Browsing by Author "Njoroge, Gladys G."

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Application of Principal Component Analysis and Hierarchical Regression Model on Kenya Macroeconomic Indicators
(EJ-MATH, European Journal of Mathematics and Statistics, 2022) Mbaluka, Morris Kateeti; Muriithi, Dennis K.; Njoroge, Gladys G.
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.
GENERAL OVERVIEW OF SAMPLE SIZE ESTIMATION FOR RANDOMIZED CONTROLLED CLINICAL TRIALS
(Chuka University, 2021) Obare, D. M.; Njoroge, Gladys G.; Muraya, M. M.
Calculation of the minimum sample size needed to meet the primary study objective is a key feature of the design of any clinical trial. The other reason a priori sample size determination is to limit participant harm or loss of clinical benefit to as few study participants as possible. This article generally reviews the basic principles that determine an appropriate sample size and provides methods for its calculation in some simple, yet common, cases. Sample size is closely tied to statistical power, which is the ability of a study to enable detection of a statistically significant difference when there truly is one. A trade-off exists between a feasible sample size and adequate statistical power
MODELLING KENYA MACROECONOMIC INDICATORS USING PRINCIPAL COMPONENT ANALYSIS
(Chuka University, 2021) Mbaluka, Morris Kateeti; Muriithi, Dennis K.; Njoroge, Gladys G.
Kenya's economic growth has been lower than in other nations, especially the European nations for a long time. Macroeconomic indicators are the main factors that affect the economic growth of a country. The study sought to model Kenya macroeconomic indicators using principal component analysis. The study used PCA to capture data of 34 macroeconomic indicators for the period 1980 to 2019. The study aimed at applying PCA to reduce the dimensionality of the macroeconomic indicators and classify them into principal components. The study aimed at improving the way macroeconomic data has been handled in the past since several assumptions about the relationship between macroeconomic variables and economic growth have been made in the previous studies. The KMO statistics was found to be 0.720 and the p-value was 0.000. The KMO statistics indicated that the correlation matrix was appropriate for component analysis and the p-value depicted a significant difference. With reference to the correlation matrix, the variable were found to be closely correlated. Principal Component analysis was used to reduce the variables using varimax technique to principal components without compromising the variability of the original data. Only 8 variables (Principal Components) were retained since they explained 85% of the overall variations after scree plot, Kaiser Criterion and parallel analysis extraction approaches were utilized. The first component explained 28% of the total variance and was highly correlated with 10 macroeconomic indicators. Since the first principal component had the highest variance it was concluded that the monetary related macroeconomic indicators greatly impact economic growth in Kenya. Future researchers should consider having more diversified variables to help explain how economic growth is impacted by the all-round macroeconomic indicators