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

Type Article
Date 2018-09
Language English
Author(s) Thorson James T.1
Affiliation(s) 1 : NOAA, Fisheries Resource Assessment & Monitoring Div, Northwest Fisheries Sci Ctr, Natl Marine Fisheries Serv, Seattle, WA 98112 USA.
Source Canadian Journal Of Fisheries And Aquatic Sciences (0706-652X) (Canadian Science Publishing, Nrc Research Press), 2018-09 , Vol. 75 , N. 9 , P. 1369-1382
DOI 10.1139/cjfas-2017-0266
WOS© Times Cited 36
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 useful alternative to the conventional delta-model with similar properties to the CPG distribution.

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