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Remarkable properties for diagnostics and inference of ranking data modelling
Cristina Mollica1, Luca Tardella1
1Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Italy.
The British Journal of Mathematical and Statistical Psychology
|February 8, 2022
Summary
The Extended Plackett-Luce model (EPL) is enhanced with new diagnostic tools to test ranking assumptions. These methods help identify unique choice paths and offer a heuristic approach for parameter inference.
Area of Science:
- Statistics
- Psychometrics
- Behavioral Economics
Background:
- The Plackett-Luce (PL) model assumes a forward ranking process, from most to least preferred.
- The Extended Plackett-Luce (EPL) model relaxes this by introducing a discrete reference order parameter for rank attribution.
- Existing goodness-of-fit methods for multistage models are limited.
Purpose of the Study:
- To derive novel diagnostic tools for assessing the appropriateness of the Extended Plackett-Luce (EPL) model.
- To identify potential idiosyncratic paths in sequential choice processes.
- To develop a heuristic method for inferring the reference order parameter.
Main Methods:
- Derivation of diagnostic statistics based on two formal properties of the EPL model.
- The properties include the inverse ordering of item probabilities and the independence of irrelevant alternatives (Luce's choice axiom).
- Development of a heuristic parameter inference method using one of the derived statistics.
Main Results:
- Novel diagnostic tools are introduced to test the EPL model's suitability for observed rankings.
- These tools can reveal non-standard sequential choice behaviors.
- A heuristic method is proposed as an alternative to maximum likelihood for parameter estimation.
Conclusions:
- The study provides essential goodness-of-fit tools for the EPL model family.
- The derived diagnostics aid in understanding the nuances of sequential decision-making.
- The heuristic method offers a practical approach for parameter inference in EPL models.
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