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# Class Note for SW 983 with Professor McDonald at KU

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
SW 983 LECTURE NOTES FACTOR ANALYSIS Uses of Factor Analysis Data Reduction Determining underlying structures These two are not mutually exclusive In carrying out 1 it is necessary to assumediscover 2 If one starts with 2 you should have some hypotheses in mind Exploratory FA searching for underlying structure Confirmatory FA testing hypotheses about underlying structure which generated set of measures X1 X2 X3 X4 X5 X6 Factor F is a construct latent variable or unmeasured variable X s are indicators or measured variables Conducting Factor Analysis 1 Examine the correlation matrix since one of the goals of factor analysis is to obtain quotfactorsquot that help explain the correlations between variables the variables must be related to each other for the factor model to be appropriate Bartlett39s test for sphericity can be used to test the hypothesis that the correlation matrix is an identity matrix If there is an underlying structure the variables should be correlated You wish to reject the null hypothesis if the data are suitable for FA KaiserMeyerOlkin measure of sampling adequacy referred to as MSA in our book is an index for comparing the magnitudes of the observed correlation coefficeints to the magnitude of the partial correlation coefficients partial correlations should be small if the variables share common factors Values closer to l gt 5 needed for factor analysis 2 Factor extraction Principle components and others the first principal component is the combination that explains the largest amount of variance in the sample Successive components explain progressively less This is less true for principle axis factoring making it more appropriate if we are looking for structure not just data reduction Communality common factor variance sums of squares of factor loadings the proportion of variability for a given variable that is explained by the factors Factor Loading correlations between variables and factors if orthogonal coefficients used to express a standardized variable in terms of the factors Factor Matrix table of factor loadings Eigen Values variance explained by each factor using standardized variables Cutoff generally at values gt 1 Scree Plot 7 plot of total variance associated with each factor Scree begins at last true factor Factor Structure Matrix 7 contains correlations between variables and factors Same as pattern matrix when factors are orthogonal Factor Pattern Matrix 7 contains factor loadings regression of variables on factors 3 Factor rotation unrotated matrix frequently not interpretable The goal of rotation is to transform complicated matrices into simpler onesl Obligue Rotation 7 factors are allowed to be correlated Generally this is a reasonable assumption with the types of variable lists we will be dealing with You can run oblique first then check the correlations of the resulting factors If small try orthogonal rotation Orthogonal Rotation factors not correlated o Varimax minimizes number of variables that have high loadings on a factor thereby enhancing interpretability Most commonly used 0 Quartimax minimizes the number of factors needed to explain a variable often results in a general factor with high to moderate loadings on most variables 0 Eguamax combination of Varimax and Quartimax 4 Interpret and label factors With orthogonal rotation the pattern and structure matrices are identical With oblique rotation they are different The pattern matrix is best for determining the clusters of variables defined by the oblique factors 5 Calculate factor scores ij Z w jiXik where i number of variables all variables are included j number of factors k number of cases 44 or create summated scale 2 x 139 where only the 1 variables with significant loadings are summed iNOTE OnTotalVarianceExplainedTable First set of variances always from PC regardless of the extraction method chosen Second set will differ if PFA or anything other than PC used as extraction method Orthogonal rotation yields third set where accounted for by each factor will differ but cumulative will be the same as extraction When factors are correlated sums of squares loadings cannot be added to obtain total variance

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