Flyer for this course
See the online flyer for a detailed description.
General outline
The course starts with a short revision of data exploration and multiple linear regression models. A non-technical introduction of generalised additive models (GAM) is provided. GAMs will be used to estimate long-term trends, seasonal patterns, covariate effects and auto-regressive correlation. We also provide a short introduction to linear mixed-effects models and generalised linear mixed-effects models (GLMM) to analyse hierarchical data (e.g. short time series from the same core or site). GLMMs and GAMMs are used to estimated trends, seasonality and covariate effects in multivariate time series. For a more detailed description, see:
https://www.courses.highstat.com/index.php/10-time-series-analysis-using-frequentist-tools
GAMMs are applied on continuous, binary, proportional and count time series data using the Gaussian, Poisson, negative binomial, Bernoulli, binomial, beta, gamma and Tweedie distributions.
Detailed outline
Module 1
- General introduction.
- Revision exercise on linear regression.
- Introduction to matrix notation.
- Theory presentation on GAM.
- Three introductory GAM exercises.
Module 2
- Theory presentation: How to include auto-regressive correlation in a regression model.
- Exercise showing how to fit a GLM with auto-regressive correlation in glmmTMB.
- Exercise on GAM with auto-regressive correlation applied to a regular spaced time-series data set.
- Exercise on GAM with auto-regressive correlation applied to an irregular spaced time-series data set.
- Exercise on detecting important changes in trends.
Module 3
- Short theory presentation on linear-mixed effects models.
- Two exercises on generalised additive mixed-effects models (GAMM) applied to multivariate time series data sets.
Module 4
- Short theory presentation of Poisson and negative binomial GLM.
- One revision exercise on Poisson GLM.
- Two exercises on Poisson and negative binomial GAM applied to univariate time series data sets.
- One exercise on Bernoulli GAM applied to a univariate time series.
Module 5
- Five exercises showing how to apply GAMM to estimate trends, seasonality and /or covariate effects in multivariate time series data sets (using various distributions).
- Bonus material
- Theory presentation on data exploration.
- Exercise on multiple linear regression analysis.
- Exercise on GAMM applied to time series of tagged animals.
- Exercise linear mixed-effects models using the bears and ants data set.
- Exercise introducing the negative binomial, generalised Poisson and Conway-Maxwell-Poisson GLMs for the analysis of count data.
- Exercise showing the application of Poisson and negative binomial GLMM for the analysis of a time series data set.
- What is DHARMa?
Free 1-hour face-to-face video meeting
The course fee includes a 1-hour face-to-face video meeting with one or both instructors. The meeting needs to take place within 12 months after the last live zoom meeting. You can discuss your own data but we strongly suggest that the statistical topics are within the content of the course. The 1-hour needs to be used in one session and will take place on a mutually convenient day.
Pre-required knowledge
Working knowledge of R and linear regression. This is a non-technical course.