Application Of Principal Component Analysis In Agronomy
Mwalo, Damaris A
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Principal component analysis lS useful in reducing dimensionality of data while retaining as much variation as possible of the original data. The analysis also identifies the important variables in the original data and may group some of these into distinct classes. In this study, principal component analysis is used on data from a split-plot designed experiment; carried out on the botanical garden of the University of Nairobi at Chiromo; during the 1984 short rains. The technique is used to study the data and reveal the important variables while grouping The variables associated with the retained components. Chapter 1 outlines the concepts behind principal component analysis and expected results in ideal conditions. That is, all population parameters are assumed to be known. Sections 1.1 and 1.2 give an introduction and derivation of principal components. The later part of section 1.2 gives the properties of the population principal components. Section 1.3 mentions some examples of work done; in the past; on the theory and application of principal component analysis. The objectives and significance of this study are In section 1,4. In practice, the data is not always well behaved and the population parameters are rarely knoHn. Therefore, their estimates must be calculated before they can be used in the analysis. Principal component analysis under such conditions is discussed in chapter 2. Section 2.1 gives an introduction of these estimates. Their properties are given in section 2.2. The comparison of the analysis wit h factor ana1y s is is discussed in section 2.3. Section 2.4 describes the rules considered when choosing a subset of the components or variables. Finally chapter 3 deals with the application of these rules on the data on which principal component analysis has been applied . The data, having been reduced is studied further for possible groups and a selection of prominent variables. The project results are in sections 3.2, 3.3, 3.4 and 3 .5 . Concluding remarks are given in section 3.6.