cp_F {gspcr}

Compute F statistic

Description

Computes the F statistic comparing two nested models.

Usage

cp_F(y, y_hat_restricted, y_hat_full, n = length(y), p_restricted = 0, p_full)

Arguments

y

numeric vector storing the observed values on the dependent variable

y_hat_restricted

numeric vector storing the predicted values on y based on the restricted model

y_hat_full

numeric vector storing the predicted values on y based on the full model

n

numeric vector of length 1 storing the sample size used to train the models

p_restricted

numeric vector of length 1 storing the number of predictors involved in training the restricted model

p_full

numeric vector of length 1 storing the number of predictors involved in training the full model

Details

Note that:

• The full model is always the model with more estimated parameters, the model with more predictor variables.

• The restricted model is the model with fewer estimated parameters.

• The restricted model must be nested within the full model.

Value

numeric vector of length 1 storing the F-statistic

Author(s)

Edoardo Costantini, 2023

Examples

# Null vs full model
lm_n <- lm(mpg ~ 1, data = mtcars) # Fit a null model
lm_f <- lm(mpg ~ cyl + disp, data = mtcars) # Fit a full model
f_M <- cp_F(
    y = mtcars$mpg,
    y_hat_restricted = predict(lm_n),
    y_hat_full = predict(lm_f),
    p_full = 2
)

# Simpler vs more complex model
lm_f_2 <- lm(mpg ~ cyl + disp + hp + drat + qsec, data = mtcars) # a more complex full model
f_change_M <- cp_F(
    y = mtcars$mpg,
    y_hat_restricted = predict(lm_f),
    y_hat_full = predict(lm_f_2),
    p_restricted = 2,
    p_full = 5
)