A Flexible Bayesian Multivariate Ordinal Regression Model for Language Sample Scale Data

Music City Center 

One common type of outcome in Language Sample Analysis (LSA) is the sum of ordinal variables, which can be difficult to model. Classical approaches often assume outcomes are independent with additional distributional assumptions. Common choices include linear regression, which assumes outcomes are continuous, and logistic regression, which assumes outcomes follow a binomial distribution. However, linear regression assumes equal intervals between outcome categories, while logistic regression ignores the dependence among ordinal outcomes. Both models may fail to reflect the inherent ordering and differences in the data. Therefore, we proposed a variation of a cumulative ordinal model. Extra flexibility was introduced by allowing the probit link function to have a covariate-specific standard deviation. Additionally, we adopted a Bayesian and hierarchical framework that facilitates parameter estimation and enables direct probabilistic inference about parameters of interest. The proposed model improved fit over logistic and linear regressions on a LSA dataset collected from a study to understand how cognitive and language challenges interfere with expository abilities.

Bayesian

Ordinal Regression

Scale Data 

Section on Bayesian Statistical Science