does autocorrelation work correctly with a non-standard time variable?

[stueller]

Per issue#19, the time variable(s) may be dropped, especially if user wants to drop a nonsignificant time term (which we need to make sure they see that dropping the term also drops the random effects).

We need to check whether variations on the time variable affects the covariance structure estimates.

[stueller]

• in arima order is implied, i.e., it assumes equally spaced time points and the spacing itself doesn't matter.
• in mixed effects models, the time variable gives order and spacing to the data, which is good in that it introduces the flexibility of unequally spaced observations, but at the cost of requiring a time variable (i.e., I don't think we can fix the slope to 0)
• nlme operates on groupedData where you can pre-specify the raw time variable and clustering (ID) variable and then fit models without the time variable as fixed or random effects. If this is pursued further, check whether changing the time variable when specifying the groupedData affects the correlation structure estimates in intercept only models.
• nlme can also operate on a data.matrix or data.frame with a correlation structure as long as an ID/clustering variable is specified. My hunch is that corARMA assumes that data are sequential and equally spaced. If this is studied further, check whether corARMA makes this assumption all of the time or only when a time variable is absent.
• PersonAlytic currently forces a time variable, which should be ok for now.

[stueller]

Z:\13 GUI\2021 Reparameterization\20210928 Demo\covariance structure and time scaling.R

[stueller]

one way to test what corARMA is doing is to fit a two models to unequally spaced data:

• with correct time value
• with equally spaced time value If the correlation structure results are the same, this suggests that corARMA is assuming equal spacing under the hood. That said, the change in the time variable can effect all other estimates. If the results are not the same, we cannot conclude anything about corARMA assumptions.