Course format:
- Self-study course.
- On-demand access to all video content online within a 12-month period.
- Daily interaction on the Discussion Board for detailed questions.
- Live chat for quick queries.
- Course fee includes a 1-hour video chat with instructors for personalized questions and data assistance.
Course content
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 estimate 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 irregularly 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?
Pre-required knowledge
Working knowledge of R and linear regression. This is a non-technical course.