Statistical Modelling I

Content for Monday, November 10, 2025

Last class we looked at tree-based machine-learning models for classifying data (i.e., presence/abscence, categorization) or estimating the pseudo-regression relationships between variables and measured outcomes. Those approaches rely on learning the distributions necessary for the likelihood from the data themselves (rather than from a theoretical probability distribution). Today we’ll look at alternative approaches using tradititional statistical models.

Resources

Bigger Picture

Techincal details

  • Statistical Models from the terra package documentation has some step-by-step examples of using terra with base R to fit statistical modles.

  • Statistical Learning from (Lovelace et al. 2019) has an extended example of fitting a variety of modeling approaches to data and evaluating their performance.

Objectives

By the end of today you should be able to:

  • Define the likelihood function and its relationship to statistical infrerence.

  • Recognize key assumptions of statistical models and how spatial data may challenge those assumptions.

  • Simulate fake data with known relationships

  • Fit simple linear and generalized linear models to spatial data

View all slides in new window Download PDF of all slides

References

Guillera-Arroita, G., J. J. Lahoz-Monfort, J. Elith, A. Gordon, H. Kujala, P. E. Lentini, M. A. McCarthy, R. Tingley, and B. A. Wintle. 2015. Is my species distribution model fit for purpose? Matching data and models to applications. Glob. Ecol. Biogeogr. 24:276–292.
Guisan, A., R. Tingley, J. B. Baumgartner, I. Naujokaitis-Lewis, P. R. Sutcliffe, A. I. T. Tulloch, T. J. Regan, L. Brotons, E. McDonald-Madden, C. Mantyka-Pringle, T. G. Martin, J. R. Rhodes, R. Maggini, S. A. Setterfield, J. Elith, M. W. Schwartz, B. A. Wintle, O. Broennimann, M. Austin, S. Ferrier, M. R. Kearney, H. P. Possingham, and Y. M. Buckley. 2013. Predicting species distributions for conservation decisions. Ecol. Lett. 16:1424–1435.
Lovelace, R., J. Nowosad, and J. Muenchow. 2019. Geocomputation with R. CRC Press.
Stoltzfus, J. C. 2011. Logistic regression: A brief primer. Acad. Emerg. Med. 18:1099–1104.