calculate_f_test: Function to compute F-statistic and p-value from deviances
In mfp2: Multivariable Fractional Polynomial Models with Extensions

calculate_f_test

R Documentation

Function to compute F-statistic and p-value from deviances

Description

Alternative to likelihood ratio tests in normal / Gaussian error models.

Usage

calculate_f_test(deviances, dfs_resid, n_obs, d1 = NULL)

Arguments

`deviances`	a numeric vector of length 2 with deviances. Typically ordered in increasing order (i.e. null model first, then full model) and used to test the difference `deviances[1] - deviances[2]`.
`dfs_resid`	a numeric vector with residual degrees of freedom.
`n_obs`	a numeric value with the number of observations.
`d1`	a numeric value giving `d1` in the formula below directly as the number of additional degrees of freedom in model 2 compared to model 1. In this case `dfs_resid` must be a single numeric value giving the residual df for model 2. This interface is sometimes more convenient than to specify both residual dfs.

Details

Uses formula on page 23 from here: https://www.stata.com/manuals/rfp.pdf:

F = \frac{d_2}{d_1} (exp(\frac{D_2 - D_1}{n}) - 1),

where D refers to deviances of two models 1 and 2. d1 is the number of additional parameters used in in model 2 as compared to model 1, i.e. dfs_resid[1] - dfs_resid[2]. d2 is the number of residual degrees of freedom minus the number of estimated powers for model 2, i.e. dfs_resid[2]. #' The p-value then results from the use of a F-distribution with (d1, d2) degrees of freedom.

Note that this computation is completely equivalent to the computation of a F-test using sum of squared errors as in e.g. Kutner at al. (2004), p 263. The formula there is given as

F = \frac{SSE(R) - SSE(F)}{df_R - df_F} / \frac{SSE(F)}{df_F},

where the df terms refer to residual degrees of freedom, and R and F to the reduced (model 1) and full model (model 2), respectively.