Hello all,
I have some data from a drug court sample set up into a modified multi-trait-multi-method matrix. I'm wondering whether it's appropriate to apply CFA.
I have two constructs: drug involvement and criminal risk. And two methods: official records and interview. Specifically, for drug involvement official records I have number of prior drug arrests/convictions (yes/no, range 0-2). Drug involvement interview I have the Texas Christian Univ. Drug Screen (range 0-9), LSI-R Alcohol/Drug scale (range 0-9), and a measure that the court uses (range 0 - 15). For criminal risk official records I have number of prior non-drug arrests/convictions (as for drug priors, range 0 - 2). For criminal risk interview I have LSI-R criminal risk (range 0 - 9).
I'm thinking that I can't run a CFA to parse out method vs. construct variance, because I have only two constructs and two measures; for some reason I think you need three of each, but I can't confirm this. Also, each of the measures is on a different scale, which I could correct by normalizing the scores, but then, I'm not sure if I'd only be introducing another problem.
I did run a multidimensional scaling analysis, which is more flexible than factor analysis, with some interesting and informative results.
Thanks!
Warren
First, with so few variables, why not just run a traditional multitrait-multimethod analysis, populating your grid with the results of paired correlations between each of your variables?
If you want to use factor analysis, though, be mindful of the requirements of factor analysis with regards to sample size.
https://www.encorewiki.org/display/~nzhao/The+Minimum+Sample+Size+in+Factor+Analysis
I would recommend the following texts.
Goldberg, L. R., & Velicer, W. F. (2006). Principles of exploratory factor analysis. In S. Stack (Ed.), Differentiating normal and abnormal personality (2nd ed., pp. 209-237). New York: Springer.
MacCallum, R. C., Widaman, K. F., Zhang, S., & Hong, S. (1999). Sample Size in Factor Analysis. Psychological Methods, 4(1), 84-99. doi: 10.1037/1082-989X.4.1.84
Thanks both. I went ahead and ran a simple factor analysis (I'm good on sample size).
If a construct has only two indicators, you can usually achieve an identified model for a CFA by assuming parallel measures (or at least, tau-equivalent measures) -- which would be modeled by imposing equality constraints between the two loadings of the indicators, and between the two error variances. That assumption would not seem justifiable for your problem, however, given the widely differing scales, variances (though as you note normalizing could help), and data sources/methods. Since the goals of your analysis presumably include comparing the adequacy of the two methods, assuming that the two indicators are equally valid and reliable would defeat that purpose. Sometimes you can get to an identified two-indicator model for CFA through constraints elsewhere in the model, rather than the parallel measures constraints, but it doesn't sound like the rest of your model is complex enough for any other constraints to do the trick.
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