I already posted about exploratory factor analysis to understand the difference with PCA. Now, I carried out an exploratory factor analysis on my data set by using the R's
psych::fa function. I have some perplexities about the interpretation of the results listed here below. A is the matrix of my data having 16 rows and 6 columns.
fa(a,nfactors=3,rotate="varimax") In fa, too many factors requested for this number of variables to use SMC for communality estimates, 1s are used instead Factor Analysis using method = minres Call: fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, scores = scores, residuals = residuals, SMC = SMC, missing = FALSE, impute = impute, min.err = min.err, max.iter = max.iter, symmetric = symmetric, warnings = warnings, fm = fm, alpha = alpha) Standardized loadings based upon correlation matrix MR1 MR3 MR2 h2 u2 V1 -0.02 0.38 0.06 0.15 0.848 V2 0.14 0.50 0.14 0.29 0.711 V3 0.97 0.06 0.24 1.00 0.005 V4 -0.03 -0.05 -0.47 0.22 0.779 V5 0.67 0.74 0.03 1.00 0.005 V6 0.46 0.39 0.79 1.00 0.005 MR1 MR3 MR2 SS loadings 1.63 1.10 0.92 Proportion Var 0.27 0.18 0.15 Cumulative Var 0.27 0.45 0.61 Test of the hypothesis that 3 factors are sufficient. The degrees of freedom for the null model are 15 and the objective function was 2.15 with Chi Square of 26.17 The degrees of freedom for the model are 0 and the objective function was 0.07 The root mean square of the residuals is 0.03 The number of observations was 16 with Chi Square = 0.67 with prob < NA Tucker Lewis Index of factoring reliability = -Inf Fit based upon off diagonal values = 0.98 Measures of factor score adequacy MR1 MR3 MR2 Correlation of scores with factors 1.00 0.99 0.99 Multiple R square of scores with factors 0.99 0.99 0.99 Minimum correlation of possible factor scores 0.99 0.97 0.98
I cannot understand from chi-square value if I can not reject the null hypothesis of goodness of fit on three factors. I have seen some examples on the web for this function, but I could not find anything similar.