I am interested in building a linear discriminant function to discriminate between 2 groups, out of 60 variables. (I'm planning to select the most discriminative of the variables for a future diagnostic test.) I have calculated the area under the ROC curve for each of these variables individually and none havehas an AUC greater than 0.73. I have a fairly small sample of 50 healthy and 50 diseased individuals (these are the two groups).
I have tried to reduce the number of variables using principal component analysis (PCA). There are 3 components accounting for 83% of the variation. But unfortunately, all 60 variables have similar weightings (loadings) in the 3 components, so I can't pick just few. I would ordinarily pick the highest weighted variables and then incorporate them in a linear discriminant function, but 60 is too many, especially given the small sample.
I wondered if, rather than use the 60 variables, it is possible to use the 3 principal components themselves to buildin a linear discriminant function? I am using Stata for the analysis. Does anyone have any suggestions (LDA)?