select_linear: Helper to select between null and linear term for a single variable

Description

To be used in find_best_fp_step(). Only used if df = 1 for a variable. Handles all criteria for selection. For parameter explanations, see find_best_fp_step(). All parameters captured by ... are passed on to fit_model().

Usage

select_linear(
  x,
  xi,
  keep,
  degree,
  acdx,
  y,
  powers_current,
  powers,
  criterion,
  ftest,
  select,
  alpha,
  ...
)

Value

A list with several components:

keep: logical indicating if xi is forced into model.
acd: logical indicating if an ACD transformation was applied for xi.
powers: fp powers investigated in step, indexing metrics.
power_best: a numeric vector with the best power found. The returned best power may be NA, indicating the variable has been removed from the model.
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.
pvalue: p-value for comparison of linear and null model.
statistic: test statistic used, depends on ftest.

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.
keep: a character vector with names of variables to be kept in the model.
degree: not used.
acdx: a logical vector of length nvars indicating continuous variables to undergo the approximate cumulative distribution (ACD) transformation.
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.
criterion: a character string defining the criterion used to select variables and FP models of different degrees.
ftest: a logical indicating the use of the F-test for Gaussian models.
select: a numeric value indicating the significance level for backward elimination of xi.
alpha: a numeric value indicating the significance level for tests between FP models of different degrees for xi.
...: passed to fitting functions.

Details

This function assesses a single variable of interest xi regarding its functional form in the current working model as indicated by powers_current, with the choice between a excluding xi ("null model") and including a linear term ("linear fp") for xi.

Note that this function handles an ACD transformation for xi as well.

When a variable is forced into the model by including it in keep, then this function will not exclude it from the model (by setting its power to NA), but will only choose the linear model.