Other Models and Applications

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The general approach offrontier models might be carried over to other models and contexts. For example, logistic frontier regression might be aimed at modeling the most probable cases. Applications of this kind are attractive for predicting poor and/or excellent credit risks and for income tax filers most likely to be evading taxes.

Policy capturing studies have been around for a long time. Generally, this approach uses regression, classification, or other data models in order to explain and predict dichotomous, categorical or ordinal outcomes. For example, it may be useful for corporate legal planners to predict the likely outcome of legal actions based on a human resources case profile. The prediction of attribute levels or ranges for the best cases might be compared to those for the average case. A planned legal strategy may be judged average or better than average and compared to the appropriate model in that case to improve decision making about out-of-court settlements, for instance.

As noted earlier, a potential limitation of these models arises in connection with outliers. In the present setting, one may have two kinds, which might be called high-liers and low-liers, respectively. High-liers would be problematical for ceiling frontier models. Such observations suggest fortunate high performance unrelated to the predictor model. Similarly, low-liers would be of concern for floor models. As noted above, these concerns can be regarded as a motivation for SFE type models. Unfortunately, SFE models are difficult to estimate at the present time. Additional research on this class of models would be helpful when low-liers or high-liers are not easy to identify or accommodate.

A generalization of frontier type models would be to what may be called percentile and stratification response type models. One may envision a modeling approach that uses a parameter, z, with range [0,1]. Such a model would seek to associate observed values with a z value so that the model with z = z₀ provides the best predict on for the z₀-percentile response variable. A closely related, percentile estimation type of model would seek to best explain the upper z₀ -percent of the potential responses. That is, if one starts with a pure frontier model, it would be possible to estimate, say, the 50^th-percentile level of the dependent variable for a given value of independent variable values. However, if we know in advance that we wish to model specifically the upper 50^th-percentile of cases, then it is conceptually possible to obtain a different model than that based on the pure frontier one.

Of course, a great advantage of OLS regression models lies in the inferential capabilities of normal distribution based theory. The NLOB criterion provides some help in this direction for the frontier models. Still, more statistical theory work along those lines would clearly be useful.

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