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\section{Hierarchical modeling}
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\section{Hierarchical modeling}
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\begin{frame}{HSB data set}
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\begin{frame}{HSB data set}
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\begin{itemize}
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\item Two levels
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\begin{itemize}
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\item Level 1: Student attributes
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\item Level 2: School attributes
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\end{itemize}
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\end{itemize}
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\vfill
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\centering
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\centering
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\begin{tabular}{llp{10cm}}
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\begin{tabular}{llp{10cm}}
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\hline
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\hline
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@ -474,8 +483,8 @@ $
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\begin{frame}{Results}
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\begin{frame}{Results}
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{Random effects}
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{Random effects}
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\begin{itemize}[<+->]
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\begin{itemize}[<+->]
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\item The estimate $\hat\sigma^2_{\upsilon_0} = 2.32$ of the variance of
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\item The (ML) estimate $\hat\sigma^2_{\upsilon_0} = 2.32$ of the variance
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mean school performance provides room for improving prediction by
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of mean school performance provides room for improving prediction by
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including additional predictors
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including additional predictors
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\item However, there is virtually no variation in the dependence of math
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\item However, there is virtually no variation in the dependence of math
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achievement on \texttt{cses} across schools ($\hat\sigma^2_{\upsilon_1} =
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achievement on \texttt{cses} across schools ($\hat\sigma^2_{\upsilon_1} =
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