Exploratory Factor Analysis in Urban and Regional Planning

Document Type : Research Paper



Exploratory Factor Analysis (EFA) is a powerful and commonly-used tool for investigating the underlying variable structure of an urban phenomenon. EFA is commonly employed to reduce many variables into a smaller set of dimensions, hoping to extract dimensions which will explain a good portion of the variance in the original data. Despite the widespread use of EFA, researchers often make questionable decisions when conducting these analyses. Appropriate use of EFA requires a series of thoughtful analytical decisions on the appropriateness of data for EFA, sufficiency of sample size, best extraction techniques to be used, the decision about the number of factors to extract and interpret, the appropriateness of particular rotation techniques, and the calculation method for the factor scores. This article reviews the major design and analytical decisions that must be made when conducting an EFA. The following six steps are proposed for an EFA application in urban and regional research area:
1. Selection of variables/indicators
Variable selection should be guided by theory and/or the findings from the past research.
2. Controlling the adequacy of the data for EFA
The researcher must decide how large the sample must be. This is a necessary consideration to obtain a stable factor structure. KMO and Bartlett’s Test of Sphericity check the adequacy of the data for EFA
3. Deciding the method and the number of factors to extract
There are several factor analysis extraction methods to choose from. The PCA is generally used for factor extraction. However, it is suggested that if data are relatively normally distributed, maximum likelihood is the best choice and if the assumption of multivariate normality is severely violated, then it is suggested to use the principal factor methods. After extraction the researcher must decide how many factors to retain for rotation. Both over-extraction and under-extraction of factors retained for rotation can have harmful effects on the results. The default in most statistical software packages is to retain all factors with eigenvalues greater than 1. Another test for factor retention is the scree test. The number of factors chosen should be such that they explain at least 60 percent of the data variation.
4. Selecting a factor rotation method
The goal of rotation is to simplify and clarify the data structure. There are two extraction methods: orthogonal and oblique. Orthogonal rotations produce factors that are uncorrelated; oblique methods allow the factors to correlate.
5. Interpreting and naming the factors
Interpretation involves the researcher examining which variables are attributable to a factor, and giving that factor a name. Usually, at least two or three variables must load on a factor so it can be given a meaningful interpretation. The naming of factors is a subjective, theoretical, and inductive process. Therefore, the researcher should be very familiar with the issue at hand.
6. Computing the factor scores
Finally, factor scores are computed for the extracted factors.
In this paper, after reviewing the EFA processes and procedures, a real application of the method in assessing the social sustainability at community level


زبردست، اسفندیار؛ خلیلی، احمد و دهقانی، مصطفی (1392)، کاربرد روش تحلیل عاملی در شناسایی بافت های فرسوده شهری، هنرهای زیبا- معماری و شهرسازی، دوره 18، شماره 2، صص 27-42.
زبردست، اسفندیار (1393)، طرح مطالعاتی سنجش وضعیت پایداری شهری در کلانشهر تهران، طرح پژوهشی کاربردی، معاونت پژوهشی پردیس هنرهای زیبا و معاونت شهرسازی و معماری، شهرداری تهران، تهران.
زبردست، اسفندیار (1394)، سنجش وضعیت پایداری در کلانشهر تهران، معاونت شهرسازی و معماری و سازمان فناوری اطلاعات و ارتباطات، شهرداری تهران، تهران.
زبردست، اسفندیار (1396)، برنامه ریزی مسکن در سطح محلی، معاونت مسکن و ساختمان، وزارت راه و شهرسازی، تهران.
Beavers, A. S; Lounsbury, J. W; Richards, J. K; Huck, S. W; Skolits, G. J & Esquivel, S. L (2013), Practical considerations for using exploratory factor analysis in educational research, Practical Assessment, Research & Evaluation, Vol., 18, No 6, pp. 1–13.
Bramley, G & Power, S (2009), Urban form and social sustainability: the role of density and housing type, Environment and Planning B, Vol. 36, No. 1, pp. 30–48.
Cerny, BA & Kaiser, HF (1977), A study of a measure of sampling adequacy for factor-analytic correlation matrices, Multivar Behav Res., Vol. 12, No. 1, pp. 43-47.
Cliff, N (1988), The eigenvalues-greater-than-one rule and the reliability of components, Psychological Bulletin, Vol. 103, pp. 276-279.
Comrey, A. L (1978), Common methodological problems in factor analytic studies, Journal of Consulting and Clinical Psychology, Vol. 46, pp. 648- 659.
Courtney, Matthew Gordon Ray (2013), Determining the Number of Factors to Retain in EFA: Using the SPSS R-Menu v2.0 to Make More Judicious Estimations, Practical Assessment, Research & Evaluation, Vol. 18, No. 8, pp. 1-14.
Darlington, Richard B (2017), "Factor Analysis", (http://node101.psych.cornell.edu/ Darlington/factor. htm). . Retrieved March 25, 2017.
Dempsey, N; Bramley, G; Power, S & Brown, C (2011), The Social Dimension of Sustainable Development: Defining Urban Social Sustainability, Sustainable development, Vol. 19, No. 5, 289-300.
Fergusen, E & Cox, T (1993), Exploratory factor analysis: A users' guide, International Journal of Selection and Assessment, Vol. 1, pp. 84-94.
Floyd, Frank J and Widaman, Keith F (1995), Factor Analysis in the Development and Refinement of Clinical Assessment Instruments, Psychological Assessment, Vol. 7, No. 3, pp. 286-299.
Gorsuch, R. L (1983), Factor Analysis (2nd. Ed), Hillsdale, NJ: Erlbaum.
Grieco, Margaret (2015), Social sustainability and urban mobility: shifting to a socially responsible pro-poor perspective, Social Responsibility Journal, Vol. 11, No. 1, pp. 82-97.
Hair, J; Anderson, RE; Tatham, RL & Black, WC (1995), Multivariate data analysis, 4th ed, Prentice-Hall Inc, New Jersey.
Henson, R. K & Roberts, J. K (2006), Use of exploratory factor analysis in published research, Educational and Psychological Measurement, Vol. 66, No. 3, pp. 393-416.
Hogarty, K; Hines, C; Kromrey, J; Ferron, J & Mumford, K (2005), The Quality of Factor Solutions in Exploratory Factor Analysis: The Influence of Sample Size, Communality, and Over-determination, Educational and Psychological Measurement, Vol., 65, No. 2, pp. 202-26.
Howard, Matt C (2016), A Review of Exploratory Factor Analysis Decisions and Overview of Current Practices: What We Are Doing and How Can We Improve?, International Journal of Human-Computer Interaction, Vol. 32, No. 1, pp. 51-62.
Kaiser, H. F (1960), The application of electronic computers to factor analysis, Educational and Psychological Measurement, Vol. 20, pp. 141-151.
Kieffer, KM (1999), An introductory primer on the appropriate use of exploratory and confirmatory factor analysis, Research in the Schools, Vol. 6, No. 2, pp. 75-92.
Kline, Paul (2014), An Easy Guide to Factor Analysis, NY, Routledge, New York.
MacCallum, RC; Widaman, KF; Zhang, S & Hong S (1999), Sample size in factor analysis, Psychological Methods, Vol. 4, No. 1, pp. 84-99. 
Osborne, J.W and A.B. Costello (2005), Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis, Practical Assessment Research and Evaluation, Vol. 10, No. 7, pp. 1-9.
Pett, M; Lackey, N and Sullivan, J (2003), Making sense of factor analysis, Sage Publications, Inc, Thousand Oaks.
Sapnas, KG & Zeller, RA (2002), Minimizing sample size when using exploratory factor analysis for measurement, Journal of Nursing Measurement, Vol. 10, No. 2, pp. 135-153.
Steiger, James H (2017), Exploratory Factor Analysis with R, accessible from: http://www.statpower.net/Content/312/R%20Stuff/Exploratory%20Factor%20Analysis%20with%20R.pdf.
Tabachnick, B and Fidell, L (2012), Using multivariate statistics, (6th Edition) Pearson Education, Inc, ??????.
Thompson, B (1992), A partial test distribution for cosines among factors across samples, In B. Thompson (Ed.), Advances in social science methodology (Vol. 2, pp. 81-97), Greenwich, CT: JAI.
Thompson, B & Daniel, L. G (1996), Factor analytic evidence for the construct validity of scores: A historical overview and some guidelines, Educational and Psychological Measurement, Vol. 56, pp.197-208.
Treiblmaier, H & Filzmoser, P (2010), Exploratory factor analysis revisited: How robust methods support the detection of hidden multivariate data structures in IS research, Information & Management, Vol. 47, pp. 197–207.
Vallance, Suzanne; Perkins, Harvey C & Dixon, Jennifer E (2011), What is social sustainability? A clarification of concepts, Geoforum, Vol. 42, pp. 342-348.
Williams, B; Brown, T & Onsman, A (2012), Exploratory factor analysis: A five-step guide for novices, Australasian Journal of Paramedicine, Vol. 8, No. 3, pp. 1-13.
Yong, An Gie & Pearce, Sean (2013), A Beginner’s Guide to Factor Analysis: Focusing on Exploratory Factor Analysis, Tutorials in Quantitative Methods for Psychology, Vol. 9(2), pp. 79-94.
Zwick, W. R & Velicer, W. F (1986), Factors influencing five rules for determining the number of components to retain, Psychological Bulletin, Vol. 99, pp. 432-442.