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.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
ISBN-13
978-1-7399636-2-0 (9781739963620)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
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
