The World of Zero-Inflated Models. Volume 3: Using GLLVM

Key topics include count data models with excess zeros and distributions such as Poisson, negative binomial, zero-inflated Poisson, zero-inflated negative binomial, and Tweedie. The book also provides practical guidance on implementing these models in R using the gllvm package. Designed for researchers, statisticians, and analysts working with multivariate ecological, environmental, or social science data, this book is also a practical resource for R users looking to apply complex statistical models effectively. Each chapter includes detailed R code and case studies, demonstrating how to fit and interpret complex models, diagnose potential issues, and refine model performance. Emphasizing practical solutions, the book helps readers apply these methods to real-world datasets.

Table of Contents:
18 Introduction 495 18.1 Dolphins from the Brazilian Amazon . . . . . . . . . . . . . 495 18.2 Ospreys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499 19 Generalised linear latent variable models 51719.1 Parasites in fish . . . . . . . . . . . . . . . . . . . . . . . . . 518 19.2 Import the dataset . . . . . . . . . . . . . . . . . . . . . . . 518 19.3 Data preparation . . . . . . . . . . . . . . . . . . . . . . . . 519 19.4 Data exploration . . . . . . . . . . . . . . . . . . . . . . . . 520 19.5 Classical multivariate analysis tools . . . . . . . . . . . . . . 523 19.6 Univariate analysis . . . . . . . . . . . . . . . . . . . . . . . 535 19.7 GLLVM -First encounter . . . . . . . . . . . . . . . . . . . . 536 19.8 GLLVM applied to the parasite data . . . . . . . . . . . . . 539 19.9 Results of the optimal GLLVM . . . . . . . . . . . . . . . . 545 19.10 Model validation . . . . . . . . . . . . . . . . . . . . . . . . 553 19.11 Visualise the covariate effects . . . . . . . . . . . . . . . . . 558 19.12 Zero-inflated distributions . . . . . . . . . . . . . . . . . . . 559 19.13 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 20 GLLVM applied to zero-inflated freshwater benthic data 57520.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 20.2 Import the dataset . . . . . . . . . . . . . . . . . . . . . . . 576 20.3 Data preparation . . . . . . . . . . . . . . . . . . . . . . . . 576 20.4 Data exploration . . . . . . . . . . . . . . . . . . . . . . . . 577 20.5 Univariate analysis . . . . . . . . . . . . . . . . . . . . . . . 582 20.6 Poisson GLLVM for the mining data . . . . . . . . . . . . . 583 20.7 Some technicalities . . . . . . . . . . . . . . . . . . . . . . . 592 20.8 NB GLLVM and ZIP GLLVM . . . . . . . . . . . . . . . . . 593 20.9 Results of the NB GLLVM with 2 latent variables . . . . . . 597 21 GLLVM applied to Irish spider data 60721.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 21.2 Import the dataset . . . . . . . . . . . . . . . . . . . . . . . 607 21.3 Data preparation . . . . . . . . . . . . . . . . . . . . . . . . 608 21.4 Data exploration . . . . . . . . . . . . . . . . . . . . . . . . 610 21.5 Classical multivariate analysis tools . . . . . . . . . . . . . . 613 21.6 GLLVM for the spider data . . . . . . . . . . . . . . . . . . 617 21.7 Generalised reduced rank regression . . . . . . . . . . . . . . 625 21.8 Concurrent ordination . . . . . . . . . . . . . . . . . . . . . 636 21.9 Regularisation . . . . . . . . . . . . . . . . . . . . . . . . . . 642 21.10 Where to go from here? . . . . . . . . . . . . . . . . . . . . 648 22 GLLVM applied to Wrasse CPUE data 65122.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 22.2 Import the dataset . . . . . . . . . . . . . . . . . . . . . . . 652 22.3 Data preparation . . . . . . . . . . . . . . . . . . . . . . . . 652 22.4 Data exploration . . . . . . . . . . . . . . . . . . . . . . . . 655 22.5 Model formulation for the Tweedie GLLVM . . . . . . . . . 660 22.6 Fitting the Tweedie GLLVMs . . . . . . . . . . . . . . . . . 662 22.7 Results for the optimal model . . . . . . . . . . . . . . . . . 666 22.8 Model validation . . . . . . . . . . . . . . . . . . . . . . . . 670 22.9 Visualising the model . . . . . . . . . . . . . . . . . . . . . . 673 22.10 Residual pattern for Goldsinny Wrasse . . . . . . . . . . . . 674 22.11 Species-specific random effects . . . . . . . . . . . . . . . . . 677 22.12 Final comments . . . . . . . . . . . . . . . . . . . . . . . . . 680