find_best_fpm_step: Function to find the best FP functions of given degree for a...

In mfp2: Multivariable Fractional Polynomial Models with Extensions

Function to find the best FP functions of given degree for a single variable

Description

Handles the FP1 and the higher order FP cases. For parameter definitions, see find_best_fp_step().

Usage

find_best_fpm_step(x, xi, degree, y, powers_current, powers, acdx, ...)

Arguments

x	an input matrix of dimensions nobs x nvars. Does not contain intercept, but columns are already expanded into dummy variables as necessary. Data are assumed to be shifted and scaled.
xi	a character string indicating the name of the current variable of interest, for which the best fractional polynomial transformation is to be estimated in the current step.
degree	degrees of freedom for fp transformation of xi.
y	a vector for the response variable or a Surv object.
powers_current	a list of length equal to the number of variables, indicating the fp powers to be used in the current step for all variables (except xi).
powers	a named list of numeric values that sets the permitted FP powers for each covariate.
acdx	a logical vector of length nvars indicating continuous variables to undergo the approximate cumulative distribution (ACD) transformation.
...	passed to fit_model().

Details

The "best" model is determined by the highest likelihood (or smallest deviance by our definition as minus twice the log-likelihood). This is also the case for the use of information criteria, as all models investigated in this function have the same df, so the penalization term is equal for all models and only their likelihoods differ.

Note that the estimation of each fp power adds a degree of freedom. Thus, all fp1s have 2 df, all fp2s have 4 df and so on.

In the case that degree = 1, the linear model (fp power of 1) is NOT returned, as it is not considered to be a fractional polynomial in this algorithm. A linear model has only one df, whereas the same function regarded as fp would have 2 fp.

Value

A list with several components:

• acd: logical indicating if an ACD transformation was applied for xi.

• powers: fp powers investigated in step.

• power_best: the best power found. power_best will always be a two-column matrix when an ACD transformation is used, otherwise the number of columns will depend on degree.

• metrics: a matrix with performance indices for all models investigated. Same number of rows as, and indexed by, powers.

• model_best: row index of best model in metrics.

ACD transformation

This function also handles the case of ACD transformations if acdx is set to TRUE for xi. In this case, if degree = 1, then 7 models are assessed (like for the non-acd case it excludes the linear case), and if degree = 2, then 64 models are assessed (unlike the 36 models for non-acd transformation). Other settings for degree are currently not supported when used with ACD transformations.

mfp2 documentation built on Nov. 15, 2023, 1:06 a.m.