Partial least-squares regression on design variables as an alternative to analysis of variance

doi:10.1016/S0003-2670(00)86303-5

Analytica Chimica Acta

Volume 191, 1986, Pages 133-148

https://doi.org/10.1016/S0003-2670(00)86303-5 Get rights and content

Abstract

The partial least-squares (PLS) algorithm has become popular for explorative multivariate data analysis and for multivariate calibration. The same PLS algorithm can also be used for confirmatory data analysis. The discussion is limited to analysis of a single response variable. A close correspondence of PLS1 regression to classical analysis of variance (ANOVA) is demonstrated. The design of an experiment is described in terms of discrete design variables for main effects and simple interactions (dummy variables). These are used as regressors X = (x₁, x₂,…,) for modelling the response variable of the experiment, y. As in conventional use of PLS1 regression, the algorithm gives a concentrated model or diagram of the most important, y-relevant variability types in the X-data. In the present case, this gives the combination of design variables that models the variations in y. A simple plot of the resulting factor loadings immediately reveals the important design variables. Statistical tests and confidence regions in the PLS solution give additional safeguards against interpretation of spurious effects. The method is applied to two data sets. One concerns assessment of personal preference for blackcurrent juice, studied in a 2⁵ factorial experiment; these data are also studied with missing values and as fractional factorials. The other ceoncers spectrophotometric absorbance-based colour assessments of pigment in strawberry jam in a 3-factor design with 2, 2 and 3 levels in the respective factors.

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¹: Present address: Norwegian Computing Center, Blindern, Oslo 3 (Norway).

²: Present address: Instituto Agroquimica y Tecnologia de Alimentos, 46010 Valencia (Spain).

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Partial least-squares regression on design variables as an alternative to analysis of variance

Abstract

Trends Anal. Chem.

Trends Anal. Chem.

Commun. Statist.

Appl. Statist.