Summary
Objective:
Recent results published by Coste et al. in discriminant analysis with ordinal responses
showed the superiority of optimal discriminating analysis for ordinal responses (ODAO)
both in terms of classification and simplicity of implementation compared to classic
methods (Fisher’s discrimination, logistic regression) applied to medical data (prognostics
of burns) and to simulated data. Nevertheless, the solutions obtained by ODAO may
be sensitive to re-sampling (i.e the estimated coefficients by ODAO may show excessive
sensitivity to the training sample). This study proposes some solutions to control
the fluctuations of sampling and to ensure model stability.
Methods:
We used intensive computational methods and bootstrapping, at the outset of model
building in order to reduce the sampling variability of estimated coefficients. Thus,
the estimation of the coefficients was not based on the minimization of a classification
criterion of the training sample, but on the minimization of an aggregate criterion
of bootstrapped replications of a classification criterion. Five aggregate criteria
were studied.
Results:
The improvement in terms of robustness appeared in 30% of the test cases with moderate
training sample size and 55% of those with small training sample size.
Conclusion:
Simulated test cases showed that bootstrapping can help construct more robust models
in difficult classification situations and small training samples which are particularly
frequent.
Keywords
Classification - ordinal responses - ODAO - adaptive random search - fluctuations
- modeling - bootstrap - robustness
