# Advice on missing value imputation

I am working on insurance data in which a customer has a field named customer_no_dependent (customer's number of dependent). Its coming out to be a significant variable( just that it has $p<0.0001$).

This variable has almost 20% missing values. For imputation, I thought to determine proxy indicators for number of dependents. I tried age (thinking a person more aged could be having more dependents). I correlated it with premium amount as well to think that a person who has more dependents could be having less disposable income. So low premium paying could be meaning more dependents. I do understand that a demographic variable can't be fully taken out from such logic.

Now, if somebody goes into detail, he can prove my imputation to be far from perfect. What should I do in such situation? Would deleting those 20% be a correct solution? 20% for my data would be close to 2 lakh rows which is large amount of information..

I know, this question can have many possible answers. I would be grateful for any pointers how to proceed.

• In my opinion, if the variable is significant (p<.0001) without imputation, and you have enough data, that is reason enough to leave it alone. What are the confidence intervals telling you? – Ralph Winters May 5 '11 at 13:30
• If you have 2 lakh (i.e. 2 hundred thousand) cases where the number of dependents is unknown, out of about 1 million, then you may be able to include the fact that you don't know the number of dependents as a factor in the analysis. – Henry May 5 '11 at 14:21
• @RalphWinters, failing to model missing data may be perfectly reasonable in some circumstances, but the statistical significance of the variable has nothing to do with whether or not some sort of imputation procedure is desirable. Much depends on what the ultimate goal of the data analysis is and how much effort you are willing to put into it. – Michael Bishop Nov 3 '12 at 23:19
• Look at Gelman and Hill's book chapter on imputation. – Michael Bishop Nov 3 '12 at 23:21
• @MichaelBishop - I am generally not a big fan of imputation. I would prefer to derive insights from a signficant variable with missing data, rather than risk populating the variable with "made up data" based upon assumptions. I have been burnt on this a several times, in which new data came in which contracted my original assumptions. An assumption will always increase the error, although imputation serves to actually Decrease the error, it is an assumption nevertheless. – Ralph Winters Nov 10 '12 at 17:32

First of all: it is not clear from your explanation whether or not you have done multiple imputation. If not: please do so: single imputation could be worse than simple complete case analysis, and can both lead to severely biased results.

Next, if I understand correctly, your problem is that you don't know which variables to use as covariates for you imputation model. If you number of possible covariates (I assume these are the other covariates in your model of interest) is limited, you could opt for the nonparametric kind of imputation that is offered by MICE (in R) and similar algorithms.

Another option is to use shrinkage (LASSO or alike) in a model predicting customer_no_dependent: this should give you a set of likely predictors. Be aware though, that this step induces even more uncertainty (you reuse the data yet again), and you should trust your confidence intervals and p-values somewhat less. The effect should be negligble if your association is truly as strong as you indicate.

If you do use the kind of parametric and commonsense induced imputation mechanism (like regressing on 'credible' predictors): simply make note of this fact, and mention that the obtained results are conditional on this extra set of assumptions.

• Thank you !!! I would take note of what you wrote. I see predicting customer no of dependents as a dependent variable and taking out the list of predictors as one way. – ayush biyani May 5 '11 at 12:39

I don't know if you have SAS experience, but I've used SAS PROCs MI and Mianalyze to perform (and then synthesize) multiple imputations in several different models. Building the "imputation model" (this yields non-biased estimates of missing data, incorporating the uncertainty one finds in non-missing data) is probably the most difficult task. The imputation model will include all or most analysis variables (i.e., predictors in your analysis model), as well as auxiliary variables-other variables that correlate with the dependent variable, the state of being missing or both. (Note: you might want to use p < .15 as a first threshold.)

One then selects parameters such as the number of iterations (both before the first imputation and between iterations), the estimation method, the sampling method, etc. Of course, preceeding all of this, one should determine what led to the missing data, and whether missing data are MCAR (missing completely at random), MAR (missing at random), or MNAR (missing not at random). Explaining these is beyond the scope of this forum, but--if you're not familiar with these terms--there are a number of good introductory-level descriptions on the web.

The above can be quite time-consuming depending on the number of candidate variables for your imputation model; however, this has the "silver-lining" advantage of clarifying what's driving the imputation. There are also a number of good diagnostic tools that allow you to evaluate and compare different imputation models.

Mplus enables one to do all of this more quickly; basically, it models the state of being missing using ML estimation. You can read more about this at statmodel.com.

I agree that single imputation or dropping all missing cases is probably not the best approach, depending, of course, are your research questions. If SAS is an available language and you'd like to talk about this in more detail, please post.

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