I have a dataset of a binary response variable and 22 predictor variables that have multicollinearity. My goal is to make a predictive model. The data was sampled every 30 seconds over three days. There is a high amount of autocorrelation between y(t) and y(t-1). I have done PCA regression with time and the y(t-1) as predictor variables. It seems to be working because my misclassification error is about 3%. Are there any statistical issues with what I have done? I did standardize my predictor variables including time.
Also, I additionally tried using stepwise logistic regression to select the best variables before doing PCA, which actually got rid of time and kept the y(t-1), and I got a similar misclassification rate of about 3% again.
I am using R.
In your case, I would suggest that you use the "Insights" software. You find it at knowledgeminer (dot) eu. You can download it and use it for 30 days free of charge and after that you can pay or not if you want to keep it and use it in the future. Do not hesitate to ask if you have more questions
My feeling is you better try some popular open source models that proved to bring on some datasets good performance such as xgboost , they will handle your correlations and better focus on feature engineering first before feeding into model .After that you could jump to other approaches such as ensembling
It is perfectly fit to use regression on principal components as you did, by the way PCA can handle binary data as clearly stressed by Cox ( Cox, D. R. (1972). The analysis of multivariate binary data. Applied statistics, 113-120. ). Most important is to try and give to your extracted components a meaning by looking at component loadings ( Giuliani, Alessandro. "The application of principal component analysis to drug discovery and biomedical data." Drug discovery today 22.7 (2017): 1069-1076. ).
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