LCGA of factor analysis of count vari...
Message/Author
 Mat Weldon posted on Friday, August 10, 2012 - 5:47 am
Hello,

I would like to fit an exploratory factor model to a set of six count variables (occurrence of different types of crime) to bring out 2-4 factors explaining the covariance between crime types, and then do a LCGA (Nagin-type) analysis of the factor scores at different ages.
The factor loadings would be fixed at all time points, representing an immutable covariance structure, but the factor scores (interpreted as a person's latent propensity to commit a type of crime) would vary with age, and the mixture would allow different age effects.
Because the factor loadings are not dependent upon the mixtures, I think I should be able to estimate the factor loadings first, and then fit an LCGA model separately on the predicted factor scores.
Here is a link to a schematic of the model:http://goo.gl/XImTA
I have two questions:
1.Can I add an offset (exposure indicator) to a factor analysis model?
2.Once estimated, can I use the factor model to predict factor scores on new data (e.g. using empirical Bayes or similar)?
Many thanks,

Mat
 Linda K. Muthen posted on Friday, August 10, 2012 - 10:17 am
1. Yes.
2. I would not use factor scores. I would use the factors as indicators.
 Mat Weldon posted on Monday, August 13, 2012 - 3:57 am
Thank you for your quick reply. If I understand you correctly, you are saying to use a path model and estimate the two parts simultaneously. Is this possible for count indicators? If so, I'm worried that the counts at the time-point level are too small (i.e. the data is too discrete) to be able to estimate the factor model. Do you know if the factor models for count variables can handle small counts (i.e. mean less than 1)?

My idea was to avoid small counts by calculating the factor model on entire career counts, and then calculate the factor scores at the time-points as fixed quantities, which is not very satisfactory I admit. I'd rather estimate the entire model if possible.

Many thanks,

Mat
 Linda K. Muthen posted on Monday, August 13, 2012 - 9:07 am
I would start out by analyzing each time point separately to see how that goes. I would not calculate on the entire career counts.