12. Practical considerations – Negative Variance Components

Introduction to Mixed Models Training session with Dr Helen Brown, Senior Statistician, at The Roslin Institute, March 2016. ************************************************ 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. ************************************************ *Recommended YouTube playback settings for the best viewing experience: 1080p HD ************************************************ 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