Timeline for Serial correlation AR(1) model for residuals: how to generalize to irregular times
Current License: CC BY-SA 4.0
10 events
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| Dec 24, 2020 at 12:06 | comment | added | Frank Harrell | Thanks. So I don't see a way for simple autocorrelated random effects on the logit scale to handle the kind of strong dependence I see in daily measurements of an ordinal clinical outcome scale. I'm thinking that doing conditional Markov lag 1 models is going to fit better for my situation, i.e., condition on ordinal outcome Y(t-1) when stating the proportional odds model for Y(t). | |
| Dec 23, 2020 at 17:07 | comment | added | Charlie | Oh - then I misunderstood. That would be expected , so far as I follow -- if you nonlinearly transform a variable that has a certain linear relationship originally, the resulting linear relationship will be different, and only capture part of the 'true' relationship that was in place before the transform. | |
| Dec 23, 2020 at 13:32 | comment | added | Frank Harrell | would you mind clarifying that? It is easy to put autocorrelation into the linear predictor (e.g., logit scale, added to the ordinary random effect for the first observation per subject) but when I simulate ordinal Y from such a model and compute correlations of Y as a function of time separation (variogram) I see damped correlations. | |
| Dec 23, 2020 at 13:14 | comment | added | Charlie | That will always happen when you nonlinearly transform a variable with a linear relationship, then recompute the linear relationship. Handling the autoregression on the linear predictor, before transforming, avoids the issue -- this is how I handle it yes. | |
| Dec 21, 2020 at 16:37 | comment | added | Frank Harrell | When I simulate AR(1) random effects I'm able to get any serial correlation $\rho$ that I want, on the linear predictor scale. But when I do the nonlinear transformation of this to the scale of interest, i.e., expit transformation to get cumulative probabilities which are then used to simulate ordinal Y under the proportional odds assumption, the correlations on the original ordinal scaled are dampened. Does your approach have the same issue? | |
| Dec 3, 2020 at 15:41 | comment | added | Charlie | For stochastic differential equation fundamentals, Gardiner, C. W. (1985). Handbook of stochastic methods (Vol. 3, pp. 2-20). Berlin: springer. For the most up to date / best explained version of what I'm specifically using, Driver, C. C., & Voelkle, M. C. (2018). Hierarchical Bayesian continuous time dynamic modeling. Psychological Methods, 23(4), 774. | |
| Dec 3, 2020 at 14:16 | comment | added | Frank Harrell | Great. Is there a fundamental reference for this continuous time AR(1) formulation? | |
| Dec 3, 2020 at 14:00 | comment | added | Charlie | The number of $\Delta t$ values does not influence the number of parameters, no -- for a univariate AR1 process there is just the single 'auto effect' parameter, in this case a 1x1 matrix 'A'. The discrete time covariance with an earlier time point is then $e^{A \Delta t}$ | |
| Dec 3, 2020 at 13:54 | comment | added | Frank Harrell | Very nice work and R package. My understanding is that the continuous time AR(1) generalization you are using requires lots of parameters because of lots of possible $\Delta t$ values. Is there an alternative formulate that is an even more continuous AR(1) with few parameters? | |
| Dec 2, 2020 at 15:35 | history | answered | Charlie | CC BY-SA 4.0 |