Download presentation
Presentation is loading. Please wait.
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
EFA and CFA: Similarities
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
Factor Coefficient/loading
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) OF COCOA SMALLHOLDERS (X7) P O V E R T Y 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
(1) (2) (3) (4) (5) (6) (7) HOS_MEMB Pearson Correlation 1 Sig. (2-tailed) . AGE_HEAD .177 .142 EDU_HEAD -.027 -.366(***) .826 .002 AGE_WIFE .227(*) .909(***) -.306(**) .061 .000 .011 EDU_WIFE .151 -.233(*) .622(***) -.172 .216 .054 .157 AGE_CHIL .671(***) -.526(***) .639(***) -.452(***) .267 .001 EDU_CHIL .400(***) .303(**) -.096 .295(**) -.058 .194 .004 .031 .504 .036 .687 .173 ***cor is signif at .01; **cor is signif at .05; *cor is signif at .10
22
20. SPSS Output Output Created 25-DEC-2008 20:23:32 Comments Input
Data D:\Ph.D Planning\Thesis Construction\Data\Final STANDARDIZED Data Construction ordered by Concept 2.sav Filter <none> Weight Split File N of Rows in Working Data File 70 Missing Value Handling Definition of Missing MISSING=EXCLUDE: User-defined missing values are treated as missing. Cases Used LISTWISE: Statistics are based on cases with no missing values for any variable used. Syntax FACTOR /VARIABLES zq13 zq1412 zq1413 zq1422 zq1423 zq1432 zq1433 /MISSING LISTWISE /ANALYSIS zq13 zq1412 zq1413 zq1422 zq1423 zq1432 zq1433 /PRINT INITIAL EXTRACTION ROTATION FSCORE /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /SAVE REG(ALL) /METHOD=CORRELATION . Resources Elapsed Time 0:00:00.03 Maximum Memory Required 7636 (7.457K) bytes Variables Created FAC1_1 Component score 1 FAC2_1 Component score 2
23
21. Communality: Extraction Method of PCA
Initial Extraction HOS_MEMB 1.000 .596 AGE_HEAD .806 EDU_HEAD .726 AGE_WIFE .805 EDU_WIFE .677 AGE_CHIL .754 EDU_CHIL .494
24
22. Total Variance Explained: Extraction Method of PCA
Component Initial Eigenvalues Extraction Sums of Squared Loadings Rotation Sums of Squared Loadings Total % of Variance Cumulative % 1 3.352 47.891 3.020 43.138 2 1.505 21.507 69.397 1.838 26.259 3 .895 12.781 82.178 4 .607 8.666 90.844 5 .378 5.403 96.247 6 .189 2.702 98.949 7 .074 1.051
25
23a. Matrix: Component and Rotated
1 2 HOS_MEMB .271 .723 AGE_HEAD .890 .119 EDU_HEAD -.731 .438 AGE_WIFE .871 .215 EDU_WIFE -.546 .615 AGE_CHIL .866 -.069 EDU_CHIL .384 .589 Component 1 2 HOS_MEMB -.062 .770 AGE_HEAD .755 .486 EDU_HEAD -.847 .087 AGE_WIFE .697 .565 EDU_WIFE -.756 .325 AGE_CHIL .813 .305 EDU_CHIL .098 .696 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
Communality Unrotated Solution Varimax Rotated Factor Score Coefficient Factor 1 Factor 2 HOS_MEMB .596 .271 .723 -.062 .770 -.131 .469 AGE_HEAD .806 .890 .119 .755 .486 .207 .184 EDU_HEAD .726 -.731 .438 -.847 .087 -.321 .171 AGE_WIFE .805 .871 .215 .697 .565 .174 .240 EDU_WIFE .677 -.546 .615 -.756 .325 .301 AGE_CHIL .754 .866 -.069 .813 .305 .253 .068 EDU_CHIL .494 .384 .589 .098 .696 .403 Eigenvalue 3.352 1.505 3.020 1.838 Percent of Variance (1)a) 47.891 21.507 43.138 26.259 Cum. of Variance (2)b) 69.397 Extraction Method: Principal Component Analysis; Rotation Method: Varimax with Kaiser Normalization (also applied to the other Factor Matrices) a) Percentage of variance explained in the total variance. b) Cumulative variance explained in the total variance.
27
24. Correlation Matrix: Access to Social Facility Dimension
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) FRE_HEALT (1) 1 FRE_HEALT (2) -.121 FRE_HEALT (3) .438(***) .219(*) DISTN_HEALT1 (4) -.097 .459 .372 DISTN_HEALT2 (5) .487(***) .356(***) .507(***) .413 DISTN_HEALT3 (6) .154 .249 .012 -.332 -.927(***) FRE_WATCO (7) -.214 .079 .282(*) -.348 .544(***) -.643 DISTN_WATCO (8) .075 .060 -.364(**) .059 -.119 .400 -.330(**) TIMEL_WATCO (9) .029 .401(***) .039 .147 .068 .287 -.200 .776(***) FRE_WATBW (10) -.020 -.068 -.101 -.311 -.245(*) .285 .728(***) -.295(*) -.272(*) DISTN_WATBW (11) -.067 -.019 -.012 .347 .492(***) -.402 -.211 .229 .193 -.206 TIMEL_WATBW (12) -.009 -.050 .025 .421 -.245 -.232 .483(***) .326(**) .245 -.049 DISTN_EDUC1 (13) -.026 -.328 -.032 .820(**) .023 -.461 .094 .228 -.275 .197 .160 -.107 DISTN_EDUC2 (14) -.182 .316 -.124 .211 .069 -.685 -.256 .667(**) .751(***) -.120 -.041 .104 -.048 DISTN_EDUC3 (15) -.424 -.181 -.448 -.573 -.653(**) .973(***) -.218 -.274 .136 .024 -.651(**) -.184 -.094(*)
28
25. Factor Matrix: Access to Social Facility Dimension
Communality Unrotated Solution Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 FRE_HEALT1 .868 .317 .316 -.233 .189 .423 -.629 -.057 FRE_HEALT2 .797 .321 .032 -.006 .576 -.374 .411 -.229 FRE_HEALT3 .720 .392 .624 -.128 .339 .153 -.130 -.077 DISTN_HEALT1 .808 .488 .301 .217 -.103 .186 .507 -.361 DISTN_HEALT2 .743 .612 .438 -.215 .165 .097 .063 .299 DISTN_HEALT3 .581 -.293 .005 -.321 .573 -.030 .099 -.231 FRE_WATCO .767 -.370 .521 .442 -.047 .175 .200 DISTN_WATCO .897 .398 -.727 .246 .179 .333 -.082 -.003 TIMEL_WATCO .882 .412 -.626 .152 .505 .201 .034 -.042 FRE_WATBW .735 -.440 .300 .632 .073 -.091 .060 DISTN_WATBW .861 .279 -.045 -.216 -.076 .190 .437 .708 TIMEL_WATBW .722 -.179 -.001 .661 .312 .358 -.035 .163 DISTN_EDUC1 .814 .161 .114 .264 -.576 .465 .254 -.305 DISTN_EDUC2 .888 .511 -.218 .484 -.094 -.528 -.209 .117 DISTN_EDUC3 -.673 -.309 -.338 .338 .233 .019 Eigenvalue 2.566 2.212 1.846 1.741 1.320 1.253 1.014 Percent of Variance (1)a) 17.106 14.749 12.309 11.604 8.798 8.356 6.760 Cum of Variance (2)b) 31.855 44.164 55.768 64.566 72.922 79.682 a) Percentage of variance explained in the total variance. b) Cumulative variance explained in the total variance.
29
Varimax Rotated Solution Factor Score Coefficient
Factor Matrix Com Varimax Rotated Solution Factor Score Coefficient F 1 F 2 F 3 F 4 F5 F6 F7 F 5 FRE_HEALT1 .868 .122 .867 -.076 .043 -.258 -.083 -.146 .539 -.023 .065 -.265 -.098 -.178 FRE_HEALT2 .797 .123 -.022 -.090 .878 .013 .026 .020 -.067 -.024 -.017 .595 .047 -.044 FRE_HEALT3 .720 -.144 .780 .085 -.037 .261 .113 .050 -.038 .395 .051 .034 .108 .040 -.031 DISTN_HEALT1 .808 .010 .154 .008 -.138 .335 .802 .096 .006 -.006 -.004 .046 .253 .561 -.030 DISTN_HEALT2 .743 -.062 .623 -.099 -.194 .200 .091 .506 -.034 .272 .005 -.054 .049 -.033 .363 DISTN_HEALT3 .581 .007 .084 .515 .448 -.269 -.187 .025 .061 -.027 .277 .309 -.085 -.161 FRE_WATCO .767 -.339 .777 .044 .197 .075 -.136 -.013 .409 -.010 -.035 .144 DISTN_WATCO .897 .930 -.072 -.107 .055 .028 .467 .018 -.091 .002 TIMEL_WATCO .882 .896 .023 -.032 .269 -.059 .445 .033 .053 .139 -.015 FRE_WATBW .735 -.127 -.052 .817 -.012 -.075 -.018 -.205 -.016 .004 .420 -.043 -.082 DISTN_WATBW .861 .072 -.021 -.094 .037 .918 .017 -.073 .048 -.066 .798 TIMEL_WATBW .722 .340 .770 .024 -.103 .052 -.008 .227 .441 .029 .068 DISTN_EDUC1 .814 -.001 -.053 -.003 -.326 .839 -.028 -.042 -.169 .588 DISTN_EDUC2 .888 .231 -.132 -.007 -.892 -.102 -.036 -.115 .019 -.523 .045 -.171 -.040 DISTN_EDUC3 .080 -.319 .846 -.077 -.190 .027 .086 -.110 .011 .454 .090 Eigenvalue 2.033 1.911 1.904 1.862 1.516 1.506 1.221 Percent of Variance (1)a) 13.554 12.738 12.695 12.411 10.108 10.037 8.138 Cum of Variance (2)b) 26.293 38.987 51.399 61.507 71.544 79.682 Com = Communality; F1, F2, …F7 = Factor 1, Factor 2, …Factor 7 a) Percentage of variance explained in the total variance. b) Cumulative variance explained in the total variance.
30
27. Factor Analysis Results
DIMENSION Desa Compong Number of Variable Number of Factor 1. Household Human Resource 7 2 2. Agricultural Asset 14 5 3. Access to Social Facility 15 4. Access to Information 6 5. Agricultural Economic Activity 3 6. Non-Agricultural Economic Activity 4 Total 51 21 Factors
31
28. Factor into MRA POVERTY (Household Income, X7)
Household Human Resource (X1) Age Structure with Education ( X11) Family Structure with Age & Education (X12) 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) 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) Agricultural Economic Activity (X5) Coffee and Orange Production (X51) Clove Production and Livestock (X52) Cocoa Production (X53) Non-Agricultural Economic Activity (X6) Family Transfer-Source Income (X61) Government Transfer-Source Income (X62) Access to Information (X4) Agriculture & Non-Agric Extension ( X41) Agricultural Marketing (X42) Adjusted Path Diagram for Testing Poverty Causal Model: DESA COMPONG, 21 INDICES E1 E5 E2 POVERTY (Household Income, X7) E3 E7 E6 E4
32
References Arsyad, M., The Dynamics of Cocoa Smallholders in Indonesia: An Application of Path Analysis for Poverty Reduction. Ph.D. Thesis, Ryukoku University Brown, T.A., Confirmatory Factor Analysis for Applied Research. The Guilford Press, NY. Kawamura, Y., 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., Foundations of Factor Analysis (Second Ed). CRC Press, NY. Pett, M.A., N.R. Lackey & J.J. Sullivan, Making Sense of Factor Analysis: The Use of Factor Analysis for Instrument Development in Health Care Research. Sage Publications, London.
Similar presentations
