Multidimensional successive categories scaling: A maximum likelihood method

Abstract

A single-step maximum likelihood estimation procedure is developed for multidimensional scaling of dissimilarity data measured on rating scales. The procedure can fit the euclidian distance model to the data under various assumptions about category widths and under two distributional assumptions. The scoring algorithm for parameter estimation has been developed and implemented in the form of a computer program. Practical uses of the method are demonstrated with an emphasis on various advantages of the method as a statistical procedure.

Analysis of saliency of facial features through psychophysical scaling

“…Our general approach is in line with the maximum likelihood scaling method developed by Takane and his colleagues (e. g., Takane, 1978;Takane, 1981;Takane & Carroll, 1981). According to their approach a set of three constituent models, the representation, error, and response models, are specified so that the likelihood of observed data may be stated in terms of parameters in these models.…”

“…According to their approach a set of three constituent models, the representation, error, and response models, are specified so that the likelihood of observed data may be stated in terms of parameters in these models. However, since the method adopted here is exactly the same as that in Hojo (1987) in which, as mentioned above, the judged intensities of smiling of front-view faces were scaled, only the representation models will be described in what follows (see Hojo, 1987, or Takane, 1981, for example, for the other two constituent models).…”

A Generalized Inner Product Model for the Analysis of Asymmetry

“…To utilize such information, the max imum likelihood principle should be applied, as has been done in symmetric MDS (Ramsay, 1977(Ramsay, , 1982Takane, 1978aTakane, , 1978bTakane, , 1981Takane and Carroll, 1981). This also enables us to compute AIC (Akaike, 1974), and therefore enables us to compare extant asymmetric MDS's and thereby to choose the best model.…”

Marginal Maximum Likelihood Analyses of Individual Differences in Additivity and Judgmental Criteria for Categorical Rating Data and Decision Making Data

“…In line with Takane's (1981) approach to nonmetric scaling we distinguish three constituent models: the representation model to account for systematic variations in data, the error model for the nature of perturbation, and the response model for the way in which subjects perform a specific task. …”

“…1958). In Takane's (1981) formulation of the multidimensional successive categories scaling, the cat egory boundaries are allowed to vary over subjects. To the knowledge of the author.…”