This link has been bookmarked by 10 people . It was first bookmarked on 19 Feb 2008, by Trisha Gao.
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30 Dec 16
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23 Nov 13
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29 Apr 13
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o, oblique rotation procedures
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Outline of Use
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any advanced multivariate technique
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quality of factor analytic research depends primarily on the quality of input data
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hat variables should be included in the analysis?
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hy certain variables are correlated.
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ld not include variables that are not believed to be related t
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t variables that can be inferre
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annot emerge unless there is a sufficient number of observed variables
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nimum of three observed variabl
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liable estimations of the correlations between the variab
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number of observations su
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reatly influenced by the presence of outlier
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mber of variables included in the analy
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Fourth,
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is correlation a valid measure of association among the variables to be analyzed
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n extraction techniqu
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PROC FACTOR pro
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factor analytic techniques
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principal component and principal factor analysi
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Communalities
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common and unique parts
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prior communality estimates
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communality estimate for a variable is the estimate of the proportion of the variance of the variable that is both error free and shared with other variables in the matrix
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(h2).
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ommunalities need to be supplied
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quared multiple correlation (R2) be
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ommunalities avai
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ll prior communalities to 1.0, w
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umber of Factor
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Kaiser-Guttman rule
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envalues greater than o
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ingle standardized original variable
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communality estimates ar
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variance to be decomposed into factors is less tha
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Percentage of Variance
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Scree Test
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nalysis of Residuals
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edicted correlation mat
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input correlation matrix.
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her the factors are not doing a good job explaining t
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we may need to extract more factors to more clos
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empirical criteria
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heoretical meaningfulness.
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chi-square values get smaller relative to the number of degrees of freedom
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riori hypothes
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mber of factors to be extracte
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f a theory or previous research suggests a certain number of factors an
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lyst wants to confirm the hypothesis or replicate the previous stud
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actor analysis with the prespecified number of factors can be run. T
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otation of Factors
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method of rotation
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ariant within rotation
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ore meaningful and interpretable solu
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otate the factors simultaneousl
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ver, after rotation th
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orthogonal rotation
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actors are maintain
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oblique rotations. Or
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ach othe
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implicity function
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e maximized
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ARIMAX method has been the most commonly used
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nterpretation of Factors
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actor loading
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factor structure matrix
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matrix of factor loadings
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n by m matrix of correlations b
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original variables and their factors
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actor pattern matrix,
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or each of the original variables on the rotated factors. T
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standardized regression coefficients
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significantly loaded on their factors
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.30 in
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umber of factors increases.
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1. Identifying significant loadings:
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2. Naming of Factors:
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ignificant loadings for each factor (column).
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larger the absolute size of the factor loading
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e FACTOR procedure with some options. METHOD=P or METHOD=PRINCIPAL specifies the method for extracting factors to be the principal-axis factoring method. This option in conjunction with PRIORS=SMC performs a principal factor analysis. The option ROTATE=PROMAX performs an oblique rotation after an orthogona
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02 Oct 10
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05 Apr 10
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03 Apr 10
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19 Feb 08
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The selection of one technique over the other is based upon several criteria. First of all, what is the objective of the analysis? Common factor analysis and principal component analysis are similar in the sense that the purpose of both is to reduce the original variables into fewer composite variables, called factors or principal components. However, they are distinct in the sense that the obtained composite variables serve different purposes. In common factor analysis, a small number of factors are extracted to account for the intercorrelations among the observed variables--to identify the latent dimensions that explain why the variables are correlated with each other. In principal component analysis, the objective is to account for the maximum portion of the variance present in the original set of variables with a minimum number of composite variables called principal components.
Secondly, what are the assumptions about the variance in the original variables? If the observed variables are measured relatively error free, (for example, age, years of education, or number of family members), or if it is assumed that the error and specific variance represent a small portion of the total variance in the original set of the variables, then principal component analysis is appropriate. But if the observed variables are only indicators of the latent constructs to be measured (such as test scores or responses to attitude scales), or if the error (unique) variance represents a significant portion of the total variance, then the appropriate technique to select is common factor analysis. Since the two methods often yield similar results, only CFA will be illustrated here.
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