Course title: Generalized and linear mixed models for biologists

Learning outcomes (knowledge, skills, social competence and attitude):

The student understands the theoretical framework for statistical methods applied to the biological sciences, specifically generalized linear models for count and binomial data and mixed models for clustered data.

• Skills

The student can:

• effectively create exploratory, diagnostic, and expository graphs from data
• choose and execute an appropriate statistical analysis for a given set of data and scientific questions

• execute, trouble-shoot, and interpret the results of linear and generalized linear mixed models.

• Social competence and attitude

The student can:

• communicate the scientific questions to be asked, justify and explain the connection to the results of a statistical analysis
• appreciate the importance of rigorous and ethical approaches to statistical analysis, avoiding data snooping

Prerequisites:

Theoretical knowledge and practical skills in applying statistical methods at the basic level:

• understanding basic concepts (types of measurement scales, probability, basic types of distributions, central limit theorem, measures of central tendency and dispersion, variance, standard deviation, standard error, confidence interval, parameter, estimator, statistical test, statistical null and alternative hypotheses, type I and type II errors, significance level);
• understanding and practical ability to perform basic statistical analyses (e.g. Student’s t-test)
• understanding of basic linear models and their implementation in R: simple analysis of regression and correlation, simple analysis of variance, multiple regression and ANCOVA.
• Basic proficiency in the R programming language.

Full description (=content of the course):

• Monday
  • exploratory graphics using ggplot (Wickham, 2009,Cleveland (1993))
    • intro to quantitative display: graphical hierarchies
    • ggplot basics
    • intermediate ggplot: smooths and facets
  • mixed/hierarchical/multilevel models: introduction (Gelman & Hill, 2006,Zuur et al. (2009))
    • conceptual basis, frequentist and Bayesian
    • definition of random effects
    • shrinkage and pooling
    • experimental designs: nesting and crossing
• Tuesday
  • linear mixed models
    • frequentist estimation
    • model diagnostics and checking
    • inference
  • generalized linear mixed models
    • frequentist estimation
    • model diagnostics and checking
    • inference
• Wednesday
  • introduction to Bayesian statistics
    • basic Bayes
    • modern computational Bayes: MCMC
  • Bayesian estimation/diagnostics/inference for (G)LMMs

Additional topics (as time/interest allows)

• time-series and spatial models
• zero-inflated models
• GLMs: alternative families and links

Bibliography

Cleveland, W. (1993). Visualizing Data. Summit, NJ: Hobart Press.

Gelman, A., & Hill, J. (2006). Data analysis using regression and Multilevel/Hierarchical models. Cambridge, England: Cambridge University Press. Retrieved from http://www.stat.columbia.edu/~gelman/arm/

Wickham, H. (2009). Ggplot2: Elegant graphics for data analysis. Springer New York. Retrieved from http://had.co.nz/ggplot2/book

Zuur, A. F., Ieno, E. N., Walker, N. J., Saveliev, A. A., & Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. Springer.