Browsing by Author "Muriithi, Dennis K."

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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.
Application of Simplex Lattice Design in Watermelon Production
(2019) Muriithi, Dennis K.
This paper discusses the use of Simplex Lattice Design approach to plan the experiment for yield of watermelon with an overall objective of optimizing the multiple responses of watermelon to organic manure. Multiple linear regression models have been adopted to express the output parameters (responses) that are decided by the input process parameters. Poultry manure, cow manure and goat manure were the independent variables to optimize the response values of interest that includes; watermelon fruit weight, number of fruits of watermelon per plant. Mixture experiments are appropriate to use when a researcher wishes to determine if synergism exists in mixing components which increases productivity. Three-component design presented in this study illustrated how to apply mixture designs in agricultural research. Mathematical Model evolved for response show the effect of each input parameter and its interaction with other parameters, depicting the trend of response. From, the equation of fruit weight and number of fruits, it can be concluded that goat manure has a more important role on watermelon production in the current study. Conclusively, the current study attained the optimal condition of 17.68 ton/Ha, 11.69 ton/Ha and 19.16 ton/Ha of poultry manure, cow manure and goat manure respectively, would guarantee the farmer a maximum yield of 22.13kg fruit weight of watermelon per plant and 7.74≈8 Fruit of watermelon per plant. The study exemplified that the development of statistical models for crop production can be useful for predicting and understanding the effects of experimental factors.
Effects of Compensation on Job Satisfaction Among Secondary School Teachers in Maara Sub - County of Tharaka Nithi County, Kenya
(Science Publishing Group, 2015) Muguongo, Mary Makena; Muguna, Andrew T.; Muriithi, Dennis K.
Abstract: Compensation plays an important role in determining employees’ job satisfaction. According to Bozeman & Gaughan (2011), the perception of being paid what one is worth predicts job satisfaction. Teachers in Kenya have always downed their tools lamenting about their compensation which raises concern about their job satisfaction. However it is not clear the influence compensation has on teachers job satisfaction to cause the many stand offs. This study therefore sought to establish the effects of compensation on job satisfaction among Secondary school teachers in Maara Sub- County Tharaka Nithi County Kenya. The objectives of the study were to determine the effects of both financial and nonfinancial compensation on job satisfaction. The study employed a descriptive survey research design. Stratified random sampling was used to select a sample size of 214 teachers drawn from the target population of 474. Responses were collected through administration of questionnaire. The validity and reliability of the questionnaire was enhanced through a pilot study carried out in three schools in Meru South Sub-County. To ensure the validity of the instruments, both face and content validity was used. Data collected was categorized coded and then tabulated using SPSS. The qualitative data was analyzed using descriptive statistics, means frequency tables and percentages. The hypotheses were tested using chi-square. The study established that the basic pay, allowances and work environment affects teachers’ job satisfaction to a great extent. The research concluded that teachers were highly dissatisfied with all aspects of compensation that they receive. The study recommends that the government reviews the teachers’ compensation to commensurate the services rendered. It is hoped that the findings of this study could assist the education planners in formulating compensation policies that would enable teachers to achieve job satisfaction.
Forecasting Commodity Price Index of Food and Beverages in Kenya Using Seasonal Autoregressive Integrated Moving Average (SARIMA) Models
(EJ-MATH, European Journal of Mathematics and Statistics, 2021) Wanjuki, Teddy Mutugi; Wagala, Adolphus; Muriithi, Dennis K.
Price stability is the primary monetary policy objective in any economy since it protects the interests of both consumers and producers. As a result, forecasting is a common practice and a vital aspect of monetary policymaking. Future predictions guide monetary and fiscal policy tools that that be used to stabilize commodity prices. As a result, developing an accurate and precise forecasting model is critical. The current study fitted and forecasted the food and beverages price index (FBPI) in Kenya using seasonal autoregressive integrated moving average (SARIMA) models. Unlike other ARIMA models like the autoregressive (AR), Moving Average (MA), and non-seasonal ARMA models, the SARIMA model accounts for the seasonal component in a given time series data better forecasts. The study relied on secondary data obtained from the KNBS website on monthly food and beverage price index in Kenya from January 1991 to February 2020. R-statistical software was used to analyze the data. The parameter estimation was done using the Maximum Likelihood Estimation method. Competing SARIMA models were compared using the Mean Absolute Error (MAE), Mean Absolute Scaled Error (MASE),.and Mean Absolute Percentage Error (MAPE). A first-order differenced SARIMA (1,1,1) (0,1,1)12 minimized these model evaluation criteria (AIC = 1818.15, BIC =1833.40). The forecasting ability evaluation statistics MAE = 2.00%, MAPE = 1.62% and MASE = 0.87%. The 24-step ahead forecasts showed that the FPBI is unstable with an overall increasing trend. Therefore, the monetary policy committee ought to control inflation through monetary or fiscal policy, strengthening food security and trade liberalization.
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
The Optimization of Multiple Responses of Watermelon to Organic Manure Using Response Surface Methodology
(2017-03) Muriithi, Dennis K.; ArapKoske, J. K.; Gathungu, Geofrey K.
This paper discusses the use of Central Composite Design approach to plan the experiments for growth and yield of watermelon with an overall objective of optimizes the multiple responses of watermelon to organic manure. Response Surface methodology (RSM) has been adopted to express the output parameters (responses) that are decided by the input process parameters. Poultry manure, cow manure and goat manure were the independent variables to optimize the response values of interest that includes; watermelon fruit weight, number of branches and vine length per plant. The predicted values were found to be in good agreement with the experimental values which define the propriety of the models and the achievement of CCD in the optimization of multiple responses of watermelon. The results of the study found that the optimal values of responses were 93.148 ton/Ha of fruit weight of watermelon in the study area, 8 branches of watermelon plant and vine length of 224 cm at 8weeks.Based on the findings of the study, it was recommended that farmers in the study area apply 17.125 tons/Ha of poultry manure, 13.27 tons/Ha of cow manure and 18.08 tons/Ha of goat manure for increased growth and yield of watermelon. Finally, this study represented the development of mathematical models for crop production based on statistics that can be useful for predicting and understanding the effects of experimental factors. Also, it would be a scientific and economic approach to obtain the maximum amount of information in a short period of time and with the lowest number of experiments.
Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index
(EJ-MATH, European Journal of Mathematics and Statistics, 2021) Kimutai, K. Emmanuel; Wagala, Adolphus; Muriithi, Dennis K.
Abstract —Time series modeling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data-adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.
Singular Spectrum Analysis: An Application to Kenya’s Industrial Inputs Price Index
(Springer, 2022-01) Kimutai, Emmanuel K.; Wagala, Adolphus; Muriithi, Dennis K.
Time series modelling and forecasting techniques serve as gauging tools to understand the time-related properties of a given time series and its future course. Most financial and economic time series data do not meet the restrictive assumptions of normality, linearity, and stationarity of the observed data, limiting the application of classical models without data transformation. As non-parametric methods, Singular Spectrum Analysis (SSA) is data adaptive; hence do not necessarily consider these restrictive assumptions as in classical methods. The current study employed a longitudinal research design to evaluate how SSA fist Kenya’s monthly industrial inputs price index from January 1992 to April 2022. Since 2018, reducing the costs of industrial inputs has been one of Kenya’s manufacturing agendas to level the playing field and foster Kenya’s manufacturing sector. It was expected that Kenya’s Manufacturing Value Added hit a tune of 22% by 2022. The study results showed that the SSA (L = 12, r =7) (MAPE = 0.707%) provides more reliable forecasts. The 24-period forecasts showed that the industrial inputs price index remains high above the index in 2017 before the post-industrial agenda targeting a reduction in the cost of industrial inputs. Thus, the industrial input prices should be reduced to a sustainable level.
TRIPLE EXPONENTIAL SMOOTHING TECHNIQUES: APPLICATION TO KENYA’S INDUSTRIAL INPUTS PRICE INDEX
(Chuka University, 2021) Koech, Emmanuel K.; Wagala, Adolphus; Muriithi, Dennis K.
A move towards industrialization is an active ingredient in achieving sustainable economic development owing to the derived benefits of the creation of employment opportunities and enhanced international trade. Through its big four agenda launched on December 12, 2017, Kenya aims to foster the manufacturing sector. One of the industrial- agenda is reducing the costs of industrial inputs. Thus, an accurate predictive model that can be used to gauge the cost of manufacturing inputs ought to be developed. The current study compared the pertinence of two Holt-Winter Exponential Smoothing (HWES) techniques in forecasting Kenya's industrial inputs price data. Unlike simple moving average, where past values are weighted equally, exponential functions assign exponentially decaying weights, over time. The study used secondary data on Kenya's monthly industrial inputs price index from January 1980 to June 2018 extracted from the OECD website. The data had 450 observations and was analyzed using R software. The findings indicated that a hybrid of both the additive and multiplicative HWES model efficiently captures the nonlinearity or seasonality of industrial inputs price index series. Specifically, the “optimal” model was a specification of the multiplicative error, additive trend, and multiplicative seasonality (“MAM”) with a performance accuracy of 2.3% in terms Mean Absolute Percentage Error (MAPE) in making 24 months step-ahead forecasts. The model outperformed the purely additive (2.44%) or multiplicative HWES model (2.55%). The estimated smoothing of alpha, beta and gamma were; 0.9647, 0.1378, and 0.0004, respectively. The prediction future prices movement is beneficial to producers, consumers and policymakers. The 24-period forecast of the industrial inputs the price index indicates a falling trend, and indication that the industrial agenda shows some prospects in the reduction of the cost of inputs