Does anyone have experience with approaches for selecting the number of sparse principal components to include in a regression model?
While I don't have direct insights about your question, I ran across some research papers, which might be of your interest. That is, of course, if I understand correctly that you are talking about sparse PCA, principal component regression and related topics. In that case, here are the papers:
The cross validation results were also used to determine the optimal number of dimensions for the LSI space. Too few dimensions did not take advantage of the predictive power of the data; while too many dimensions resulted in over-fitting. Fig. 4 shows the distribution of average errors for models with different numbers of LSI dimensions. The models with four dimensional LSI spaces produced both the fewest average number of errors and the fewest median number of errors, so the final model was built using a four dimensional LSI space.
I can post a copy if you aren't an ieee member.
This is from a paper I wrote in undergrad. I had a problem where I needed to decide how many dimensions (Latent Semantic Indexing is similar to PCA) to use in my logistic regression model. What I did was pick a metric (i.e. the error rate when using a flagging probability of .5) and looked at the distribution for this error rate for different models trained on different number of dimensions. I then picked the model with the lowest error rate. You could use other metrics like area under ROC curve.
You could also use something like stepwise regression to pick the number of dimensions for you. What type of regression are you preforming specifically?
What do you mean by sparse btw?