Number of parameters in exploratory factor analysis
Hi everyone. Below is the output of an exploratory factor analysis using the command factor and the maximum likelihood estimation. There are six indicators (bg2cost1-bg2cost6) and two factors, so I thought there 18 parameters were needed to be estimated, including 12 factor loadings and six uniqueness (i.e. the variances of six error terms). However, the output shows that "Number of params = 11".
I know that exploratory factor analysis needs some restrictions for statistical identification, such as fixing the variances of factors at 1 and fixing the correlation between factors at 0. Apart from these, are there other restrictions imposed on the example below, so that we only need to estimate 11 parameters?
PS. The output is quoted from the Stata manual (Example 5 for factor). From the manual and some other textbooks, I didn't find the answer, so I am here for seeking your help. Thank you very much.
I know that exploratory factor analysis needs some restrictions for statistical identification, such as fixing the variances of factors at 1 and fixing the correlation between factors at 0. Apart from these, are there other restrictions imposed on the example below, so that we only need to estimate 11 parameters?
PS. The output is quoted from the Stata manual (Example 5 for factor). From the manual and some other textbooks, I didn't find the answer, so I am here for seeking your help. Thank you very much.
Code:
. webuse bg2, clear
. factor bg2cost1-bg2cost6, factors(2) ml
Factor analysis/correlation Number of obs = 568
Method: maximum likelihood Retained factors = 2
Rotation: (unrotated) Number of params = 11
Schwarz's BIC = 83.4482
Log likelihood = -6.842448 (Akaike's) AIC = 35.6849
--------------------------------------------------------------------------
Factor | Eigenvalue Difference Proportion Cumulative
-------------+------------------------------------------------------------
Factor1 | 1.02766 0.28115 0.5792 0.5792
Factor2 | 0.74651 . 0.4208 1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(15) = 269.07 Prob>chi2 = 0.0000
LR test: 2 factors vs. saturated: chi2(4) = 13.58 Prob>chi2 = 0.0087
Factor loadings (pattern matrix) and unique variances
-------------------------------------------------
Variable | Factor1 Factor2 | Uniqueness
-------------+--------------------+--------------
bg2cost1 | -0.1371 0.4235 | 0.8018
bg2cost2 | 0.4140 0.1994 | 0.7888
bg2cost3 | 0.6199 0.3692 | 0.4794
bg2cost4 | 0.3577 0.0909 | 0.8638
bg2cost5 | -0.3752 0.4355 | 0.6695
bg2cost6 | -0.4295 0.4395 | 0.6224
-------------------------------------------------
