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24AICandLRT(1)

# 24AICandLRT(1) - Choosing among possible random effects...

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Choosing among possible random effects structures Sometimes random effects structure specified by the experimental design e.g. for experimental study, need a random effect for each e.u. Sometimes subject matter information informs the choice e.g. expect a correlation among people in the same family Sometimes you need to use the data to help choose an appropriate structure two commonly used approaches and one less commonly used. AIC or BIC Likelihood ratio test c 2011 Dept. Statistics (Iowa State University) Stat 511 section 24 1 / 15 INFORMATION CRITERIA: AIC and BIC Goal is a model that: Fits the data reasonably well Is not too complicated Deviance: 2 l ( ˆ θ ) , where l ( ˆ θ ) is the log likelihood function evaluated at the mle’s. Smaller values (or more negative values) = better fit of model to data. Adding parameters (i.e. a more complicated model) always reduces deviance. Akaike’s Information criterion AIC = 2 l ( ˆ θ ) + 2 k , where k is the total number of model parameters. The +2k portion of AIC can be viewed as a penalty for model complexity. Small values of AIC are preferred. Beware: sometimes calculated as 2 l ( ˆ θ ) 2 k , for which large is better c 2011 Dept. Statistics (Iowa State University) Stat 511 section 24 2 / 15 Schwarz’s Bayesian Information Criterion BIC = 2 l ( ˆ θ ) + k log ( n ) Similar to AIC except the penalty for model complexity is greater (for n 8 ) and grows with n. AIC and BIC can be used to compare any set of models. Pairs do not need to be nested (i.e., one is not a special case of the other) reduced vs. full model comparison only works for nested models Assume that models fit to same data If based on REML lnlL, models MUST have the same fixed effects structure. Different fixed effect imply different error constrasts, so different data Value of AIC or BIC uninformative (depends | Σ | ) c 2011 Dept. Statistics (Iowa State University) Stat 511 section 24 3 / 15 Interpretation of differences between two AIC/BIC values: 1. Choose the model with the smallest AIC/BIC. period. 2. Look at the difference between a model and the best model (smallest AIC/BIC).

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