# Regression with variables that are dependent off another

Say I am running a regression to predict race time in an upcoming race. For each runner, I have a demographic information and one past race performance. For some subset of runners, I have another race performance.

My model would therefore look like:

Future Race ~ Demographic Info + Past Race1 + Past Race2


However, for many modelling packages in r, the regression simply drops incomplete data rows.

I could present a simpler model of simply:

Future Race ~ Demographic Info + Past Race1


This seems to drop useful information. Are there modelling approaches to dealing with this incomplete data beyond simple deletion or imputation (generating random values from the distribution)?

• Note that imputation need not generate random values: multiple imputation uses correlations with other independent variables (such as the demographic info) to generate meaningful guesses for the distribution of values, ultimately generating a number of bootstrap datasets. The variation across datasets captures the uncertainty in these correlations.
– mkt
Dec 4, 2017 at 17:41
• Possibly too simple to mention, but why not use (a) model including past race data for the subset for which it is available (b) model for other predictors only for the same subset (c) model for other predictors for all data. That is perhaps as complex as most researchers would want to be. It's hard to be optimistic about imputing past race performance from demographic data. Dec 4, 2017 at 18:25