OPTIMAL SCALING INTEGRATED WITH PRINCIPAL COMPONENT REGRESSION: MODELING CASSAVA YIELDS,A CASE OF WESTERN KENYA

Abstract

Cassava is a major food crop grown in the tropical and subtropical parts of the world. Cas- sava yields have been estimated, among other methods, based on weather factors,Fisher (1925) and based on plant parameters Lohse et al. (1985) .Most of the existing models do not incorporate all factors of production, a few that attempt this only puts into account the plant and weather factors, leaving out pests and diseases. In this research work, a model for predicting cassava yield based on all factors of produc- tion using the principal component regression integrated with optimal scaling is devel- oped. All factors of production are considered in this model. Moreover, the relationship between the di erent factors of production is established and the yield estimated based on the key components adduced to the factors of production in trial data in Western region of Kenya. Principal component regression and optimal scaling are used. Pearson correlation prior to principal component analysis indicated signi cance correlation among the factors of production. A prior to principal component regression, analysis using the variance in ation factor also indicated correlation in key factors of yield forecasting, vari- ance in ation factor of 1666.667 (R2=0.999 ). The coe cients derived from this model were unstable and therefore not reliable for yield prediction .Using the amount of ex- plained variance criterion (70%-80%),the rst eight principal components which accounts for almost 70% of total model variance are selected. Eight (8) key components are ob- tained as key determinants of yield; the most vital component having an eigen value of 2.149 and the least important having an eigen value of 1.005. The post principal compo- nent regression model was tted. The PCR model indicates non-correlation among the eight principal components with the VIF attributed to the overall PCR model being2.564

,(R2=0.610 (Adj R2=0.590) . The model developed incorporates all factors of production, regardless of whether the variables are continuous or categorical. It can factor in pests and diseases which are key factors of crop yield that have been neglected in existing models. The model developed will serve as a vital statistical tool in the crop production industry and impact on policy making.