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When to use Gaussian family instead of Poisson?
The Poisson is a reasonable starting point as it has support for the non-negative integers, but it is often too restricted a distribution to model the features of animal abundance data. Commonly used alternatives are the Negative Binomial (use family = nb () in mgcv::gam () for example) for data with more variance that that assumed by the Poisson.
Which is equivalent to a Poisson regression model?
Loglinear model is also equivalent to poisson regression model when all explanatory variables are discrete. For more on poisson regression models see the next section of this lesson, Agresti (2007), Sec. 3.3, Agresti (2002), Section 4.3 (for counts), Section 9.2 (for rates), and Section 13.2 (for random effects) and Agresti (1996), Section 4.3.
What is the Poisson distribution of a GLM model?
Poisson regression is a type of a GLM model where the random component is specified by the Poisson distribution of the response variable which is a count. Before we look at the Poisson regression model, let’s quickly review the Poisson distribution.
Which is an example of a Poisson distribution?
Situations in which there are many opportunities for some phenomena to occur but the chance that the phenomenon will occur in any given time interval, region of space or whatever is very small, lead to the distribution of the number of occurrences of the phenomena having a Poisson distribution. Here are some examples:
When to use the gamma or Gaussian distribution?
If you are dealing with continuous non-negative outcome, then you could consider the Gamma distribution, or Inverse Gaussian distribution.
When to use a Poisson or Poisson distribution?
If your outcome is discrete, or more precisely, you are dealing with counts (how many times something happen in given time interval), then the most common choice of the distribution to start with is Poisson distribution.
What happens when you add offset to Poisson family?
Assuming you use the default/canonical link for the Poisson family (the log link), you would add + offset (log (n_traps)) to the model formula, which would have the effect of turning the response from a count into a count per trap, but this is all happening internal to the model, you still retain the discrete, non-negative nature of the response.