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Principal Component and Principal Axis Factoring of Factors Associated with High Population in Urban Areas: A Case Study of Juja and Thika, Kenya
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 4, July 2015, Pages: 258-263
Received: Mar. 11, 2015; Accepted: Mar. 23, 2015; Published: Jun. 4, 2015
Authors
Josephine Njeri Ngure, School of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, KenyaSchool of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
J. M. Kihoro, School of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Waititu, Co-ooerative University College of Kenya, Nairobi, Kenya
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Abstract
Development in the world / a country today is being influenced by the population in urban areas as a result of which living standards rise in all parts of the country despite the rural areas. The main goal of our government today is to balance development of urban and rural areas of Kenya so that no areas are left behind as others head forward in terms of development.. In this research, PCA and PAF methods of factor reduction were applied. PCA is a widely used method for factor extraction. Factor weights are computed in order to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left. The factor model is then rotated for analysis. PAF restricts the variance that is common among variables. It does not redistribute the variance that is unique to any one variable. Parallel analysis, catell's scree test criterion and Eigen value rule were applied. Results indicated that parallel analysis was generally the best the scree test was generally accurate while the Kaiser's method tended to overestimate the number of components. In this research, business and employment were deduced as major factors associated with high population in the two towns. Amenities like telephone networks, markets were also associated with high population in the two towns. I recommend the Kenyan government to apply the knowledge of PCA and PAF to determine the major reasons associated with high population in other major urban areas (towns and cities) especially according to 2009 population and housing census results so as to assist in allocation of revenue in the now current devolution system of government. This will ensure no areas (counties) are left behind in terms of development. The government should strive to provide social amenities and utilities in the rural areas. It should also provide jobs to the citizens in the rural areas so as to prevent very high increase in urban areas. The people in rural areas can also hold vocational training on self employment being headed by the government. PAF method demonstrated better results than the PCA since it took good care of measurement errors. PAF method was also able to recover weaker factors than PCA could. PAF removed the unique and error variance and so its results were much more reliable.PAF was also preferred because it accounted for the co-variation whereas PCA accounted for the total variance.
Keywords
Principal Component Analysis, Principal Factor Analysis or Common Factor Analysis or Principal Axis Factoring, Factor Analysis, Kaiser Meyer Olkin
Josephine Njeri Ngure, J. M. Kihoro, Anthony Waititu, Principal Component and Principal Axis Factoring of Factors Associated with High Population in Urban Areas: A Case Study of Juja and Thika, Kenya, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 4, 2015, pp. 258-263. doi: 10.11648/j.ajtas.20150404.15
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