On the monotonicity of the residual heteroscedasticity item response model

The residual heteroscedasticity (RH) model is a recently popularized asymmetric model that aims to model complex item response behavior. In this paper, we probe the conditions under which the existing form of the RH model does not guarantee monotonic boundary response functions (BRFs), a necessary condition for ensuring at least ordinal-level measurement. We derive the conditions under which RH BRFs are not monotonic and we use this result to propose a Bayesian computational strategy that enforces monotonicity. Through real and simulated data illustrations, we demonstrate that failures of monotonicity occur in real data and that our proposed computational solution effectively enforces monotonicity and yields accurate item parameter estimates. Finally, we demonstrate that any IRT model developed by specifying a residual variance function is likely to encounter similar issues with monotonicity. We recommend our reparameterization for both data generation in simulation studies and for fitting the RH model to real data.