Parameter expansion for fitting regression models with non-negativity constraints.

Regression models often require constraints that can be expressed as non-negativity constraints. This could be because it makes sense for the underlying modeling context, or it could be necessary to prevent the fitted values violating the natural constraints of the response distribution. Examples of the latter include log-link binomial regression and additive variance regression, while an example of the former is non-negative linear regression. Non-negativity constraints may apply directly to the regression parameters, in which case we call the model parameter-constrained, or they may apply to the linear predictor, in which case we call the model predictor-constrained. In this article, we show that it is possible to fit the predictor-constrained model using a parameter-constrained method applied to a model with additional dummy parameters, a technique called parameter expansion. This is advantageous because parameter-constrained models are often easier and more reliable to fit. After considering a range of models in which predictor-constrained estimation is desirable, we study the application of parameter expansion to a general regression model that includes the specific models as special cases. We then undertake a more in-depth study of parameter expansion for the log-link binomial model. Simulation results are presented demonstrating the computational advantages of parameter expansion. [ABSTRACT FROM AUTHOR]