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To address this problem, GLMs are usually extended by including random effects in the linear predictor.
The approach used here extends the Dominici work by including random effects that reflect two levels of variability.
18 45 Nevertheless, we took into account the effect of hospital level clustering by including random effects for each hospital.
These models incorporated the structure of the data by including random effects for person, practice and year.
Model 3 generalizes Model 2, by including random effects of the therapeutic group not only in the intercept but also in the slope of the price.
The dependency structure of the data relating to clusters and households was taken into account by including random effects in the models.
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In both analyses, we will control for clustering at each level by appropriately including random effects terms in the model.
The practical impact of clustering was investigated by fitting three linear mixed models, including random effects of herd and cow, random effect of herd, and no random effect, respectively, with absence of any lesion as the dependent variable, to a subset of the data including only observations from cows with multiple trimmings (4933 records).
Model fits were assessed by their respective Deviance Information Criterion DICC) scores [[ 44]] including random effects.
We examined the sensitivity of the PM2.5 association with mortality from diabetes to the stochastic structure of the Cox survival model by extending the standard Cox model to include random effects (REs) defined by CD.
We accounted for this degree of clustering by constructing multilevel models that included random effects at the practice level.
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