1st Edition

Spatial Linear Models for Environmental Data

By Dale L. Zimmerman, Jay M. Ver Hoef Copyright 2024
    416 Pages 26 Color & 72 B/W Illustrations
    by Chapman & Hall

    416 Pages 26 Color & 72 B/W Illustrations
    by Chapman & Hall

    Many applied researchers equate spatial statistics with prediction or mapping, but this book naturally extends linear models, which includes regression and ANOVA as pillars of applied statistics, to achieve a more comprehensive treatment of the analysis of spatially autocorrelated data. Spatial Linear Models for Environmental Data, aimed at students and professionals with a master’s level training in statistics, presents a unique, applied, and thorough treatment of spatial linear models within a statistics framework. Two subfields, one called geostatistics and the other called areal or lattice models, are extensively covered. Zimmerman and Ver Hoef present topics clearly, using many examples and simulation studies to illustrate ideas. By mimicking their examples and R code, readers will be able to fit spatial linear models to their data and draw proper scientific conclusions.

     Topics covered include:

    • Exploratory methods for spatial data including outlier detection, (semi)variograms, Moran’s I, and Geary’s c.
    • Ordinary and generalized least squares regression methods and their application to spatial data.
    • Suitable parametric models for the mean and covariance structure of geostatistical and areal data.
    • Model-fitting, including inference methods for explanatory variables and likelihood-based methods for covariance parameters.
    • Practical use of spatial linear models including prediction (kriging), spatial sampling, and spatial design of experiments for solving real world problems.

    All concepts are introduced in a natural order and illustrated throughout the book using four datasets. All analyses, tables, and figures are completely reproducible using open-source R code provided at a GitHub site. Exercises are given at the end of each chapter, with full solutions provided on an instructor’s FTP site supplied by the publisher.


    1. Introduction

    2. An Introduction to Covariance Structures for Spatial Linear Models

    3. Exploratory Spatial Data Analysis

    4. Provisional Estimation of the Mean Structure by Ordinary Least Squares

    5. Generalized Least Squares Estimation of the Mean Structure

    6. Parametric Covariance Structures for Geostatistical Models

    7. Parametric Covariance Structures for Spatial-Weights Linear Models

    8. Likelihood-Based Inference

    9. Spatial Prediction

    10. Spatial Sampling Design

    11. Analysis and Design of Spatial Experiments

    12. Extensions

    Appendix A: Some Matrix Results


    Dale L. Zimmerman is Professor of Statistics at the University of Iowa, and Jay M. Ver Hoef is Senior Scientist and Statistician, Alaska Fisheries Science Center, NOAA Fisheries. Both are Fellows of the American Statistical Association and winners of that association’s Section for Statistics and the Environment Distinguished Achievement Award.

    "Spatial Linear Models for Environmental Data is a readable, practical, and comprehensive book, covering both the foundation and application of spatial linear models. The authors begin the book with four real data examples, which they revisit regularly as new topics are introduced. Every chapter includes frequent and informative figures and graphics. There is plenty of discussion of the ideas behind the models and analyses. I especially appreciated the chapters on sampling design and design of experiments, since even the best models are useless unless you have informative data."
    Lisa Madsen, Professor of Statistics, Oregon State University