Application of Principal Component Analysis and Hierarchical Regression Model on Kenya Macroeconomic Indicators

Abstract

The aim of this paper was to apply Principal Component Analysis (PCA) and hierarchical regression model on Kenyan Macroeconomic variables. The study adopted a mixed research design (descriptive and correlational research designs). The 18 macroeconomic variables data were extracted from Kenya National Bureau of Statistics and World Bank for the period 1970 to 2019. The R software was utilized to conduct all the data analysis. Principal Component Analysis was used to reduce the dimensionality of the data, where the original data set matrix was reduced to Eigenvectors and Eigenvalues. A hierarchical regression model was fitted on the extracted components, and R2 was used to determine whether the components were a good fit for predicting economic growth. The results from the study showed that the first component explained 73.605 % of the overall Variance and was highly correlated with 15 original variables. Additionally, the second principal component described approximately 10.03% of the total Variance, while the two variables had a higher positive loading into it. About 6.22% of the overall variance was explained by the third component, which was highly correlated with only one of the original variables. The first, second, and third models had F statistics of 2385.689, 1208.99, and 920.737, respectively, and each with a p-value of 0.0001<5% was hence implying that the models were significant. The third model had the lowest mean square error of 17.296 hence described as the best predictive model. Since component 1 had the highest Variance explained, and model 1 had a lower p-value than other models, Principal component 1 was more reliable in explaining economic growth. Therefore, it was concluded that the macroeconomic variables associated with the monetary economy, the trade and openness of the economy with government activities, the consumption factor of the economy, and the investment factor of the economy predict economic growth in Kenya. The study recommends that PCA should be utilized when dealing with more than 15 variables, and hierarchical regression model building technique be used to determine the partial variance change among the independent variables in regression modeling.