Most of the answers have helped clarify what modeling for explanation and modeling for prediction are and why they differ. What is not clear, thus far, is how they differ. So, I thought I would offer an example that might be useful.
Suppose we are intereted in modeling College GPA as a function of academic preparation. As measures of academic preparation, we have:
- Aptitude Test Scores;
- HS GPA; and
- Number of AP Tests passed.
Strategy for Prediction
If the goal is prediction, I might use all of these variables simultaneously in a linear model and my primary concern would be predictive accuracy. Whichever of the variables prove most useful for predicting College GPA would be included in the final model.
Strategy for Explanation
If the goal is explanation, I might be more concerned about data reduction and think carefully about the correlations among the independent variables. My primary concern would be interpreting the coefficients.
In a typical multivariate problem with correlated predictors, it would not be uncommon to observe regression coefficients that are "unexpected". Given the interrelationships among the independent variables, it would not be surprising to see partial coefficients for some of these variables that are not in the same direction as their zero-order relationships and which may seem counter intuitive and tough to explain.
For example, suppose the model suggests that (with Aptitude Test Scores and Number of AP Tests Successfully Completed taken into account) higher High School GPAs are associated with lower College GPAs. This is not a problem for prediction, but it does pose problems for an explanatory model where such a relationship is difficult to interpret. This model might provide the best out of sample predictions but it does little to help us understand the relationship between academic preparation and College GPA.
Instead, an explanatory strategy might seek some form of variable reduction, such as principal components, factor analysis, or SEM to:
- focus on the variable that is the best measure of "academic
performance" and model College GPA on that one variable; or
- use factor scores/latent variables derived from the combination
of the three measures of academic preparation rather than the
Strategies such as these might reduce the predictive power of the model, but they may yield a better understanding of how Academic Preparation is related to College GPA.