Factor Analysis SAS Interpretation

Generated by the SAS System ('Local', W32_VSHOME) on February 12, 2012 at 04:25:42 PM

Factor Analysis Results 15:40 Sunday, February 12, 2012 1

The FACTOR Procedure



The FACTOR Procedure

Input Data Type Raw Data

Number of Records Read 150

Number of Records Used 150

N for Significance Tests 150

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the number of respondents are 150 and there areno missing values as data of all 150 respondents have been used.



The FACTOR ProcedureInitial Factor Method: Principal Components




Partial Correlations Controlling all other Variables

Avail Style Fit Personal Finish Diff CelEnd Ads

Avail 1.00000 0.04151 0.15645 0.13856 0.00067 0.03030 -0.13512 0.02435

Style 0.04151 1.00000 -0.13013 0.11647 -0.01944 -0.16006 0.27526 -0.01958

Fit 0.15645 -0.13013 1.00000 -0.01542 0.25167 0.00221 -0.03682 -0.01400

Personal 0.13856 0.11647 -0.01542 1.00000 -0.02799 0.23547 -0.11180 -0.06296

Finish 0.00067 -0.01944 0.25167 -0.02799 1.00000 0.07027 0.02126 0.02900

Diff 0.03030 -0.16006 0.00221 0.23547 0.07027 1.00000 0.05473 -0.04179

CelEnd -0.13512 0.27526 -0.03682 -0.11180 0.02126 0.05473 1.00000 0.07985

Ads 0.02435 -0.01958 -0.01400 -0.06296 0.02900 -0.04179 0.07985 1.00000

SalesPer -0.11202 -0.00098 0.02603 0.00992 0.02067 0.07403 -0.05865 0.10873

Price 0.11472 -0.06499 -0.04448 0.14094 -0.09021 -0.02037 0.12393 0.11076

Brand -0.07377 0.00197 0.12394 0.19050 -0.19512 -0.10635 0.00362 0.08619

Var 0.20055 0.04904 -0.02802 -0.03462 -0.10111 0.14419 -0.08907 0.01128

Partial Correlations Controlling all otherVariables

SalesPer Price Brand Var

Avail -0.11202 0.11472 -0.07377 0.20055

Style -0.00098 -0.06499 0.00197 0.04904

Fit 0.02603 -0.04448 0.12394 -0.02802

Personal 0.00992 0.14094 0.19050 -0.03462

Finish 0.02067 -0.09021 -0.19512 -0.10111

Diff 0.07403 -0.02037 -0.10635 0.14419

CelEnd -0.05865 0.12393 0.00362 -0.08907

Ads 0.10873 0.11076 0.08619 0.01128

SalesPer 1.00000 0.11714 -0.05083 -0.03895

Price 0.11714 1.00000 -0.04183 -0.01254

Brand -0.05083 -0.04183 1.00000 -0.14828

Var -0.03895 -0.01254 -0.14828 1.00000

Generated by the SAS System ('Local', W32_VSHOME) on February 12, 2012 at 04:25:42 PMGenerated by the SAS System ('Local', W32_VSHOME) on February 12, 2012 at 04:25:42 PM



Kaiser's Measure of Sampling Adequacy: Overall MSA = 0.49326416

Avail Style Fit Personal Finish Diff CelEnd

0.54472282 0.47217369 0.50604929 0.45524702 0.49071945 0.50173726 0.50412190

Kaiser's Measure of Sampling Adequacy:Overall MSA = 0.49326416

Ads SalesPer Price Brand Var

0.50409099 0.46299909 0.46559553 0.44672146 0.54449346

Prior Communality Estimates: ONE

Eigenvalues of the Correlation Matrix:Total = 12 Average = 1

Eigenvalue Difference Proportion Cumulative

1 1.67149508 0.25462956 0.1393 0.1393

2 1.41686552 0.14526322 0.1181 0.2574

3 1.27160230 0.03604750 0.1060 0.3633

4 1.23555480 0.14888043 0.1030 0.4663

5 1.08667437 0.03581886 0.0906 0.5568

6 1.05085552 0.17755786 0.0876 0.6444

7 0.87329765 0.00975646 0.0728 0.7172

8 0.86354119 0.09972146 0.0720 0.7892

9 0.76381973 0.11982134 0.0637 0.8528

10 0.64399838 0.06444084 0.0537 0.9065

11 0.57955755 0.03681965 0.0483 0.9548

12 0.54273790 0.0452 1.0000

6 factors will be retained by the MINEIGEN criterion.

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The Measure of sampling adequacy is measured by the Kaiser-Meyer-Olkin (KMO) statistic. As a measure of sampling adequacy, the KMO predicts if data are likely to

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factor well based on correlation and partial correlation. KMO can be used to identify which variables to drop from the factor analysis because they lack multicollinearity. In the given tables it is observed that the Model KMO is .493 and hence less than the cut off value of .5 indicating the lack of sampling adequcy. Secondly, the individual KMO's of itmes like Style, Finsih, Personal, Sales Per, Price and Brand are also below .5 and hence the items lack in mlticollinearity and hence are likely candidate for removal from the analysis

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The eigenvalue for a given factor measures the variance in all the variables which is accounted for by that factor. The ratio of eigenvalues is the ratio of explanatory importance of the factors with respect to the variables. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant with more important factors. In this table Factor 1 to Factor 6 have eigen values above 1 and we will only consider these six factors for the study. Technique- column-wise for each factor- cell1^2+cell2^2+cell3^2+……

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Factor Pattern

Factor1 Factor2 Factor3 Factor4 Factor5 Factor6

Avail 0.56053 0.31533 -0.08600 -0.06041 0.34468 -0.37898

CelEnd -0.54139 0.08597 -0.07501 0.33955 0.44901 0.17926

Personal 0.28882 0.55205 0.30446 -0.24629 0.19963 0.39324

Price 0.00441 0.49075 0.35892 0.36497 0.03699 -0.16634

Finish 0.26893 -0.57375 0.09040 0.26954 0.44303 0.16135

Var 0.43733 0.31039 -0.45695 0.17716 -0.06353 -0.26028

SalesPer 0.00938 -0.00376 0.44753 0.48918 -0.29913 0.17036

Brand -0.26941 0.17732 0.48485 -0.59570 0.06368 -0.03891

Style -0.43464 0.31720 -0.30528 0.05318 0.49895 0.11554

Fit 0.39318 -0.41145 0.35557 -0.15335 0.42049 -0.15437

Diff 0.51677 0.17400 0.04257 0.24103 -0.02974 0.52945

Ads -0.18426 0.08534 0.40408 0.37432 0.06745 -0.50098

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this is the unrotated component matrix were no assumptions regarding the collinerity or non collinearity of factors are made. If the rotated component matrix is given interpretation of the factor analysis has to be done based on the the rotated component matrix and not the factor pattern or unrotated component matrix.. Also all calculations for eigen values and communalities has to be based on rotated component matrix and not the unrorated component matrix.

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Unrotated component matrix




Variance Explained by Each Factor


1.6714951 1.4168655 1.2716023 1.2355548 1.0866744 1.0508555

Final Communality Estimates: Total = 7.733048


0.68710333 0.64786095 0.67447459 0.73602340 0.70464196 0.63843013 0.65515815


0.60016353 0.55818087 0.53191456 0.69953515 0.59956096

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Communality, h2, is the squared multiple correlation for the variable as dependent using the factors as predictors. The communality measures the percent of variance in a given variable explained by all the factors jointly and may be interpreted as the reliability of the indicator. Technique- row-wise for each variable ----cell1^2+cell2^2+cell3^2+………..

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The FACTOR ProcedureRotation Method: Varimax




Orthogonal Transformation Matrix

1 2 3 4 5 6

1 0.53469 -0.55264 0.33922 -0.24287 0.47877 -0.07357

2 0.43219 0.25925 -0.63114 0.22894 0.43079 0.33117

3 -0.32607 -0.27004 0.32190 0.55258 0.19847 0.61025

4 -0.15786 0.21609 0.08752 -0.73853 0.08235 0.60706

5 0.34742 0.68245 0.61260 0.18597 0.05660 -0.02234

6 -0.52477 0.20502 0.00506 -0.05699 0.73200 -0.37881

Rotated Factor Pattern


Avail 0.79219 -0.06033 0.16739 0.01884 0.12426 0.10989

Var 0.60352 -0.09626 -0.21937 -0.41547 0.07287 -0.00068

Style 0.10855 0.78056 -0.13501 0.05642 -0.01483 -0.07190

CelEnd -0.21954 0.75829 0.04363 -0.06776 -0.05246 0.15072

Finish -0.10696 0.07189 0.77825 -0.27259 0.06492 -0.06202

Fit 0.16777 -0.19780 0.75091 0.20705 -0.02026 0.00779

Brand -0.08894 -0.02931 -0.06055 0.82795 -0.03031 0.02611

Diff 0.01141 -0.11164 0.08475 -0.27586 0.73654 -0.00799

Personal 0.19562 0.06493 -0.04971 0.42108 0.71539 0.04443

Ads 0.03384 0.03904 0.08525 0.05223 -0.30332 0.70391

Price 0.13995 0.09788 -0.13894 0.05643 0.19515 0.66497

SalesPer -0.41308 -0.19051 0.01005 -0.18245 0.23975 0.51028

Variance Explained by Each Factor


1.3290548 1.3064084 1.3058007 1.2760303 1.2711075 1.2446458

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This table is an outcme of the application of variamax rotation. A variamx rotation is done on the assumption that factors are not correlated that is there is orthoginality among the factors. In this table the Factor 1 is not correlated with Factor 2, 3, 4, 5, 6

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.79219?^2+ (-.06033)^2 +.16739^2 + .........+.10980^2 = Communality of the item Availability

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.79219^2+ .60352^2+ .10855^2+ ...............+ (-.41308)^2 = eigen value of the Factor 1

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All these arew the factor loadings. The factor loadings are the correlation coefficients between the variables (rows) and factors (columns). Thus .04363 is the correlation between Cell End and Factor 3

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From this table it is apparent that items Avail and Var load in Factor 1 Items Style and Cell End loadin Factor 2 Items Finish and Fit load in Factor 3 Item Brand loads in Factor 4 Diff anD Personal load in Factor 5 Item Price and Sales Per load in Factor 6. Factor loadings should be atleast .5 and all cross loadings or -ve loadings in the range of .2 should be taken care off,primarily by removing the items which cross load. After identifying the appropriate factors it is necessary to lable/ name the factors based on the items that have loaded under it.

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Rotated Component Matrix. In here Varimax rotation has been applied.




Final Communality Estimates: Total = 7.733048


0.68710333 0.64786095 0.67447459 0.73602340 0.70464196 0.63843013 0.65515815


0.60016353 0.55818087 0.53191456 0.69953515 0.59956096

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Factor Analysis SAS Interpretation