Hello,

The following book can now be ordered (exclusively) from www.highstat.com:

The World of Zero-Inflated Models. Volume 1: Using GLM.


For a table of contents and two free chapters, see:

http://highstat.com/index.php/the-world-of-zero-inflated-models


Kind regards,

Alain


Outline of Volume 1.

In Chapter 2 we revise data exploration and multiple linear regression 
using red knot data. Stable isotope ratios of nitrogen in animal tissues 
are modelled as a function of 3 covariates. This chapter serves as a 
blueprint for all other chapters in the sense that it shows the general 
outline of a statistical analysis.

Chapter 3 starts with a revision of the Poisson distribution and the 
Poisson GLM for the analysis of count data. We use a small puffin data 
set. We also introduce the NB GLM and two relatively unknown, but 
useful, members of the family, namely the GP GLM and the CMP GLM. 
Surprisingly, the latter two models tend to perform better than the NB 
GLM in the case of overdispersion. The latter two can also be used to 
deal with underdispersion. Most models are fitted with the glmmTMB 
package in R. Model validation tools are explained, and the concept of 
simulating data from a model (to verify whether it complies with all 
assumptions of the model) is introduced. We first do the simulation 
steps ourselves, then quickly migrate to the DHARMa package, which is 
rapidly gaining popularity.

In Chapter 4 we introduce zero-inflated models for count data, and these 
are executed with the glmmTMB package. We start with a basic 
introduction using simulated data, and discuss zero-inflated Poisson 
(ZIP), zero-inflated NB (ZINB), zero-inflated generalised Poisson (ZIGP) 
and zero-inflated CMP (ZICMP) models. We then apply them all on the 
puffin data set.

In Chapter 5 we analyse data on parasites in Brazilian sandperch. Such 
data nearly always bring you within zero-inflation territory. Now that 
we are familiar with Poisson, NB, GP, CMP models, and their 
zero-inflated cousins, it is time to learn how we can manoeuvre among 
them. How do we decide to apply an NB GLM or a ZIP model? In this 
chapter, we will keep the binary part of the model simple.

Chapter 6 is about ZIGP models. Data on mistletoe tree infections are 
used. The ZIGP models contain covariates in both the count and binary 
parts of the model.

Hurdle models for count data are discussed in Chapter 7 using dolphin 
sighting data. In a hurdle model we perform 2 analyses. First, the 
sighting abundances are converted into absence/presence data, and a 
Bernoulli GLM is applied. Then the zero counts are set to NA (or 
dropped), and a truncated Poisson (or NB) GLM is applied. In the third 
step, the two components are combined to calculate the expected values 
of the hurdle model. Chapter 7 is relatively long as it contains many 
topics that may be relevant: Bernoulli GLM, quasi-separation, truncated 
Poisson and NB distributions, and zero-altered Poisson (ZAP) and 
zero-altered NB (ZANB) models.

In the last 2 chapters of this volume, we discuss models for the 
analysis of continuous data with an excessive number of zeros. Biomass 
of lobsters are analysed using Tweedie GLMs in Chapter 8, and a ZAG 
model is applied on the same data in Chapter 9. The ZAG is a hurdle 
model for continuous data. Our recommendation is to opt for the Tweedie 
GLM approach.


-- 
Dr. Alain F. Zuur
Highland Statistics Ltd.
9 St Clair Wynd
AB41 6DZ Newburgh, UK
Email: [log in to unmask]
URL:   www.highstat.com

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