Fixing Boundary Violations

1.2 A Possible Explanation

As with the use of the logit or probit model for a binary dependent variable, the fundamental reason to use the TRM model is to avoid boundary violations. Given that the distributional assumption has already determined an admissible region of the dependent variable, any solution that generates an out-of-bounds predicted value is ineligible and regarded as a failed estimate. While this problem is common for the binary dependent variable (Aldrich and Nelson, 1984), little attention is paid to the TRM model. If the widespread belief in political science is that the logit or probit model should be applied to a binary dependent variable, the same conclusion should be made about the TRM model for a truncated normal dependent variable.

While we may never know why political scientists seldom use the TRM model,³ a possible reason stems from the fact that, unlike the logit or probit model, TRM cannot solve the problem of boundary violations. (Orme and Ruud, 2002, 213) Empirical applications show that "The truncated normal model routinely defied convergence and, as often as not, produced nonsense estimates." (Greene, 1999, 158, n60) To validate this concern, we investigated three political science studies and found that they all suffer from boundary violations by either the OLS or TRM model.

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Footnote

³ Political scientists, on the other hand, do pay more attention to the censored regression and the sample-selected model. Unlike these two models, the analytical purpose of the TRM model is not to recover the information of the underlying untruncated normal distribution, nor to correct the selection bias. Rather, the main task is to derive the best parameter estimates from the eligible parameter space. In econometrics, many efforts have been made in the theoretical study of the maximum likelihood estimator for the TRM model. See Olsen (1978), Orme (1989), Hausman and Wise (1977), Chung and Goldberger (1984), and Greene (1983).