A Variance Estimator for Constrained Estimates of Change in Relative Categorical Frequencies

Consistent estimators of change and state becomes an issue when sample data come from a mix of permanent and temporary observation units. A joint maximum likelihood estimator of state and change creates estimates of state that depend on antecedent viz. posterior survey results and may differ from estimates of state derived from a single-date analysis of the sample data. A constrained estimator of change in relative categorical frequencies that eliminates this potential inconsistency is proposed and a model based estimator of their sampling variance is developed. The performance of the constrained estimator is quantified against six criteria and a joint maximum likelihood estimator in simulated sampling from 15 populations with three combinations of permanent and temporary samples, four to six categorical class attributes, and constant size between sampling dates. Bias of the constrained estimators was negligible but larger than for joint maximum likelihood estimators. Mean absolute deviations and variances of constrained estimators were generally at par with the joint estimators. Constrained estimators of root mean square errors and achieved coverage of nominal confidence intervals of constrained estimators were occasionally better. A generalized variance function for the constrained estimates of change is provided as a computational shortcut.