Normalized Generalized R-squared for Binomial GLMs

Computes the normalized generalized R-squared coefficient for binomial GLMs. The normalization scales the R-squared by its maximum possible value for the specified set of terms.

Usage

.socket_compute_gR2_n(terms, full_glm, null_glm = NULL, algorithm, control)

Arguments

terms

Character vector of variable names for which to compute normalized R-squared. If `NULL` (default), computes for all non-intercept terms in the model.

full_glm

A fitted GLM object of class `glm` with binomial family.

null_glm

A fitted GLM object of class `glm` (the null model). If `NULL` (default), uses an empty model (intercept-only if intercept is present, otherwise no predictors).

algorithm

`"auto"` by default. It chooses between `"brute_force"` and `"multi_start"`

algorithm.control

`list` of control parameters:

• `n_exact` Integer specifying the sample size threshold for using exact methods (brute force). Default is 15.

• `thresholds` Numeric vector of threshold values for multi-start initialization.

• `n_random` Integer number of random starts for multi-start optimization.

• `max_iter` Integer maximum number of iterations per start.

• `topK` Integer number of top candidates to consider at each iteration.

• `tol` Numeric tolerance for convergence.

• `patience` Integer number of iterations without improvement before stopping.

Value

A list with components:

R2

The generalized R-squared coefficient for the set of terms

R2_n

The normalized generalized R-squared coefficient

algorithm

The algorithm used to compute the maximum R-squared

terms_tested

The names of the terms included in the test

Details

The normalized generalized R-squared is computed as: $$ R^2_n = \frac{R^2}{R^2_{\max}} $$ where \(R^2_{\max}\) is the maximum possible R-squared value for the specified set of terms.

Different algorithms are used based on sample size:

• For small samples (\(n \leq n_{\text{exact}}\)), brute force search finds the exact maximum

• For larger samples, a greedy multi-start algorithm finds approximate maximum

Examples

set.seed(123)
dt <- data.frame(X = rnorm(20),
                 Z = factor(rep(LETTERS[1:3], length.out = 20)))
dt$Y <- rbinom(n = 20, prob = plogis((dt$Z == "C") * 2), size = 1)
mod <- glm(Y ~ Z + X, data = dt, family = binomial)

# Compute generalized partial correlations for all variables
(results <-  gR2_normalized_binom(mod))
#> Error in gR2_normalized_binom(mod): could not find function "gR2_normalized_binom"
# equivalent to
mod0=glm(Y~1,data=dt,family=binomial)
(results <-  gR2_normalized_binom(mod, mod0))
#> Error in gR2_normalized_binom(mod, mod0): could not find function "gR2_normalized_binom"

# Compute for specific variables only
(results <-  gR2_normalized_binom(mod,terms = c("X","Z")))
#> Error in gR2_normalized_binom(mod, terms = c("X", "Z")): could not find function "gR2_normalized_binom"