Assignment: Exploratory Factor Analysis

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  • Topic: Factor analysis, Principal component analysis, Eigenvalue, eigenvector and eigenspace
  • Pages : 6 (1408 words )
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  • Published : February 20, 2013
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Table 4.14 KMO and Bartlett's Test
Kaiser-Meyer-Olkin Measure of Sampling Adequacy..896
Bartlett's Test of SphericityApprox. Chi-Square4.120E3

Bartlett's test of sphericity indicates whether the correlation matrix is an identity matrix, which would indicate that the variables are unrelated. The significance level gives the result of the test. Very small values (less than .05) indicate that there are probably significant relationships among the variables. A value higher than about .10 or so may indicate that this data are not suitable for factor analysis. Hence, the researcher concludes the data is suitable for factor analysis since Kaiser-Meyer-Olkin Measure of Sampling Adequacy value is .896.

Table 4.15 Total Variance Explained
ComponentInitial EigenvaluesExtraction Sums of Squared LoadingsRotation Sums of Squared Loadings
Total% of VarianceCumulative %Total% of VarianceCumulative %Total% of VarianceCumulative % 127.67949.42749.42727.67949.42749.42711.27920.14120.141 25.92210.57660.0035.92210.57660.00310.88019.42939.570 34.5028.03968.0424.5028.03968.0428.52815.22854.798

Extraction Method: Principal Component Analysis.

The above table gives eigenvalues, variance explained, and cumulative variance explained for the factor solution. The first panel gives values based on initial eigenvalues. For the initial solution, there are as many factors as there are variables. The "Total" column gives the amount of variance in the observed variables accounted for by each factor. The "% of Variance" column gives the percent of variance accounted for by each specific factor, relative to the total variance in all the variables. The "Cumulative %" column gives the percent of variance accounted for by all factors up to and including the current one. For instance the Cumulative % for the second factor is the sum of the % of Variance for the first and second factors. In the above table , there are a few factors that explain a lot of the variance which is a sign of good factor analysis and the rest of the factors explain relatively small amounts of variance. The Extraction Sums of Squared Loadings group gives information regarding the extracted factors or components. In the "Rotation Sums of Squared Loadings" group, the variance accounted for by rotated factors or components may be different from those reported for the extraction, but the Cumulative % for the set of factors or components will always be the same. Table 4.16 Rotated Component Matrixa

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