Term-level partial R-squared and Cohen's f-squared

partial_r2() calculates term-level effect sizes for a linear model. Each row describes what happens when one model term is removed after accounting for the other terms in the model.

Usage

partial_r2(model, details = FALSE)

Arguments

model: An stats::lm() or honest_lm object.
details: Logical. If FALSE, return only the term, degrees of freedom, partial R-squared, and f-squared. If TRUE, also return the partial F statistic, p-value, full-model residual sum of squares, reduced-model residual sum of squares, and their difference.

Value

A tibble with one row per model term and columns:

term: The model term being evaluated.
df: The degrees of freedom for the term. Multi-level categorical predictors usually have more than one degree of freedom.
partial_r2: The partial R-squared for the term. This is the proportion of the reduced model's residual sum of squares that is explained by adding the term back to the model. Partial R-squared values do not generally add up to the model R-squared.
f2: Cohen's f-squared for the term, calculated as partial_r2 / (1 - partial_r2).
statistic: The partial F statistic, returned when details = TRUE.
p_value: The p-value for the partial F test, returned when details = TRUE.
ss_full_error: The residual sum of squares for the full model, returned when details = TRUE.
ss_reduced_error: The residual sum of squares for the model with the term removed, returned when details = TRUE.
delta_ss: The increase in residual sum of squares when the term is removed, returned when details = TRUE.

Details

Partial R-squared asks how much additional residual variation is explained by a term, given the other terms already in the model. Cohen's f-squared is a related effect size that expresses that contribution relative to the residual variation left in the full model.

These are term-level quantities, not coefficient-level quantities. A categorical predictor with more than two levels, such as location, gets one row because it is one model term, even though it creates multiple coefficient rows in summary().

For each term, partial_r2() compares the full model to a reduced model that drops that term. It uses the same single-term deletion logic as stats::drop1() with an F test.

For a term with df degrees of freedom:

partial_r2 = delta_ss / ss_reduced_error

f2 = delta_ss / ss_full_error

where ss_full_error is the residual sum of squares for the full model, ss_reduced_error is the residual sum of squares after dropping the term, and delta_ss = ss_reduced_error - ss_full_error.

These effect sizes answer adjusted, model-dependent questions. If predictors are correlated, a term's partial R-squared describes its contribution after accounting for the other terms in that specific model. For models with interactions, term-level interpretation can be more subtle because main effects and interactions depend on each other.

Examples

fit <- lm(mpg ~ wt + hp + factor(cyl), data = mtcars)
partial_r2(fit)
#> # A tibble: 3 × 4
#>   term           df partial_r2    f2
#>   <chr>       <dbl>      <dbl> <dbl>
#> 1 wt              1      0.420 0.724
#> 2 hp              1      0.122 0.139
#> 3 factor(cyl)     2      0.176 0.213

partial_r2(fit, details = TRUE)
#> # A tibble: 3 × 9
#>   term      df partial_r2    f2 statistic p_value ss_full_error ss_reduced_error
#>   <chr>  <dbl>      <dbl> <dbl>     <dbl>   <dbl>         <dbl>            <dbl>
#> 1 wt         1      0.420 0.724     19.5  1.44e-4          161.             277.
#> 2 hp         1      0.122 0.139      3.74 6.36e-2          161.             183.
#> 3 facto…     2      0.176 0.213      2.88 7.36e-2          161.             195.
#> # ℹ 1 more variable: delta_ss <dbl>