ZIBGe-GLMM

Software package for Zero-Inflated Bivariate Geometric Generalized Linear Mixed Model (ZIBGe-GLMM) Bayesian inference [1]

Quickstart

Make sure the following software is installed and up-to-date:
- R
- JAGS
- Boost

Also, make sure that the following R packages are installed and up-to-date:
- runjags
- rjags
- Rcpp
- BH

Install the custom /module for JAGS (see /module/README) and run /example.R to generate example data and generate a posterior parameter sample.

Contents

The contents of this package can be divided into four groups:

Data generation

ZIBGe(μ, ν, θ, π₁, π₂,π₃) distribution PMF
/dZIBGe.cpp

MCMC algorithm to generate ZIBGe-distributed data
/mcmcsample.R

Functions defined in /mcmcsample.R
/rZIBGe.rda

Script to generate data
/generate.R

Data generated using /generate.R
/generated.rda

JAGS model scripts invoked using runjags

Generate posterior sample for data in /generated.rda
/constantmodel.R

Generate posterior sample for Aeshna viridis population data
/populationmodel.R

Same as above, using the BZIP model in [2] instead
/populationmodel_BZIP.R

R data file loaded in /populationmodel.R and /populationmodel_BZIP.R
/populationdata.rda

Custom JAGS module for ZIBG likelihood computations

Directory containing installation files (see /module/README)
/module/

Data

Aeshna viridis (green hawker) population data collected by Bureau Biota (Groningen, NL) [3]
/data/

Figure 1. A female green hawker. Photo copyright by Bureau Biota (Groningen, NL).

Technical details

Probability Mass Function (PMF) evaluations of the ZIBGe distribution need to be carefully implemented to avoid round-off errors when working with large multinomial coefficients. This problem is particularly pronounced when both components of the evaluated point are large. Therefore, multiple precision floating points are needed to store intermediate results since a double data type only supports precision up to 15 decimal digits. The PMF is implemented in a C++ function (to be interfaced with Rcpp in R) to utilize the cpp_bin_float class from Boost's Multiprecision library (see [4]). Using high precision is computationally demanding, so to counteract this, powers already computed in each previous term are re-used to avoid evaluating the summands in the PMF directly.

Likelihoods that cannot be computed using JAGS's built-in distributions are often dealt with using the zeros or ones trick (see [5], § 9.4). However, doing so prevents the use of multiple precision floating points. The modular character of JAGS makes it easy to extend the build-in distributions using custom (multivariate) distributions or sampling algorithms (see [6]). Analogous to /dZIBGe.cpp, the custom /module facilitates likelihood computations using high-precision intermediate computations.

Straightforward sampling methods, such as inverse transform sampling or rejection sampling, are inapplicable to the ZIBGe distribution; the former due to the nested sums appearing in its cumulative distribution function, and the latter because of the absence of a suitable proposal distribution. Therefore, a simple Metropolis-Hastings MCMC algorithm is used to generate ZIBG samples instead (see /mcmcsample.R).

References

[1] van Oppen, Y. B., Milder-Mulderij, G., Brochard, C., Wiggers, R., de Vries, S., Krijnen, W. P., & Grzegorczyk, M. A. (2022). Modeling dragonfly population data with a Bayesian bivariate geometric mixed-effects model. Journal of Applied Statistics, 1-23.

[2] Majumdar, A., & Gries, C. (2010). Bivariate zero-inflated regression for count data: A Bayesian approach with application to plant counts. The International Journal of Biostatistics, 6(1).

[3] Milder-Mulderij, G., Brochard, C., Wiggers, R., & de Vries, S. (2020). Alternatief krabbenscheerbeheer in Fryslân, Groningen en Drenthe. Interpretatie op basis van vier jaar onderzoek op diverse locaties. Bureau Biota.

[4] Maddock, J., & Kormanyos, C. (2018). Boost multiprecision.

[5] Lunn, D., Jackson, C., Best, N., Thomas, A., & Spiegelhalter, D. (2012). The BUGS Book: A Practical Introduction to Bayesian Analysis (CRC, Boca Raton, FL).

[6] Wabersich, D., & Vandekerckhove, J. (2014). Extending JAGS: A tutorial on adding custom distributions to JAGS (with a diffusion model example). Behavior Research Methods, 46(1), 15-28.

DISCLAIMER

All software in this repository is covered by this disclaimer:

While every effort is made to deliver high quality products, no guarantee is made that the products are free from defects. The software is provided "as is", and you use the software at your own risk.

No warranties are made as to performance, merchantability, fitness for a particular purpose, or any other warranties whether expressed or implied.

No oral or written communication from or information provided by the author shall create a warranty.

Under no circumstances shall the author be liable for direct, indirect, special, incidental, or consequential damages resulting from the use, misuse, or inability to use this software, even if the author has been advised of the possibility of such damages.