Description
Course Content
Important note: Time constraints may preclude all topics being covered.
- Preliminaries
- Quick review of some common discrete and continuous probability models useful in ecotoxicology
- Quick review of basic R functions
- The General Linear Model
- Recasting the simple regression model in matrix notation
- Estimating and inference for model parameters
- Recasting the one-way ANOVA model in matrix notation
- Factor coding methods
- Orthogonal designs
- Using contrast vectors to make to test specific hypotheses
- Statistical pre-processing of ecotox. data
- Examination of alternative methods for computing ACRs (acute-to-chronic ratios)
- Computation of an ‘optimal’ ACR
- Testing for bi-modality in toxicity data
- Explanation of ‘new’ methods in revised Australian and New Zealand Guidelines
- Writing R functions to compute skewness, kurtosis, and bimodality coefficients
- Procedures for checking distributional assumptions
- Transforming data
- Concentration-Response Modelling
- Taxonomy of C-R models including threshold models and models incorporating hormesis
- Writing R functions and using intrinsic non-linear solvers to find maximum likelihood estimates of C-R model parameters
- Exploration of features and capabilities of the R package drc
- Using the C-R model to obtain a toxicity estimate together with its uncertainty
- New Methods for SSD Modelling
- Issues with fitting probability distributions to toxicity data
- Problems of identifiability
- Curse of small sample sizes
- Review of Burrlioz software – strengths and weaknesses
- New approaches to fitting SSDs
- Model averaging
- Mixture modelling
- Bayesian methods
- Exploration of new on-line tools from Europe and North America
- Correcting the HCx for species selection bias
- Optimal experimental design
- Advanced techniques for determining the optimal spacing in a C-R experiment. Using R to determine:
- Allocation of fixed experimental effort between control and test concentrations
- D-Optimal designs for C-R experiments
Breakout topics
A1 Review of vectors and matrices
- Special matrices
- Matrix algebra
- Solving systems of linear equation
- Regression models in matrix notation
A2 Likelihood Estimation
- Definition of likelihood function
- Maximising the likelihood function for simple pdfs
- Using R non-linear solvers to find maximum likelihood estimates for more complex cases