fuelSubset {FDboost}

Spectral data of fossil fuels

Description

For 129 laboratory samples of fossil fuels the heat value and the humidity were determined together with two spectra. One spectrum is ultraviolet-visible (UV-VIS), measured at 1335 wavelengths in the range of 250.4 to 878.4 nanometer (nm), the other a near infrared spectrum (NIR) measured at 2307 wavelengths in the range of 800.4 to 2779.0 nm. fuelSubset is a subset of the original dataset containing only 10% of the original measures of the spectra, resulting in 231 measures of the NIR spectrum and 134 measures of the UVVIS spectrum.

Usage

data("fuelSubset")

Format

A data list with 129 observations on the following 7 variables.

heatan

heat value in mega joule (mJ)

h2o

humidity in percent

NIR

near infrared spectrum (NIR)

UVVIS

ultraviolet-visible spectrum (UV-VIS)

nir.lambda

wavelength of NIR spectrum in nm

uvvis.lambda

wavelength of UV-VIS spectrum in nm

h2o.fit

predicted values of humidity

Details

The aim is to predict the heat value using the spectral data. The variable h2o.fit was generated by a functional linear regression model, using both spectra and their derivatives as predictors.

Source

Siemens AG

Fuchs, K., Scheipl, F. & Greven, S. (2015), Penalized scalar-on-functions regression with interaction term. Computational Statistics and Data Analysis. 81, 38-51.

Examples

    data("fuelSubset", package = "FDboost")
    
    ## center the functional covariates per observed wavelength
    fuelSubset$UVVIS <- scale(fuelSubset$UVVIS, scale = FALSE)
    fuelSubset$NIR <- scale(fuelSubset$NIR, scale = FALSE)

    ## to make mboost::df2lambda() happy (all design matrix entries < 10)
    ## reduce range of argvals to [0,1] to get smaller integration weights
    fuelSubset$uvvis.lambda <- with(fuelSubset, (uvvis.lambda - min(uvvis.lambda)) /
                                          (max(uvvis.lambda) - min(uvvis.lambda) ))
    fuelSubset$nir.lambda <- with(fuelSubset, (nir.lambda - min(nir.lambda)) /
                                          (max(nir.lambda) - min(nir.lambda) ))


    ### fit mean regression model with 100 boosting iterations,
    ### step-length 0.1 and
    mod <- FDboost(heatan ~ bsignal(UVVIS, uvvis.lambda, knots=40, df=4, check.ident=FALSE)
                   + bsignal(NIR, nir.lambda, knots=40, df=4, check.ident=FALSE),
                   timeformula = NULL, data = fuelSubset)
    summary(mod)
    ## plot(mod)