R: Function selection procedure based on closed testing...

select_ra2 {mfp2}

R Documentation

Function selection procedure based on closed testing procedure

Description

Used in find_best_fp_step() when criterion = "pvalue". For parameter explanations, see find_best_fp_step(). All parameters captured by ... are passed on to fit_model().

Usage

select_ra2(
  x,
  xi,
  keep,
  degree,
  acdx,
  y,
  powers_current,
  powers,
  criterion,
  ftest,
  select,
  alpha,
  ...
)

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`	integer > 0 giving the degree for the FP transformation.
`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

In case criterion = "pvalue" the function selection procedure as outlined in Chapters 4 and 6 of Royston and Sauerbrei (2008) is used.

Step 1: test the best FPm function against a null model at level select with 2m df. If not significant, the variable is excluded. Otherwise continue with step 2.
Step 2: test the best FPm versus a linear model at level alpha with 2m - 1 df. If not significant, use a linear model. Otherwise continue with step 3.
Step 3: test the best FPm versus the best FP1 at level alpha with 2m - 2 df. If not significant, use the best FP1 model. Otherwise, repeat this step for all remaining higher order FPs until FPm-1, which is tested at level alpha with 2 df against FPm. If the final test is not significant, use a FPm-1 model, otherwise use FPm.

Note that the "best" FPx model used in each step is given by the model using a FPx transformation for the variable of interest and having the highest likelihood of all such models given the current powers for all other variables, as outlined in Section 4.8 of Royston and Sauerbrei (2008). These best FPx models are computed in find_best_fpm_step().

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 its functional form.

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, i.e. FALSE in this case.
powers: (best) fp powers investigated in step, indexing metrics. Always starts with highest power, then null, then linear, then FP in increasing degree (e.g. FP2, null, linear, FP1).
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.

References

Royston, P. and Sauerbrei, W., 2008. Multivariable Model - Building: A Pragmatic Approach to Regression Anaylsis based on Fractional Polynomials for Modelling Continuous Variables. John Wiley & Sons.