03 for age means: averaged over the sample, one additional year of age increases the predicted probability of the outcome by 3 percentage points. Unlike odds ratios, AMEs are directly comparable across models and across groups, which is why they are the preferred reporting style in much of the social sciences.

When to Use This

To report logistic regression results on the probability scale instead of (or alongside) odds ratios
To compare predictor effects across groups (run on a group_by()-fitted model)

Technical Details

Continuous predictors use a centered numerical derivative of the predicted probability; factor predictors use the average discrete change against the reference level. Standard errors come from the delta method with the analytic gradient of the AME with respect to the coefficients and the model's Wald covariance matrix, matching the default in Stata's margins and R's margins package. Weighted models average with their frequency weights (unrounded, Charter §5.1); at weights == 1 the weighted AME reduces exactly to the unweighted one.

Linear regression: AMEs are not needed there — for a linear model without interactions or transformations, the unstandardized coefficient B is the marginal effect, already shown in the linear_regression coefficients table. Calling marginal_effects() on a linear_regression result says so instead of duplicating the table.

Validation: SPSS has no AME procedure, so this function is Tier 4 (Internal) under the Validation Charter — verified against the analytic logit-AME formula and an independent finite-difference delta-method recomputation, not against SPSS output.

Examples

data(survey_data)
survey_data$high_satisfaction <- as.integer(survey_data$life_satisfaction >= 4)

model <- logistic_regression(survey_data,
                             high_satisfaction ~ age + income + education)
marginal_effects(model)
#> Average Marginal Effects: high_satisfaction ~ age + income + education
#>   age: AME = 0.000, p = 0.730 
#>   income: AME = 0.000, p < 0.001 ***
#>   education: Intermediate Secondary vs. Basic Secondary: AME = 0.059, p = 0.023 *
#>   education: Academic Secondary vs. Basic Secondary: AME = 0.015, p = 0.600 
#>   education: University vs. Basic Secondary: AME = -0.014, p = 0.715 
#> AME = average change in predicted probability. Use summary() for detailed output.

# Weighted model
model_w <- logistic_regression(survey_data, high_satisfaction ~ age + income,
                               weights = sampling_weight)
marginal_effects(model_w)
#> Average Marginal Effects: high_satisfaction ~ age + income [Weighted]
#>   age: AME = 0.000, p = 0.639 
#>   income: AME = 0.000, p < 0.001 ***
#> AME = average change in predicted probability. Use summary() for detailed output.

# --- Three-layer output ---
ame <- marginal_effects(model)
ame                 # compact overview
#> Average Marginal Effects: high_satisfaction ~ age + income + education
#>   age: AME = 0.000, p = 0.730 
#>   income: AME = 0.000, p < 0.001 ***
#>   education: Intermediate Secondary vs. Basic Secondary: AME = 0.059, p = 0.023 *
#>   education: Academic Secondary vs. Basic Secondary: AME = 0.015, p = 0.600 
#>   education: University vs. Basic Secondary: AME = -0.014, p = 0.715 
#> AME = average change in predicted probability. Use summary() for detailed output.
summary(ame)        # full detailed output
#> 
#> Average Marginal Effects Results
#> --------------------------------
#> - Formula: high_satisfaction ~ age + income + education
#> - Scale: Predicted probability
#> - Std. errors: Delta method
#> - N: 2115
#> 
#>   ------------------------------------------------------------------------------------------------------------ 
#>   Term                                                      AME     SE       z      p  CI Lower  CI Upper  sig 
#>   ------------------------------------------------------------------------------------------------------------ 
#>   age                                                     0.000  0.001   0.344   .730    -0.001     0.001      
#>   income                                                  0.000  0.000  16.833  <.001     0.000     0.000  *** 
#>   education: Intermediate Secondary vs. Basic Secondary   0.059  0.026   2.268   .023     0.008     0.110    * 
#>   education: Academic Secondary vs. Basic Secondary       0.015  0.029   0.525   .600    -0.041     0.071      
#>   education: University vs. Basic Secondary              -0.014  0.038  -0.365   .715    -0.088     0.061      
#>   ------------------------------------------------------------------------------------------------------------ 
#> 
#> Factor rows show the average discrete change vs. the reference level.
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05