For one of my use case, i am building a credit approval model.
For one of the numeric variable i have missing values. I am using a linear regression model to replace these missing values rather than a mean as it could reduce the variability in the model.
While reading one of the research article it was suggested to use the most correlated variable as independent variable with the variable for which i am trying to impute missing values in regression.
I need to understand what is the logic for this as the research paper did not had enough literature around it.
Similarly, for all the numeric variable it was suggested to normalize them using a z-score to measure them in SD than in absolute numbers. What and why do i need to normalize my variable. For once i know there could be multicollinearity.
request expert advice on both the above questions.
Thank you. Shivi
Imputation is a big area and in general I generally do not impute values, but leave the values missing. You sound like you have many variables, so why not use the actual data and then there is no doubt in any biases involved by imputation.
When you do a multivariate regression, you are assuming the variables are normally distributed. The variables may be of different magnitudes or units. The concept of using the normalized values relates to both of these points, (a) that the z scores are putting all variables on an equal footing so to speak with a mean of zero and a variance of 1 and any extreme values will be noted easily. Multicollinarity is a separate issue and for this you can look at the correlation matrix of the variables.
I agree with Mortlock on both issues raised. However, if the available data are scanty,, you may not wish to ignore the data on the missing values. I do not see why the substitute input should be the most correlated. It could as well be least correlated. You will end up using the mean value. As for the issue of using z. values. it is the normal practice to transform the different units of research variables to one unitless. measure. The z. values have no units. That is the only way you can add , subtract .divide or multiply them and obtain a result that is unitless and also in conformity.
Using linear regression to impute missing data isn't a great idea. If you do it I would use all variables to predict the missing items not just the most correlated predictors.
A better approach is to use multiple imputation or full information maximum likelihood to impute the missing items as these procedures allow you to incorporate information from multiple variables and also take into account the error inherent in imputation (which otherwise leads you to underestimate noise in the data and inappropriately inflates sample size).
Chapter Dealing with missing data. Online Supplement 2 to Serious st...
Hi Shivi,
Missing data represent a typical problem in social research both when the unit of analysis is the individual, and the data is constructed through survey or is territorial with data drawn from national and/or international statistical sources.
In addition to the atomistic assumption , data matrices also require completeness. To meet this assumption, information must be avaible for all the cases in the matrix on all the properties/variables for which information was originally collected. Missing data may depend on a variety of factors which are either of random or systematic nature. In the case of missing data due to random factors, we can identify two instances: (a)
completely random, and (b) partially random.
I suggest you read my article dedicated to the treatment of the missing data that I send in attachment.
Greetings
Thank you all for the excellent and very helpful answers above. Really appreciate.
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