12. Practical considerations – Negative Variance Components

Introduction to Mixed Models
Training session with Dr Helen Brown, Senior Statistician, at The Roslin Institute, March 2016.
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These training sessions were given to staff and research students at the Roslin Institute. The material is also used for the Animal Biosciences MSc course taught at the Institute.
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*Recommended YouTube playback settings for the best viewing experience: 1080p HD
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Content:
Practical considerations
- Zero variance component estimates
- Significance testing
- Model checking
- Sample size estimation
- Explaining a mixed model

Negative Variance Components
- Estimation method allows negative estimates of variance components
- BUT random effects are assumed normally distributed
--- Negative variances are not permissible
--- Likely to be an underestimate of true VC which is small or zero
- Greater chance of negative VC by chance when :-
--- Ratio of true VC to residual is small
--- Small number of random effect categories, eg few biological replicates
--- Small number of observations per random effect category, eg few technical replicates

What to do when a Variance Component is Negative?
A. Fix variance component at zero
--- Packages often do this by default
B. Remove random effect from model
--- Same fixed effect estimates result from A and B but different DFs cause differences in significance tests
C. Define model in terms of correlation parameters
--- Correlations may be negative

A Negative Variance Component Occasionally Indicates Negative Correlation
- Eg Animal feeding experiment
--- Animals grouped in cages, weight measured
--- Greediest animals in cage get most food
--- Cage effects fitted as random gives negative cage variance component
- To model negative correlation within cages redefine model in terms of correlated error terms in R matrix and omit cage as random

Variance matrix for a covariance pattern model
- Variance matrix for model with cages fitted as random:
- Redefined in terms of correlation (?) between animals
--- no random effects
--- correlation allowed between animals in same cage