Population aging is accompanied by the burden of chronic diseases and disability. Chronic diseases are among the main causes of disability, which is associated with poor quality of life and high health care costs in the elderly. The identification of which chronic diseases contribute most to the disability prevalence is important to reduce the burden. Although longitudinal studies can be considered the gold standard to assess the causes of disability, they are costly and often with restricted sample size. Thus, the use of cross-sectional data under certain assumptions has become a popular alternative. Among the existing methods based on cross-sectional data, the attribution method, which was originally developed for binary disability outcomes, is an attractive option, as it enables the partition of disability into the additive contribution of chronic diseases, taking into account multimorbidity and that disability can be present even in the absence of disease. In this paper, we propose an extension of the attribution method to multinomial responses, since disability is often measured as a multicategory variable in most surveys, representing different severity levels. The R function constrOptim is used to maximize the multinomial log-likelihood function subject to a linear inequality constraint. Our simulation study indicates overall good performance of the model, without convergence problems. However, the model must be used with care for populations with low marginal disability probabilities and with high sum of conditional probabilities, especially with small sample size. For illustration, we apply the model to the data of the Belgian Health Interview Surveys.