Sunday, December 18th, 2016
A proper linear model is one in which the weights given to the predictor variables are chosen in such a way as to optimize the relationship between the prediction and the criterion. The most commong example is simple regression analysis in where the predictor variables are weighted in such a way as to maximize the correlation between the subsequent weighted composite and the actual criterion.
An improper linear model is one in which the weights are chosen by some nonoptimal method. They may be chosen to be equal or they may be chosen on the basis of the intuition of the person making the prediction.
The logic of multiple regression is unassailable: it finds the optimal formula for putting together a weighted combination of the predictors. However, the complex statistical algorithm adds little or no value. One can do just as well by selecting a set of scores that have some validity for predicting the outcome and adjusting the values to make them comparable (by using standards or ranks). A formula that combines these predictors with equal weights is likely to be just as accurate in predicting new cases as the multiple-regression formula that was optimal in the original sample. Even more, formulas that assign equal weights to all the predictors are often superior, because they are not affected by accidents of sampling.
For example, marital stability is weel predicted by a formula:
Marital Stability = Frequency of Lovemaking – Frequency of Quarrels.
You don’t want your result to be a negative number.
Hundreds of studies have proven that Proper Linear Models (regressions, etc.) are better at predicting dependent variables from independent variables than intuitively predicting the dependent variable. But even Improper Linear Models (experts define variables as positive or negative and then a simple linear function is built without being regressed) beat experts studying the independent variables and forecasting the outcome (heuristics).
Summing-up: an algorithm that is constructed on the back of an evelope is often good enought to compete with an optimally weighted formula, and certainly good enough to outdo expert judgment.