# FP

0th

Percentile

##### Fractional Polynomials

Fractional polynomials transformation for continuous covariates.

Keywords
datagen
##### 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 $\sum_{j = 1}^k (\beta_j x^{p_j} + \gamma_j x^{p_j} \log(x)) + \beta_{k + 1} \log(x) + \gamma_{k + 1} \log(x)^2$, where the degree of the fractional polynomial is the number of non-zero regression coefficients $\beta$ and $\gamma$.

##### 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

• FP
##### Examples
# NOT RUN {
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]

# }

Documentation reproduced from package mboost, version 2.9-1, License: GPL-2

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