Three problems with the conventional delta-model for biomass sampling data, and a computationally efficient alternative

Abstract

Ecologists often analyse biomass sampling data that result in many zeros, where remaining samples can take any positive real number. Samples are often analysed using a “delta-model” that combines two separate generalized linear models, GLMs (for encounter probability and positive catch rates), or less often using a compound Poisson-gamma (CPG) distribution that is computationally expensive. I discuss three theoretical problems with the conventional delta-model: difficulty interpreting covariates for encounter probability, the assumed independence of the two GLMs, and the biologically implausible form when eliminating covariates for either GLM. I then derive an alternative “Poisson-link model” that solves these problems. To illustrate, I use biomass samples for 113 fish populations to show that the Poisson-link model improves fit (and decreases residual spatial variation) for >80% of populations relative to the conventional delta-model. A simulation experiment illustrates that CPG and Poisson-link models estimate covariate effects that are similar and biologically interpretable. I therefore recommend the Poisson-link model as a useful alternative to the conventional delta-model with similar properties to the CPG distribution.