I am working on a small dataset with 22 observations and using 30 variables under eight dimensions to prepare an index. I am using factor analysis for the same. But the condition for factor analysis is that the sample size or the no. of observations should be more than 100-150. and another condition is that no. of variables should be less than the sample size. literatures suggest to use Bayesian factor analysis or regularized confirmatory factor analysis in case of small sample size.
can anyone help me with this and suggest me with solutions for dealing with these problems. Can I perform Bayesian or regularized factor analysis in STATA?
Thanks!
Stata's bayesmh fits a variety of Bayesian regression models using an adaptive Metropolis–Hastings (MH) Markov chain Monte Carlo (MCMC) method. Gibbs sampling is also supported for selected likelihood and prior combinations.
To fit a Bayesian model, in addition to specifying a distribution or a likelihood model for the outcome of interest, you need to also indicateand specify prior distributions for all model parameters.
For simplicity, you could model mpg using a normal distribution with a known variance of, say, 35 and use a noninformative flat prior (with a density of 1) for the mean parameter. Because bayesmh uses MCMC, a simulation-based method, the results will be different every time you run the command. (Inferential conclusions should stay the same provided MCMC converged.) You may want to specify a random-number seed for reproducibility in your analysis.
Hello Sujata,
Unfortunately, 22 cases isn't sufficient to evaluate models that have to reproduce 435 unique relationships (= 30 * 29 / 2), let alone the 30 variances. Any solution you come up with should be considered one to evaluate further with additional information if and when you are able to obtain it.
Good luck with your work.
Thank you for your valuable suggestions.
I tried reading the concept of Bayesian estimation method but couldn't understand its use in factor analysis. when I tried to do Bayesian estimation in Stata, there were options to do different kinds of regression analysis only hence, couldn't understand how do I use it to solve the problem of small sample size.
Any suggestion or idea about one-parameter Maximum Likelihood estimation methods under anti-image assumption?
One more issue with my data is that variables are not normally distributed. I am doing one-common factor analysis that is factor analysis specific to dimensions. All the 30 indicators have been grouped under eight dimensions on theoretical basis that the following group of variables should belong to one specific dimension. after that I did factor analyses on each dimensions and then checked whether the pre-determined group of variables under one dimension actually belong to just one or more than one factor, but getting Heywood cases in case of few variables.
Thanks!
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