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## CFA PCA Path Analysis

#### Assistance with running CFA, PCA or Path Analysis

Confirmatory factor analysis checks whether the number of factors and the loadings of measured (indicator) variables on them conforms to what is expected on the basis of pre-established theory. variables are selected on the basis of the previous assumption and factor analysis is applied to examine if they load as predicted on the required number of factors. The researcher's prior assumption is that each factor is incorporated with a detailed subset of independent variables.

Path analysis is an extension for regression analysis. Here, from the correlation matrix, two or more models are compared simultaneously. The graphical illustrations are shown using an arrow and square, which shows the path and causation. The weights of regression are predicted by the model developed in path analysis. After the regression weights are estimated we calculate the goodness of fit stats to check the fitting of the model. ### Sample output after running factor analysis using SPSS software

The table estimates the Kaiser-Meyer-Olkin value , which is the proportion of examining sufficiency, which ranges somewhere between 0 and 1. However, the estimation of 0.6 is least recommended.The sample is sufficient if, KMO is greater than 0.5.In this table, KMO = 0.830 which indicates that the sample is sufficient and we can proceed with the factor analysis. Bartlett’s test of sphericity is performed by taking α = 0.05. Here p-value is .000 less than 0.05, and hence, factor analysis is valid.  The table indicates that initial eigenvalues has all the 7 variables with the percentage of the variance of all the variables with the cumulative percentage of variance. After running factor analysis in SPSS, we get 2 factors which explain 84.202 % of the variance. Any factor which has eigenvalue less >1 would be selected into a particular factor.

### The below gives detailed information about the factor loading values in each factor with each variable   ### Communalities

This is the proportion of each variable’s variance that can be explained by the factors we estimated. It is noted as H2 and is defined as the sum of the squared factor loadings for all the variables. ### Extraction

The values in the column indicate the proportion of each variable’s variance that has been explained by the clutched factors. Variables with high values are represented in the common factor space. They are the reproduced variances from the factors that you have extracted. ### Initial

The principal factor axis factors, the initial values on the diagonal of the association matrix are prepared by the squared various associations of the variable with the other independent variables. ### Factor

The rotated factors that have been extracted using different varimax, direct oblimin methods