24AICandLRT - Choosing among possible random effects...

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