I wonder if there is a way to model this following model in SAS (preferably with some built-in functions):
Y_{ij} = \beta_{i}(t_{j}) X_{i} + e_{ij},
which basically is a form of functional mixed-effects model without the random-effects parts. Here each subject i has observations at time t_{j} (j=1,...,n_{i}), and X_{i} is the covariates not varying with time within subjects but varying between subjects. The random errors follow iid normal distribution.
The closest form of model I found so far is the functional-coefficient model which normally is used for time-series data, although I'm not sure if it's applicable to time-invariant covariates. Anyone knows if there is a way to model this using some exiting software (preferrably SAS)?