I have a data set with quite a lot of missing values, more in some variables than others. I performed bivariate analyses and I want to select variables for multivariate analysis. I understand that some suggest including all variables with a p value of < 0.25 in the bivariate analysis to go into the multivariate analysis, and then performing backward elimination. I'm using binary logistic regression (the outcome variable is binary).
My problem is that I have one variable that is a strong independent predictor, but there are many missing values for this variable; the number of cases included in the analysis would almost double should I omit this variable. Should I omit this variable, some other variables would reach statistical significance in the regression.
My questions are:
1. What are your thoughts on whether this variable should go into the regression?
2. What are your thoughts on why those other variables reach statistical significance in the regression? Do you think it's simply because of the larger number of cases included in the analysis?
The fact that the variable has a missing value in a record may also be another data point.
I would recommend using the median to fill up missing values, and add a feature indicating that data was missing and was filled.
That new feature turns out to be useful in some cases.
Another possibility is that you make a sample where records with blank values are omitted. If the the sample is representative find the regression on the sample. Of course, when using the regression there should be the variable value provided.
The answer for your second question is that your independent variables are not so independent and there exists the collinearity.
Although collinearity is generally not considered appropriate it might still happen that the remaining variables together can describe the result as well as your best one. Try the options out :)
Statistical significance is strongly dependent on the sample size, i.e. the number of missing values.
The fact that a predictor has a small pvalue does not mean that it has a high predictive power in the model, it just means it has a small variation.
You should try different imputing methods and assess how they affect the estimates in the model, which is what you should focus on.
Also pvalues are invalid if computed on the same sample used to perform variable selection, so the two steps should be independent.
The most reasonable model would be the one that includes all relevant predictors and control variables.
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