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FACTOR ANALYSIS

FACTOR ANALYSIS. 1. Definition. Family of statistical methods that represent the relationship among a set of observed variables in terms of hypothesized smaller number of latent construct (or common factors, see Knoke). 2. Function (a).

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FACTOR ANALYSIS

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  1. FACTOR ANALYSIS

  2. 1. Definition • Family of statistical methods that represent the relationship among a set of observed variables in terms of hypothesized smaller number of latent construct (or common factors, see Knoke)

  3. 2. Function (a) • To identify the factors which statistically explain the variation and co-variation among measurement • Proving that one factor consists of some observed variables • Data/Variable Reduction

  4. 3. Function (b) • Summarize the association of factors • Simplify the correlation • Constructing Representative Factors for the concept or dimensions specified

  5. 4. Principal and Objective • Extracting a number of factors (common factor) from a set of original variables • The number of factor is less than the original variable in the dimension • Factor CANNOT be measured directly (Unobserved Variable or Latent Variable) • Objective: getting a small numbers of factor (main component) to explain the variance as wider as possible

  6. 5. Classification (a) 1. Exploratory Factor Analysis (EFA) 2. Confirmatory Factor Analysis (CFA)

  7. 6. Classification (b) • EFA: We don’t know how many factors are needed to describe interrelationship among indicators (exploring) • CFA: We know the association between observed variables (indicator) and latent variables or factors (hypothesized). Principally CFA is confirming based on the theory/concept/dimension

  8. 7. Classification (c)* EFA and CFA: Similarities (1) Based on the Common Factor (2) Same Estimation Method (ML) (3) Quality : Determined by the size of resulting parameter estimates

  9. 8. Steps 1. Extracting Factors (Initial Solution) 2. Rotating Factor (Results more interpretable) 3. Constructing Factor Matrix (Representative Variables)

  10. 9. Modeling Method • Structural Equation Modeling (SEM) • Using Software; LISREL and (or) AMOS Software • SPSS (optional)

  11. 10. Rotating Principal

  12. 11. Both is Solution • Initial Solution • Rotated Solution • Why Rotated? 1. More interpretable 2. The Clear Cluster of variables in the dimension 3. The loading in the unrotated solution depend heavily on the relative number of variables, rotated factors are more stable (see also Kawamura)

  13. 12. Factoring Types • Common Factor Analysis • Component Factor Analysis • Image Factor Analysis • Canonical Factor Analysis • Alpha Factor Analysis

  14. 13. Important Output (a) • Communality • Eigenvalue • Factor Coefficient • Factor-score Coefficient

  15. 14. Important Output (b) • Communality: (1) Variance of a variable accounted for by all (common) factors from Factor 1 to Factor P. (2) How strong a variable is associated with the dimension

  16. 15. Important Output (c) • Eigenvalue (1) The variability of the factor. (2) The variance accounted for by a factor • Factor Coefficient/loading The degree of association of a variable (Z) with a Factor (Factor k)

  17. 16. Important Output (d) • Factor Score (1) The direct effect of a variable on a factor (2) Like Regression Coefficient. (3) A high value of this coeff means a high direct effect of a variable on a factor (see Kawamura)

  18. 17. INDEX CONSTRUCTION • Extraction important factors • Classification of representative variables in each of the extracted important factors (see also Kawamura) • Calculation an Index for each one of these factors (SPSS Factor can create automatically) as the new set of variables and ready to be regressed

  19. Case Study

  20. 18. HYPOTHETICAL MODEL (CONCEPTUALLY, Arsyad 2010) Household Human Resource (X1) Internal Factor Agricultural Economic Activity (X5) Agricultural Assets (X2) P O V E R T Y OF COCOA SMALLHOLDERS (X7) Access to Social Facility (X3) Non-Agricultural Economic Activity (X6) External Factor Access to Information (X4) Independent Var. Intermediate Var. Dependent Var. Note: An arrow indicates a causality and a curve indicates a correlation

  21. 19. Correlation Matrix: Household Resource Dimension ***cor is signif at .01; **cor is signif at .05; *cor is signif at .10

  22. 20. SPSS Output

  23. 21. Communality: Extraction Method of PCA

  24. 22. Total Variance Explained: Extraction Method of PCA

  25. 23a. Matrix: Component and Rotated • Component Matrix (Initial Solution) • Extraction Method: PCA • 2 Components extracted • Extraction Method: PCA • (Rotation Solution) Method: Varimax with Kaiser Normalization • Rotation converged in 3 iterations • Reduction : 2 factors (Component 1 and Component 2)

  26. 23b. Factor Matrix: Household Human Resource Dimension

  27. 24. Correlation Matrix: Access to Social Facility Dimension

  28. 25. Factor Matrix: Access to Social Facility Dimension

  29. 26. Rotated Solution

  30. 27. Factor Analysis Results

  31. 28. Factor into MRA Adjusted Path Diagram for Testing Poverty Causal Model: DESA COMPONG, 21 INDICES Household Human Resource (X1) Age Structure with Education ( X11) Family Structure with Age & Education (X12) E1 E5 Agricultural Asset (X2) Cultivated Land Area with Farm Equipment ( X21 ) Total Paddy Field Area with Farm Equipment (X22) Paddy Upland Area with Farm Equipment (X23) Clove Area with Farm Equipment (X24) Paddy Field Area (X25) Agricultural Economic Activity (X5) Coffee and Orange Production (X51) Clove Production and Livestock (X52) Cocoa Production (X53) E2 POVERTY(Household Income, X7) Access to Social Facility (X3) Source of Water for Cooking ( X31 ) Access to Public Health Center (X32 ) Water Utilization (X33) Distance to Secondary School and Primary Public Health (X34) Primary & Auxiliary Health Centers(X35) Social Services Utilization (X36) Distance to Social Services (X37) Non-Agricultural Economic Activity(X6) Family Transfer-Source Income (X61) Government Transfer-Source Income (X62) E3 E7 E6 Access to Information (X4) Agriculture & Non-Agric Extension ( X41) Agricultural Marketing (X42) E4

  32. References • Arsyad, M., 2010. The Dynamics of Cocoa Smallholders in Indonesia: An Application of Path Analysis for Poverty Reduction. Ph.D. Thesis, Ryukoku University • Brown, T.A., 2006. Confirmatory Factor Analysis for Applied Research. The Guilford Press, NY. • Kawamura, Y., 1978. Urbanization, Part-Time Farm Households and Community Agriculture: Japan’s Experience after World War II. Ph.D. Thesis, Cornell University.

  33. References (c) • Mulaik, S.A., 2010. Foundations of Factor Analysis (Second Ed). CRC Press, NY. • Pett, M.A., N.R. Lackey & J.J. Sullivan, 2003. Making Sense of Factor Analysis: The Use of Factor Analysis for Instrument Development in Health Care Research. Sage Publications, London.

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