Timeline for Serial correlation AR(1) model for residuals: how to generalize to irregular times
Current License: CC BY-SA 4.0
9 events
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| Dec 12, 2020 at 23:20 | comment | added | TrungDung | Please see my newest post in the Stan forum (discourse.mc-stan.org/t/…) | |
| Dec 3, 2020 at 14:03 | comment | added | Frank Harrell |
as in the previous comment, the one thing holding me back from making this easy to implement in a Bayesian model (here, using Stan) is the need to connect and limit the dimensionality of all the needed random effects in the model. This is easy for $Y(t_{min})$ (residual for earliest measurement for a given subject) but any help in formulating this data generating process in general would be most appreciated.
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| Dec 2, 2020 at 17:41 | comment | added | Frank Harrell |
thinking in terms of the data generating process, which is needed in formulating the Bayesian model for Stan etc., and setting $\mu=0$ since I am dealing with residuals, I let $z$ be an $n$-vector of N(0,1) for $n$ subjects and start the process for subject $i$ with $Y_{i}(t_{min}) = \omega z_i$. Then updating to get $Y_{i}(t_{next})$ I'm unclear on which random effect to use for $z$. If I generate a new $z$ for each subject at each time the dimensionality is too large.
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| Dec 2, 2020 at 15:22 | comment | added | TrungDung | Yes, I use the notation $Y$ but it is actually for the residuals. If you want to ignore $Y(t)$ when specifying for $Y(t+\Delta t)$, you just come back something like simple linear regression. | |
| Dec 2, 2020 at 14:46 | comment | added | Frank Harrell | On the other hand I can just add a lagged time to my dataset. | |
| Dec 2, 2020 at 13:53 | comment | added | Frank Harrell | Is there a form for which the $Y(t + \Delta t)$ distribution can ignore $Y(t)$? I'd like to be able to deal with "tall and thin" datasets where information from the current record (one time for one subject) can stand alone. | |
| Dec 2, 2020 at 13:34 | comment | added | Frank Harrell | I make be mistaken about that. The $Y(t)$ refer to residuals in my model, not to raw response values. I think it is OK for residuals to depend on earlier residuals. | |
| Dec 2, 2020 at 10:56 | comment | added | Frank Harrell | This is very helpful and will address many modeling problems including prediction. But for my particular problem, which is comparing two treatments in a randomized clinical trial, I require an approach that provides causal inference on the effect of treatment. For that purpose, the multivariate process has to be a marginal one with respect to $Y(t)$, i.e., $Y(t)$ cannot condition on $Y(s)$ where $s < t$ since that would be conditioning on an earlier treatment effect. | |
| Dec 2, 2020 at 10:09 | history | answered | TrungDung | CC BY-SA 4.0 |