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I am fitting the following model in "mgcv" package in R using option family=betar to predict a percentage cover response variable (cyano %):

    g6 = gam(cyano/100 ~ s(SEGLOWFLOW) + s(SEGJANAIRT) + 
             s(LOCHAB) + s(LOCSED) + s(T2PastoralHeavy) + 
             s(SEDO) + s(USDAYSRAIN) + s(USAVGSLOPE) + 
             s(USHARDNESS), data=nati1, 
             family = betar(link='logit'))

I get the following warning message:

    Warning message:
    In object$family$saturated.ll(G$y, wts, theta) :
      saturated likelihood may be inaccurate

The summary output gives me negative explained deviance values:

    R-sq.(adj) =  0.0871   Deviance explained = -29.9%
    -REML = -2370.5  Scale est. = 1         n = 463

Although the diagnostics plots (gam.check) look fine and the predictions make sense, I am worried about the warning message and the negative deviance explained value.

Any thoughts will be appreciated.

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    $\begingroup$ I tried fixing some mistakes, but I am not sure whether you are using betareg anywhere. You do use family=betar, though. Please check the accuracy of your post and pardon if my edit might have introduced any new mistakes. $\endgroup$
    – Richard Hardy
    Commented Jul 15, 2016 at 17:18
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    $\begingroup$ Great, thanks heaps. I only used betar family in the mgcv library. $\endgroup$
    – jatalah
    Commented Jul 18, 2016 at 0:23
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    $\begingroup$ I'm running into the same question. Is it just that REML and dev.explained don't give sensible values with betar ? $\endgroup$
    – puslet88
    Commented Feb 23, 2019 at 14:26
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    $\begingroup$ Does your response variable contain 0's or 1's? If so, you likely need to increase eps within betar(). $\endgroup$
    – cpp
    Commented Aug 3, 2020 at 16:35
  • $\begingroup$ @jatalah did you end up sorting out what was causing this warning message? I'm running into the same thing. $\endgroup$
    – tnt
    Commented Mar 15, 2023 at 19:19

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