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Abstract:
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Ordinal mixed models constitute a flexible class of models to analyze ordinal data from various fields. Examples are data that originates from the heavily used online reviewing systems of movies, music, pain reports and customer surveys. Ordinal mixed models take the ordinal nature of data into account and allow modelling of more complex dependency structures. Furthermore, they provide a flexible and simple skeleton to model the information at hand, i.e. selecting terms in a modelling process as known from classical statistics. Ordinal mixed models can among others be estimated through the Laplace Approximation, for example using the ordinal package in R. However, this package is not optimized for large datasets. We propose to implement ordinal mixed models with the Template Model Builder (TMB) package in R. TMB provides a simple and flexible framework that enables fast optimization of the Laplace Approximation to the marginal log-likelihood. It is optimized to make fast computations for models with both many random effects and parameters [1]. We compare an implementation using the TMB package to the ordinal package through timings on both simulated and real data. We find that an implementation with TMB gives substantial speed-ups for models with many observations, parameters and random effects and allow estimation of ordinal mixed models with even larger datasets. [1] Kristensen et al.(2016), TMB: Automatic Differentiation and Laplace Approximation
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