Fixing Boundary Violations: Applying Constrained
Optimization to the Truncated Regression Model
5.4 Identifying Boundary Violations
At last, to understand what those boundary violations are about, we translate the type II boundary violations into type I violations as Table 5 shows. The translation proceeds as follows: First, we hold the baseline profile at the combination that generates the greatest or least predicted value while fixing the predictor in interest at its minimum. Second, by varying the predictor from its minimum to maximum, we add its contribution, which results in the greatest and least predicted value. Third, we evaluate whether the parameter estimate has a type-II violation by checking its admissibility. As Table 5 makes evident, TRM has 13 boundary violations in both models, while TRMCO's predicted values are all admissible. Most of the boundary violations for the TRM solution are lower-bound violations, except for Capital Flow in Model II. This result nicely illustrates why we need to adopt the TRMCO model as a replacement for the TRM and OLS models.
Table 5 Translation of Boundary Violations into Predicted Values For Model I and II
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