# FP: Fractional Polynomials In mboost: Model-Based Boosting

 FP R Documentation

## Fractional Polynomials

### Description

Fractional polynomials transformation for continuous covariates.

### Usage

```FP(x, p = c(-2, -1, -0.5, 0.5, 1, 2, 3), scaling = TRUE)
```

### Arguments

 `x` a numeric vector. `p` all powers of `x` to be included. `scaling` a logical indicating if the measurements are scaled prior to model fitting.

### Details

A fractional polynomial refers to a model ∑_{j = 1}^k (β_j x^{p_j} + γ_j x^{p_j} \log(x)) + β_{k + 1} \log(x) + γ_{k + 1} \log(x)^2, where the degree of the fractional polynomial is the number of non-zero regression coefficients β and γ.

### Value

A matrix including all powers `p` of `x`, all powers `p` of `log(x)`, and `log(x)`.

### References

Willi Sauerbrei and Patrick Royston (1999), Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials. Journal of the Royal Statistical Society A, 162, 71–94.

`gamboost` to fit smooth models, `bbs` for P-spline base-learners

### Examples

```
data("bodyfat", package = "TH.data")
tbodyfat <- bodyfat

### map covariates into [1, 2]
indep <- names(tbodyfat)[-2]
tbodyfat[indep] <- lapply(bodyfat[indep], function(x) {
x <- x - min(x)
x / max(x) + 1
})

### generate formula
fpfm <- as.formula(paste("DEXfat ~ ",
paste("FP(", indep, ", scaling = FALSE)", collapse = "+")))
fpfm

### fit linear model
bf_fp <- glmboost(fpfm, data = tbodyfat,
control = boost_control(mstop = 3000))

### when to stop
mstop(aic <- AIC(bf_fp))
plot(aic)

### coefficients
cf <- coef(bf_fp[mstop(aic)])
length(cf)
cf[abs(cf) > 0]

```

mboost documentation built on April 26, 2022, 9:07 a.m.