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
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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
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.
Josephine Njeri Ngure,
J. M. Kihoro,
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.
Baer, Ruth A., Gregory T. Smith University of Kentucky, Gregory T. Smith University of Kentucky and K. Kristin B. Allen Comprehensive Care Center, Lexington (2004), ‘Assessment of mindfulness by self-report .the Kentucky inventory of mindfulness skills’, Sage publication .
Bartlett, M. S. (1954), A note on the multiplying factors for various chi square approximations, New York: HarperCollins.
Catell, R. B. (1966), The scree test for number of factors, Multivariate Behavioral Research, published online.
Chajewski, Michael (2008), ‘Item analysis with alpha standard error and principal axis factoring for continuous variable scales (with plots).’, The college Board Research and Development, Journal of Psychometrics.
Chen, Xingdong, Chao Chen and Li Jin (2011), ‘ministry of education key laboratory of contemporary anthropology, fudan university, shanghai china’, Journal of Scientific Research.
Choi, N, D Fuqua and W Griffin, B (2001), Exploratory analysis of the structure of scores from the multidimensional scales of perceived self efficacy, Sage publications.
Davis, James E, Allan Shepard, Nancy Stanford and L.B Rogers (1974), ‘Application of pca to combined gas chromatographic-mass spectromic data: department of chemistry, Purdue university, west Lafayette, ind.47907, anal chem.’.
Dodou and Winter (April 2012), ‘Factor recovery by principal axis factoring and maximum likelihood factor analysis as a function of factor pattern and sample size. department of biomechanical engineering, faculty of mechanical, maritime and materials engineering, delft university of technology, mekelweg 2, 2628 cd delft, the Netherlands.’, Journal of Applied Statistics Vol. 39 .
George J. Knafl, PhD Professor & Senior Scientist firstname.lastname@example.org (2000), ‘Current topics in statistics for applied researchers factor analysis, Oregon health and science university’.
J.L, Horn (01/06/1965), ‘A rationale and test for the number of factors in factor analysis, volume 30, issue no.2’, Journal of Psychometrika.
Joost C. F. de Winter, Dimitra Dodou (2012), Common factor analysis versus principal component analysis: a comparison of loadings by means of simulations, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology Mekelweg 2, 2628 CD Delft, The Netherlands. E-mail: email@example.com.
Kim, J.O and C.W Mueller (1978a), Introduction to factor analysis: what it is and how to do it, Newbury park, CA: sage publication.
Milner, J. S. and Wimberley (October 1980), ‘Prediction and explanation of child abuse’, Journal of Clinical Psychology.
Novembre, John and Matthew Stephens (18th September 2009), ‘Interpreting principal component analysis of spatial population genetic variation’, Nature publishing group.
R, Hubbard and Allen S.J (1987), ‘An empirical comparison of alternative methods for principal components extraction’, Journal of Business Research, 15, 173-190.
Raschka, Sebastian (13th April 2014), ‘Implementing a principal component analysis (pca) in python step by step’.
Shlens, Jon (25th March 2003), A tutorial on principal component analysis, derivation, discussion and singular value decomposition.
Smith, Lindsay I (February 26 2002), A Tutorial on Principal Component Analysis. Sofroniou N. and Hutcheson, G.D (1999), The Multivariate Social Scientist: an introduction to generalized linear mmodel., Sage publications.
Stevens, J (1996), Applied multivariate statistics for the social (3rd edn). Tabachnick, B.G and L.S. Fidell (2001), Using multivariate statistics (4th edn)., New York: HarperCollins.
Taylor and Francis Online (1974), ‘Application of pca to multitemporal landsat data’, International journal of remote sensing.
W.R, Zwick and Velicer W.F (1986), ‘Comparison of five rules for determining the number of components to retain’, Psychological Bulletin, 432-442.
Zainab Gimba, PhD, M..K. (2012), ‘Department of banking and finance, ramat polytechnique. cause and effects of rural-urban migration in borno state’, Asian journal of Business and Management Sciences.