Bayesian estimation of category typicality using ordered probit models

Representations of exemplars (e.g., apple) within a semantic category (e.g., fruit) are graded, such that certain members are perceived as being more representative (or “typical”) than others. Researchers have traditionally examined normative trends in category typicality by reporting the relative frequencies by which respondents report relevant exemplars when prompted with a category label (Barsalou, 1985). In many cases, however, the methods of computing normative typicality estimates do not match the distributional characteristics of the aggregated responses; for example, researchers often report arithmetic means on response distributions that are highly skewed. Here, we propose the use of rank-ordered probit models (Liddell & Kruschke, 2021) for estimating the normative typicality of exemplars ranked within common semantic categories using responses from a large-scale survey. These models estimate the probabilities of ordinal rankings using beta distributions with freely-varying parameters, which we estimate using approximate Bayesian computation. The probability densities from the estimated distributions are then used to estimate exemplar representativeness within categories. We show that a) the model accurately recovers normative trends in the observed data and b) likelihoods estimated from the resulting distributions are useful for computing normative typicality estimates of category exemplars.