Biomedical subjects

M Regenwetter

Publications and source records attributed to M Regenwetter.

3 recordsLinked to original sources

PubMed1998

The Choice Probabilities of the Latent-Scale Model Satisfy the Size-Independent Model When n Is Small.

Two probabilistic models for subset choices are compared. The first one, due to Marley (1993), was dubbed the latent-scale model by Regenwetter, Marley, and Joe (1996). The second one is Falmagne and Regenwetter's (1996) size-independent model of approval voting. We show that for up to five choice alternatives, the choice probabilities generated by the latent-scale model can be explained also by the size-independent model. The proof uses the König-Hall theorem of graph theory and the characterization of the size-independent model by the approval-voting polytope of Doignon and Regenwetter (1997). The problem remains open for the case with more than five choice alternatives. Copyright 1998 Academic Press.

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PubMed1997

An Approval-Voting Polytope for Linear Orders

A probabilistic model of approval voting on n alternatives generates a collection of probability distributions on the family of all subsets of the set of alternatives. Focusing on the size-independent model proposed by Falmagne and Regenwetter, we recast the problem of characterizing these distributions as the search for a minimal system of linear equations and inequalities for a specific convex polytope. This approval-voting polytope, with n! vertices in a space of dimension 2(n), is proved to be of dimension 2(n)-n-1. Several families of facet-defining linear inequalities are exhibited, each of which has a probabilistic interpretation. Some proofs rely on special sequences of rankings of the alternatives. Although the equations and facet-defining inequalities found so far yield a complete minimal description when n<=4 (as indicated by the PORTA software), the problem remains open for larger values of n.

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PubMed1996

Random Utility Representations of Finite m-ary Relations

Block and Marschak (1960, in Olkin et al. (Eds.), Contributions to probability and statistics (pp. 97-132). Stanford, CA: Stanford Univ. Press) discussed the relationship between a probability distribution over the strict linear rankings on a finite set C and a family of jointly distributed random variables indexed by C. The present paper generalizes the concept of random variable (random utility) representations to m-ary relations. It specifies conditions on a finite family of random variables that are sufficient to construct a probability distribution on a given collection of m-ary relations over the family's index set. Conversely, conditions are presented for a probability distribution on a collection of m-ary relations over a finite set C to induce (on a given sample space) a family of jointly distributed random variables indexed by C. Four random variable representations are discussed as illustrations of the general method. These are a semiorder model of approval voting, a probabilistic model for betweenness in magnitude judgments, a probabilistic model for political ranking data, and a probabilistic concatenation describing certainty equivalents for the joint receipt of gambles. The main theorems are compared to related results of Heyer and Niederee (1989, in E. E. Roskam (Ed.), Mathematical psychology in progress (pp. 99-112). Berlin: Springer-Verlag; 1992, Mathematical Social Sciences, 23, 31-44).

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