Meaningful Comparisons With Ordinal-Scale Items

Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial fun...

Ethically robust comparisons of bidimensional distributions with an ordinal attribute

We provide foundations for robust normative evaluation of distributions of two attributes, one of which is cardinally measurable and transferable between individuals and the other is ordinal and non-transferable. The result that we establish takes the form of an analogue to the standard Hardy, Littlewood, and Pólya (1934) theorem for distributions of one cardinal attribute. More specifically, w...

Applying Multigroup Confirmatory Factor Models for Continuous Outcomes to Likert Scale Data Complicates Meaningful Group Comparisons

Large-scale Ordinal Collaborative Filtering

This paper proposes a hierarchical probabilistic model for ordinal matrix factorization by actively modelling the ordinal nature of ranking data, which is typical of large-scale collaborative filtering tasks. Two algorithms are presented for inference, one based on Gibbs sampling and one based on variational Bayes. The model is evaluated on a collaborative filtering task, where users have rated...

On the convergence rate of ordinal comparisons of random variables

y 00 (except at t = 0). One additional differentiation to get y 000 guarantees full column rank equal to three for the coefficient matrix of vector x. For the example, this rank condition is equivalent to the 1-full condition on the Jacobian O j; k of (11) for the time-varying linearization. (We may take j = 1 and k = 3.) Thus we have smooth observability on the interval [0; T ] for the time-va...