Variable order entry in REGRESSION with METHOD=ENTER
I'm running a linear regression model in SPSS Statistics. I'm specifying forced entry (METHOD=ENTER) for predictor variables. I've noticed that there is a Variables Entered/Removed table printed that lists the variables entered, but not in the order in which they were specified. Also, if I happen to specify a set of predictors with linear dependencies, such as k dummy variables to represent a k-level categorical factor while including the constant or intercept, the dummy that's excluded is not necessarily the last one listed. How are variables entered with METHOD=ENTER?
Resolving the problem
REGRESSION operates by creating a correlation matrix and then uses what's known as a sweep algorithm to move variables into or out of the equation one at a time. If you use ENTER on the METHOD subcommand (which of course is the default) it still applies a selection process.
It determines which variable to include at a given point by taking the one with the highest tolerance value. The tolerance is 1 minus the proportion of variance (1-R^2) accounted for if you regressed a given predictor on all the other predictors already in the equation. At the first step, when the tolerance for all predictors is 1, or in other cases when there are tied tolerances, in its search process, it goes through in order and replaces the current maximum tolerance with the tolerance for the new predictor if that new tolerance is greater than or equal to the existing current maximum tolerance value. Thus the first variable that will get entered is the last one listed. After that, the intercorrelations among the predictors entirely determine the order of entry unless there is another tie.