Abstract: Interval scale grouped data have peculiar structures of their own rights among various archetypes of polytomous data that deserve special statistical treatments. Maximum likelihood type approaches along with heteroscedastic and transformation models are adapted to take into account this kind of architecture with current state-of-art computation capabilities. Meanwhile, misclassification rates instead of sum of squared residuals are suggested for model fitting and selection in light of the data formation. Successful applications of these methods are demonstrated by a set of empirical data regarding the endotracheal tube size selection for small children in the emergency room of a hospital.
Key words and phrases: Constrained optimization, maximum likelihood estimators, misclassification rates, transformation models.