Optimal designs for binomial sampling under a mixture hypothesis

Sample size selection for estimation of parameters in a beta-binomial model is studied using optimal design theory. Single binary observations are optimal for minimum variance estimation of the average probability. Tables of D-optimal sampling designs are given: for estimation of both parameters; and for estimation of the dispersion parameter alone. The results indicate that a sub-sampling design at each design point should be advised as a complement to the usual design weight when designing for over-dispersed binary regression models.