How to do future prediction with year as a qualitative predictor in regression model?

Question

This is a general question. Hypothetically, I have a polynomial regression model where year is a qualitative predictor with multiple classes, converted into binary dummy predictors. E.g., if I have data for years 2000 thru 2002, the qualitative predictor would be

\begin{align} year = \begin{cases} 0 & if \ 2000 \\ 1 & if \ 2001 \\ 2 & if \ 2002 \end{cases} \end{align}

and the dummy variables would be

\begin{align} year0 = \begin{cases} 0 & if \ 2000 \\ 1 & if \ otherwise \end{cases} \end{align}

and etc. for year1, year2. And year0 is left out of the model to avoid the "dummy variable trap".

Can I still make an prediction for a particular future year with this model? The future year is not one of the dummy predictors.

Answer 1

You can make a prediction. You're going to have to make some assumptions, but that's often the case anyway.

For example, you can assume future years are most like the most-recent year, i.e. set the dummy variable for 2002 to 1.

Alternatively, you can assume future years are most like the average behavior of the three years in the sample, i.e. set the dummy variable for 2001 to 1/3, and the dummy variable for 2002 to 1/3.

Or you could forget the qualitative predictor, and use year as a continuous variable in the regression. By assuming a linear trend over the three years, you would be extrapolating linearly to future years.

One approach or the other might make more sense depending on the context. Or none of it might make sense depending on the context; you might be overfitting by including year in the first place.