The present paper provides two response models: one for binary ranking and the other for sorting. The former is a behavior of choosing, in a random order, only those comparison stimuli which are judged to be very similar to a standard stimulus, and the latter is that of selecting stimuli which are judged very similar to each other to form them into clusters. The key assumption of these models is that the subject perceives any two stimuli as very similar to each other when their dissimilarity, which varies over time, is below response thresholds that are associated with those stimuli. Maximum likelihood estimation procedures are used for the estimation of parameters of these models. The proposed models are applied, for illustrative purposes, to the similarity data collected by the binary ranking and sorting methods. We discuss some advantages of the binary ranking method to be used for collecting similarity data and a practical limitation of our response model for sorting.
We consider the polynomial regression model. In this model a hierarchical structure, or natural ordering, in the parameter space can be assumed. Maximum likelihood estimators may be found for the parameters of each order model in the hierarchy. We introduce the class of estimators given by weighted combinations of these maximum likelihood estimators under certain restrictions. This class is obtained by considering a Bayes estimator class and contains the subset regression estimator as a special case. The optimal weights which minimize the predictive mean squared error are obtained exactly, using an alternative method to that of Kanda (1985). The estimated weights which minimize the estimated predictive mean square error in a similar way to the Mallow's Cp-statistic are also exactly presented and some numerical examples are shown.
An algorithm to analyze ordinal data based on a general linear model is presented, which is applicable to many scaling problems, such as ordinal multiple regression, external analysis of preference data, and general Fechnerian scaling. Especially, external analysis of preference data is discussed in detail, and the efficacy of the algorithm is examined by analyzing a preference data.
This paper proposes a model to analyze the structure and context effects involved in dissimilarity judgment. With some restrictions incorporated, the model is also interpreted as a kind of the distance-density model, and further interpreted as a mixed distance and content model. Algorithms for multidimensional scaling based on the proposed model are implemented using nonlinear optimization methods. The algorithms are evaluated through a Monte Carlo study, and applications are demonstrated with real data. Problems regarding the model, the algorithms and possible applications are discussed.