Multivariate Analysis (PCR, PLS)

In this exercise we will study a data set used in the paper by Liland et al (2009) (http://www.sciencedirect.com/science/article/pii/S0169743909001476) were PLS-regression was used to predict the percentage of cow-milk in mixtures of cow, goat and ewe milk.

load("_data/maldidata.rdata")

An excerpt from the paper explains why this is interesting:

"Quality assurance is an important issue in modern food production. The products are expected to have the right taste, smell, texture and appearance. In addition they should be safe, wholesome, authentic and have a composition that complies with regulations. As a practical example this paper will analyse data simulating milk adulteration. In real life such adulteration could occur where one type of milk is replaced by, or mixed with, another deliberately, by accident or because of failing routines.

There are several reasons why detection of the concentrations of cow, goat and ewe milk is of importance. Pure products of goat milk may be used as a supplement of milk for humans who are born with allergic reactions towards cow milk. Some mixed milk products are produced with regard to specifications which specify the mixture of milk from cow, goat and/or ewe. Professionals and consumers want to control the origin of milk in order to be sure that they get products following specifications and labelling. Farmers producing more than one type of milk might be tempted to add cow milk to goat or ewe milk as this would result in higher quantities of the better paid milk variants"

For the exercise we will need pls package.

library(pls)