Zero-one-inflated beta regression time series model in stan

Modeling
#1

Hi,

Did anybody had a chance to implement in stan zero-one-inflated beta regression time series model? While I found separate implementations in stan of zero-one-inflated beta regression (markhw) and time series, I have hard time to understand how to combine both. The paper “Beta autoregressive moving average models” combines beta regression with time series (https://link.springer.com/article/10.1007/s11749-008-0112-z) but doesn’t discuss 0-1-inflated beta regression. I appreciate any suggestions.

#2

I guess the big thing you gotta decide is which parameters you want to depend on time.

With respect to this zero inflated beta thread: Zero one inflated beta regression in STAN, I guess you could make either \alpha (the mixing distribution) or \gamma (the bernoulli probability) depend on time.

At that point you can pick a time series model for that parameter and rock and roll maybe? If the underlying time series is written in terms of normals, then maybe you gotta add a link function in there like:

\gamma_t = \text{inv_logit}(\mu_t)

if \mu_t is your time series model.

1 Like
#3

Awesome. Thank you very much.

Do you mind if I ask a follow up question? My data set contains time series of 5 years for 200 individuals (one data point for each year). Should I consider them as repeated measurements?

One more. If I define mu_t as in https://link-springer-com.ezproxy.lib.purdue.edu/article/10.1007/s11749-008-0112-z

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then mu_t is not defined for AR term since link g(y_{t-i}) is inf if g is logit. What mu_t you have in mind?

#4

Suppose I pick up bernoulli probability gamma to depend on time and gamma_t=inv_logit(mu_t). I am struggling to understand what should be mu_t. Is it x_t*b where x_t is covariate and b is coefficient? Or something more elaborate?

#5

I was just making something up, honestly :D.

The assumption was that \mu_t represents some sort of underlying time series process (maybe a Gaussian process, maybe a random walk), and that it lived on an unconstrained space. If you wanted that to determine a probability parameter then you’d have to throw a link function in there.

So that time series could include regression terms and such depending on what type of time series it was. That make sense?

#6

Yes, it does. Something like \mu_t=x_t^T\beta+...?
What I am missing is how to cast random walk y_t=y_{t−1}+\epsilon_t or AR y_t=ϕy_{t−1}+\epsilon_t into this. Perhaps y_t=x_t^T\beta+ϕ(y_{t−1}-x_{t-1}^T\beta)+\epsilon_t? In this case \mu_t=x_t^T\beta? Or something else? Bit confused…

#7

Good question. I’m not sure. Maybe something like:

\theta_t \sim N(\theta_{t - 1}, \sigma)\\ \mu_t = x_t^T \beta + \theta_t

So you have a bit driven by measured covariates and then some unexplained time series term. But this probably warrants and poke around the forums for specific time series models.