A One-Way Components of Variance Model for Categorical Data

A components of variance model for categorical data from unbalanced designs which is directly analogous to a one-way random effects ANO VA modelfor quantitative data is proposed. The variance components provide separate reliability measures for each of the response categories and disagreement measures between pairs of response categories in terms of (within subject) intraclass and interclass correlation coefficients. The estimation procedures involve usual MA NOVA calculations which can be expressed as compounded functions of the multinomial observations. Thus, the variances of these estimates can be obtainedfrom linearized Taylor series results. These procedures are illustrated with data from a psychiatric diagnosis study.