Joint versus separate estimation of state and change in category frequencies from repeat stratified two-phase sampling with a fallible classifier.

Joint maximum likelihood estimates (JML) of category frequencies and change from repeat stratified two-phase sampling surveys with a fallible classifier are often seriously biased and have large root mean square errors when they are obtained for small populations (<5,000) with three or more categories and a moderate to small phase II sample size (<1,000). JML estimates of state also depend on antecedent or posterior data, a recipe for inconsistency. In these situations, a separate maximum likelihood estimation (SML) of category frequencies at each survey date appears preferable. SML estimates of net change are obtained as the difference in states. SML standard errors of change are obtained via an estimate of the temporal correlation and variances of state. A bivariate binary logistic model of change provided the estimate of temporal correlation. SML generally outperformed JML significantly in terms of bias and root mean square errors in eight case studies.