# Interpreting R output from exploratory factor analysis regarding rejection of null hypothesis of goodness of fit

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)
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
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
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.

thanks,

• "(...) 16 rows and 6 columns": Are you saying you are using an FA model with 16 subjects and 6 items? – chl Jun 15 '11 at 12:32
• And sorry if I repeat myself, but it would have been good to address earlier comments on your series of questions and you should register your account (this also help getting notified by new replies or comments). – chl Jun 15 '11 at 12:36
• Yes, I am using FA model with 16 subjects and 6 items (I know that this is a very little sample, but it is a preliminary analysis). I also registered myself just right now. thank you – giovanna Jun 16 '11 at 12:51