Likelihood function #
The likelihood statement specifies the probability distribution that will be used to describe the response variable. The available options depend on your data, so knowing what type of variable you’re working with is essential.
Syntax #
# Likelihood. For counts, one or both of: poisson, negative-binomial.
likelihood:
- poisson
- negative-binomial
Usage #
In some cases – a model for soil stability observations – there is only one plausible, implemented likelihood function (ordinal-latent-normal). In other cases – species richness – there might be several available options (poisson, negative-binomial, and their zero-inflated counterparts). In cases where you specify multiple likelihoods, the model API will create a separate analysis for each, and the relative performance of each can be evaluated using model diagnostics, posterior predictive checks, and information criteria.
Options #
| Option | Description | Example |
|---|---|---|
beta | Continuous variables with values between 0 and 1 | Ocular cover |
beta-binomial1 | Overdispersed binomial data | |
binomial | “Successes” in a given number of trails | The number of “hits” of invasive species in \(n\) point intercepts along a transect |
gamma2 | Continuous, non-negative quantities | |
gen-pois | Underdispersed count data | |
hurdle-ordinal-latent-beta | Ordinal data arising from a beta distributed latent variable | Plant cover measured using Daubenmire cover classes |
lognormal3 | Continuous, non-negative quantities | |
negative-binomial | Overdispersed counts (with support for either fixed stratum-level or hierarchical site-level variances modeled using a moment match for \(\kappa\) ) | |
negative-binomial-simple | Overdispersed counts (with fixed stratum-level dispersion modeled directly using \(\kappa\) ) | |
ordinal-latent-normal | Ordinal data arising from a normally distributed latent variable | Soil stability |
poisson | Counts | Richness or shrub density |
zero-inflated-beta-binomial | Binomial data that exhibit overdispersion and excess zeros | |
zero-inflated-binomial | Binomial data with an excess of zero counts | |
zero-inflated-negative-binomial | Count data that exhibit overdispersion and excess zeros | |
zero-inflated-poisson | Count data with an excess of zero counts |
A misnomer. We don’t use the canonical beta-binomial parameterization. It was too slow / unwieldy. Instead, we use a binomial model with an extra epsilon term in the model for the mean. ↩︎
“The log of a lognormal random variable is… normal. It’s symmetric.” See Glen_b’s answer here. ↩︎
“The log of a gamma distributed random variable is left-skew. Depending on the value of the shape parameter, it may be quite skew or nearly symmetric.” See again Glen_b’s answer here. ↩︎