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My model:

    gam(response ~ s(days, k=9) + s(days, by=subject, k=9, m=1) + covariates.

I used this approach https://stackoverflow.com/questions/78182559/autocorrelation-in-gam-r to extract out the subject specific residuals and plot an acf and pacf plot per subject. I noticed for certain subjects that an AR=1 might be useful based on the PACF plots, but this isn't the case for all subjects. How would I go about adjusting for this for only certain subjects? I wasn't sure. Happy to be redirected to another resource. Thank you

PACF plot for subject 19

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  • $\begingroup$ Nick’s answer is the route I would probably go, but does the same issue persist if you eschew the GI decomposition and just fit y ~ subject + s(days, by = subject)? The m = 1 bit is often a source of problems; if you want to keep the GI decomposition, you can use a newer basis “sz”; y ~ s(days) + s(days, subject, bs = "sz"), which avoids the m = 1 thing because it is designed to be orthogonal to the average smooth. $\endgroup$ Commented Apr 9 at 7:55

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You can't allow different levels to have different residual autocorrelation structures in most regression interfaces, including gam() or bam(). Rather, I would recommend you look into the {mvgam} 📦 to do this. It can handle many of the predictor features and terms that gam() can, but it can incorporate far more flexible time series options to model the latent residuals.

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