Add support for a continuous time AR(1) analogue to cor_ar()
#741 aperta il 29 ago 2019
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Descrizione
The discrete time AR(1) correlation structure can be generalised to the continuous time setting.
A continuous time AR(1) or CAR(1) correlation structure can be defined as
h(s, ϕ) = ϕs, s ≥ 0, ϕ ≥ 0
where s is a non-negative real. In contrast to the AR(1), the correlation parameter ϕ is constrained to be non-negative. The CAR(1) correlation function is a univariate special case of the exponential spatial correlation function.
The nlme package has an implementation of this correlation function in its nlme::corCAR1().
A cor_car1() function in brms mirroring cor_ar() but for the CAR(1) correlation would be very useful for modelling longitudinal data for example in settings where the observations are not regularly spaced in time.
There is a small amount of discussion of this on the Stan Discourse site.