I have a data set consisting of data collected from a questionnaire that I wish to validate. I have chosen to use confirmatory factor analysis to analyse this data set.
The instrument consists of 11 subscales. There is a total of 68 items in the 11 subscales. Each item is scored on an integer scale between 1 to 4.
Confirmatory factor analysis (CFA) setup
I use the
sem package to conduct the CFA. My code is as below:
cov.mat <- as.matrix(read.table("http://dl.dropbox.com/u/1445171/cov.mat.csv", sep = ",", header = TRUE)) rownames(cov.mat) <- colnames(cov.mat) model <- cfa(file = "http://dl.dropbox.com/u/1445171/cfa.model.txt", reference.indicators = FALSE) cfa.output <- sem(model, cov.mat, N = 900, maxiter = 80000, optimizer = optimizerOptim) Warning message: In eval(expr, envir, enclos) : Negative parameter variances. Model may be underidentified.
Straight off you might notice a few anomalies, let me explain.
- Why is the optimizer chosen to be
ANS: I originally stuck with the default
optimizerSem but no matter how many iterations I run, either I run out of memory first (8GB RAM setup) or it would report
no convergence Things "seemed" a little better when I switched to
optimizerOptim where by it would conclude successfully but throws up the error that the model is underidentified. Upon closer inspection, I realise that the output shows
NA so I am not sure what is exactly happening.
maxiteris too high.
ANS: If I set it to a lower value, it refuses to converge, although as mentioned above, I doubt real convergence actually occurred.
So by now I guess that the model is really underidentified so I looked for resources to resolve this problem and found:
I followed the 2nd link quite closely and applied the t-rule:
- I have 68 observed variables, providing me with 68 variances and 2278 covariances between variables = 2346 data points.
- I also have 68 regression coefficients, 68 error variances of variables, 11 factor variances and 55 factor covariances to estimate making it a total of 191 parameters.
- Since I will be fixing the variances of the 11 latent factors to 1 for scaling, I would remove them from the parameters to estimate making it a total of 180 parameters to estimate.
- My degrees of freedom is therefore 2346 - 180 = 2166, making it an over identified model by the t-rule.
- Is the low variance of some of my items a possible cause for the underidentification? I asked a previous question on items with zero variance which led me to think about items which are very close to zero. Should they be removed too? Confirmatory factor analysis using SEM: What do we do with items with zero variance?
- After reading much, I surmise that the underidentification might be a case of empirical underidentification. Is there a systematic way of diagnosing what kind of underidentification it is? And what are my options to proceed with my analysis?
I have more questions but let's take it at these 2 for now. Thanks for any help!