MaxDiff Choice Probability Estimations on Aggregate and Individual Level

This paper considers methods of estimation of choice probability using Maximum Difference (MaxDiff) technique, also known as Best-Worst Scaling (BWS). The paper shows that on the aggregate level the choice probabilities can be obtained using analytical closed-form solution and other approaches such as Thurstone scaling, Bradley-Terry maximum likelihood, and Markov modeling via Chapman-Kolmogorov equations for steady-states probabilities. On the individual level, to account for the exact combinations presented in each task, the Cox hazard model is employed, as well as new approaches of least squares objective for maximum difference, and maximum likelihood in order statistics. The results are useful in the practical MaxDiff applications for items prioritization in marketing research.