Epitope profiling via mixture modeling of ranked data

Abstract

Abstract. We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the raw numerical responses is difficult or subject to criticism. We review standard distance-based and multistage ranking models and in this last context we propose an original generalization of the PlackettLuce model to account for the order of the ranking elicitation process. The usefulness of the novel model is illustrated with its maximum likelihood estimation for a real data set. Specifically, we address the heterogeneous nature of experimental units via model-based clustering and detail the necessary steps for a successful likelihood maximization through a hybrid version of the Expectation-Maximization algorithm. The performance of the mixture model using the new distribution as mixture components is compared with those relative to alternative mixture models for random rankings. A discussion on the interpretation of the identified clusters and a comparison with more standard quantitative approaches are finally provided.

Bayesian analysis of ranking data with the Extended Plackett–Luce model

“…The implicit assumption in the PL scheme is the forward ranking order, meaning that at the first stage the ranker reveals the item in the first position (most-liked alternative), at the second stage she assigns the second position and so on up to the last rank (least-liked alternative). Mollica and Tardella (2014) suggested the extension of the PL by relaxing the canonical forward order assumption, in order to explore alternative meaningful ranking orders for the choice process and to increase the flexibility of the PL parametric family. Their proposal was realized by indexing the ranking order with an additional model parameter ρ = (ρ(1), .…”

“…In our analysis, we considered the hyperparameter setting c = d = 1. Differently from Mollica and Tardella (2014), we focus on a restrictionS K of the whole permutation space S K for the generation of the reference order, defined through the introduction of order constraints on the discrete parameter. Our choice can be motivated not only from a computational perspective, as widely illustrated in the next section, but also by the fact that in a preference elicitation process, not all the possible K!…”

“…The basic idea is the decomposition of the ranking process into K − 1 stages, concerning the attribution of each position according to the forward order, that is, the ordering of the alternatives proceeds sequentially from the most-liked to the least-liked item. The implicit forward order assumption has been released by Mollica and Tardella (2014) in the Extended Plackett-Luce model (EPL). This relaxation allows for a more flexible dependence structure, hence for a better and possibly more parsimonious fitting of the observed ranking data.…”

“…This relaxation allows for a more flexible dependence structure, hence for a better and possibly more parsimonious fitting of the observed ranking data. The PL extension in Mollica and Tardella (2014) relies on the introduction of the discrete reference order parameter, indicating the rank assignment order, and its estimation was originally considered from the frequentist perspective. However, in that work there was no specific attention to the inferential ability to recover this extra parameter, as well as quantifying the estimation uncertainty.…”

Analysis of ranking data

“…See also Mollica and Tardella (2014) for the use of MM algorithm in a new extension of the Plackett-Luce model to account for the order of the ranking elicitation process.…”