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1

The output variable is a USD amount if person makes a purchase and 0 otherwise. Don't model this using a Poisson distribution, unless your purchases are on the order of 1, 2, ... USD. The Poisson is not only characterized by many zeros, but also by low non-zero outcomes. If you have a high Poisson parameter, then you will get probability mass over high ...

0

You can't use these extended families outside of gam() or bam()` from the mgcv package. With gamm4 you're stuck with the families that lmer() and glmer() from the lme4 package supports. Options would be to use the gamlss package for ZIP models as I don't think it has a Tweedie family, or use the glmmTMB package which has lots of options, including tw() for ...

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You've got a lot of questions here. 1. what does | persons do? As you suggest, it sets the zero-inflation model to $\textrm{logit}(p_z) = \beta_{z0} + \beta_{z1} \cdot \textrm{persons}$. The authors decided that the number of people in the group could affect whether the group didn't fish at all, but wouldn't affect the fishing success if the group did ...

1

I would recommend to start out from a tobit model, i.e., a normally distributed response censored at zero. This is a relatively simple model because (1) the normal distribution is relatively "easy" or "nice" and (2) the probability for observing a zero and the expectation of the positive observations is driven by the same effects in the regression model. ...

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