A generalized model specification system in Mata

We present the development and usage of the generalized model specification system (GMSS) Mata library to support the specification of regression models. This library allows users to gain access to all the options in Stata’s premier optimization routines. The library consists of classes for distributions and link functions. In addition, the library defines optimization routines callable from moptimize() moptimize() moptimize() moptimize(). The library consists of approximately 30 distributions for which users may specify associated covariates for each of the parameters. General models (zero-inflated, zero-altered, zero-marginalized, zero-truncated, and heaped) are usable with any count distribution in the library. Users are also free to develop and add distributions and link functions. All distributions have default link functions, but users are free to specify links as well. An ado-file is available for those users who prefer Stata-language implementations. Support commands for estat estat estat estat and predict predict predict predict are also included in the library. Factor-variable specification of covariate lists is allowed, and the library automatically generates associated constraint matrices. Example usage of do-files calling the Mata routines will be presented along with usage of the ado-file specification. While there is substantial overlap with specific existing models, the GMSS library includes many new distributions for interested developers and applications.