  Mixed spatial autoregressive (SAR) models with numerical covariates have been
well studied. However, as non-numerical data, such as functional data and
compositional data, receive substantial amounts of attention and are applied to
economics, medicine and meteorology, it becomes necessary to develop flexible
SAR models with multiple data types. In this article, we integrate three types
of covariates, functional, compositional and numerical, in an SAR model. The
new model has the merits of classical functional linear models and
compositional linear models with scalar responses. Moreover, we develop an
estimation method for the proposed model, which is based on functional
principal component analysis (FPCA), the isometric logratio (ilr)
transformation and the maximum likelihood estimation method. Monte Carlo
experiments demonstrate the effectiveness of the estimators. A real dataset is
also used to illustrate the utility of the proposed model.
