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# A Factor Analysis of the Attempts To Identify Underlying Variables

Factor Analysis Factor analysis attempts to identify underlying variables or factors that explain the pattern of correlations within a set of observed variables Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance observed in a much larger number of manifest variables Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis for example to identify collinearity prior to performing a linear regression analysis The factor analysis procedure offers a high degree of flexibility Seven methods of factor extraction are available Five methods of rotation are available including direct oblimin and promax for nonorthogonal rotations Three methods of computing factor scores are available and scores can be saved as variables for further analysis Rotation In rotating the factors we would like each factor to have nonzero or significant loadings or coefficients for only some of the variables Likewise we would like each variable to have nonzero or significant loadings with only few factors and if possible with only one If several factors have high loadings with the same variable it is difficult to interpret them Statistics For each variable number of valid cases mean and standard deviation For each factor analysis correlation matrix of variables including significance levels determinant and inverse reproduced correlation matrix including anti-image initial solution communalities eigenvalues and percentage of variance explained Kaiser-Meyer-Olkin measure of sampling adequacy and Bartletts test of sphericity unrotated solution including factor loadings communalities and eigenvalues rotated solution including rotated pattern matrix and transformation matrix for oblique rotations rotated pattern and structure matrices factor score coefficient matrix and factor covariance matrix Plots Scree plot of eigenvalues and loading plot of first two or three factors Assumptions The data should have a bivariate normal distribution for each pair of variables and observations should be independent The factor analysis model specifies that variables are determined by

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