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Could someone explain what assumptions I am making (perhaps implicitly) when I specify family = nbinom2() versus family = truncated_nbinom2() in glmmTMB. In my model, I specify both the conditional formula using the argument formula and zero-inflation formula using the argument ziformula. According to the post here, family = nbinom2() is specifying a zero-inflated model whereas family = truncated_nbinom2() is specifying a zero-altered model.

How does the interpretation of the model results, specifically zero-inflation model, change for the two model families?

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  1. family = nbinom2() does not specify a zero-inflated model. It specifies a negative binomial distribution using the "quadratic parameterization" (hence the "2") $V = \mu + \mu^2/\phi$, where $V$ is the variance, $\mu$ is the mean, and $\phi$ is the dispersion parameter.

  2. family = truncated_nbinom2() specifies a negative binomial distribution where the zeroes are not observed. The parameters are fit on observed values $\geq 1$ only. Consequently, in principle, there could be zero inflation, zero deflation, or no alteration in the probability of observing a zero at all; the fitted negative binomial parameters will be the same, and there will be no zero inflation/deflation parameter estimated since no zeros are observed.

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  • $\begingroup$ Thank you for your answer, @jbowman. In my model, I specify both the conditional formula using the argument formula and zero-inflation formula using the argument ziformula. Is my model accounting for only zero-inflation when family = nbinom2() and both zero-inflation/deflation when family = truncated_nbinom2() ? $\endgroup$
    – StatisticsFanBoy
    Commented May 12 at 17:52
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    $\begingroup$ Yes, it is. You don't need to use ziformula with truncated_nbinom2(), as the zeros are all ignored anyway. $\endgroup$
    – jbowman
    Commented May 12 at 17:57
  • $\begingroup$ With truncated_nbinom2(), dropping ziformula results in the following error: Zeros are compatible with a truncated distribution only when zero-inflation is added. Any idea why this happens, @jbowman? $\endgroup$
    – StatisticsFanBoy
    Commented May 12 at 18:06
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    $\begingroup$ Did you pass zeros to the routine? truncated_nbinom2() assumes there are no zeros in the data, so if you pass any, they must be due to zero-inflation. $\endgroup$
    – jbowman
    Commented May 12 at 19:02

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