addressing multicollinearity and low levels in PCA I am trying to build a multiple regression model to predict properties prices and I would like to cunduct PCA to choose the most relevant variables.


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*I know that the the variables should be uncorrelated. What would be the best way to check and deal with multicollinearity? I have 80 variables. I have tried correlation plot and VIF function in r and deleted those ones with VIF around 10 (>=9.9 should I be more/less conservative??).

*After I created dummy variables out of my categorical variables I applied
prin_comp <- prcomp(pca.train, scale. = T) and then it returned an error: Error in prcomp.default(pca.train, scale. = T) : 
cannot rescale a constant/zero column to unit variance.
I do realize that some of the levels whithin the factors(there are about 17 of them with such a condition) don´t appear very often in the dataset and as a dummy variable contain mostly zeros. What can I do about such an unfair level distribution?
I am new to stats so any help would be appreciated.
 A: *

*If you genuinely care about prediction and not at all about explanation (cause and effect), then with a large enough sample size you needn't exclude any of your predictors, even the very collinear ones.  If your sample size is on the small side, e.g., < 1600, then you have a considerable number of choices to make in reducing from 80 predictors.  You could continue to judge based on VIF or you could look up variable selection or regularization methods.

*You probably have variables that have no variation when the data set is reduced to just those cases missing no data (the complete cases).  Eliminating these variables should help; or you could embark on imputation of missing values. 
EDIT:  Since from your comments you are reluctant to exclude predictors, and since apparently missing data are not much of an issue, you could, for predictive purposes, conduct PCA on the majority of variables, while keeping others intact outside of the PCA, e.g., preserving all categories.  Levels (dummy variables) with nearly all zeroes will prove relatively uninformative; I wouldn't expect much predictive power to come from a category with 3 "1"s out of 2500 cases.  But at least you wouldn't be ruling anything out as a possible predictor.
As to a subjective rating of quality, there's nothing wrong with adding that if you feel it will be valid and reliable.  If it's collinear with other predictors,  you won't have lost anything by trying it.
More problematic is your statement that you want to "explain what influences the property price."  For this you would have the unenviable task of reducing your 80 predictors to a subset that covers the different domains you and other experts might have identified (location, style, various aspects of quality, etc.) while also avoiding the inflation of coefficient standard errors that comes with correlated predictors.  Ideally this would be a collaborative task for which you would allow plenty of time and multiple iterations of analysis.
