Pemodelan Kalibrasi Peubah Ganda dengan Pendekatan Regresi Sinyal P-Spline

Abstract

In modelling g ( ) ( , , , ), 1 2 p E y = f x x K x serious problems will be occurred if the number of variables (p) exceeds the number of observations (n) and multicollinearity exists within independent variables. The data with this condition can often be found in calibration models. A calibration model describes functional relationship between one set of measurements which are easy or cheap to acquire (X), and other measurements, which are either expensive or labor intensive ( y ). Therefore, most calibration models approach require data reduction prior to modelling. An alternative solution for calibration modelling without data reduction is P-spline Signal Regression (PSR). PSR is one of nonparametric approach that assumes regression coeficients are in the smooth function space. This can be done by representing regression coeficients as a linear combination of basis B-spline. Adding penalty is used to solve multicollinearity of the model and increase the smoothness of regression coeficients. Spectra of gingerol are identified have a multiplicative scatter effect, so scatter correction is needed. PSR model with multiplicative scatter correction at gingerol data produce RMSEP and R2 Y vs Ŷ respectively 0.06862 and 95.71%. Those values are less than the result that is given by PCR model using either scatter correction or wavelet transformation pre-processing.