Journal of Statistical Theory and Practice

, Volume 1, Issue 2, pp 265–278

# Priority and Choice Probability Estimation by Ranking, Rating and Combined Data

• Stan Lipovetsky
Article

## Abstract

Ranking data is commonly used in marketing and advertising research for priority estimation among the compared items by Thurstone scaling. Rating data is also often used in TURF, or total unduplicated reach and frequency analysis to find the best items. Both ranks and rates data sets can be elicited and utilized simultaneously to obtain a combined preference estimation. This work develops several techniques of priority evaluation. It considers maximum likelihood of the order statistics for the ranking data with the probit, logit, and multinomial links for the Thurstone scale. Non-linear optimization with the least squares or maximum likelihood objective is introduced for TURF modeling. Combined estimation by both rank and rate data is suggested in singular value decomposition and Geary-Khamis equation approaches. The proposed methods produce priorities among the compared items and probabilities of their choice.

62F07

## Keywords

ranking rating Thurstone scale TURF order statistic nonlinear optimization maximum likelihood choice probability SVD Geary-Khamis equations

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