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\lhead{\sf Mixed-effects models workshop}\chead{\sf Exercises \#2}
\rhead{\sf 2009-07-01 (p. \thepage)}
\lfoot{\sf Lattice graphics}\cfoot{}\rfoot{}
\pagestyle{fancy}
\newcommand{\code}[1]{\texttt{\small #1}}
\newcommand{\R}{\textsf{R}}
\begin{document}
Load the \code{classroom} data frame that you saved in the previous
set of exercises and attach the \code{lattice} package.
\begin{Schunk}
\begin{Sinput}
> load("classroom.rda")
> library(lattice)
\end{Sinput}
\end{Schunk}
\begin{enumerate}
\item Create a histogram of the \code{mathkind} (mathematics score in
  kindergarten) variable.
\begin{center}
\includegraphics{figs/ex2-histogram}
\end{center}
\item Create an empirical density plot of \code{mathkind}.
\begin{center}
\includegraphics{figs/ex2-density}
\end{center}

\item Create an empirical density plot of \code{mathkind} by sex using
  the optional argument \code{groups = sex}.  It is probably a good
  idea to suppress the points in the ``rug''.  Remember to use
  \code{auto.key} so you can tell which curve is which.
\begin{center}
\includegraphics{figs/ex2-densitysex}
\end{center}

\item Create an empirical density plot of \code{mathkind} with one
  curve for minority students and one for non-minority students.
\begin{center}
\includegraphics{figs/ex2-densityminority}
\end{center}

\item Create a scatter-plot of
  the \code{mathgain} versus the kindergarten score.  Add a reference
  grid and a scatterplot smoother curve with the optional argument
  \code{type = c("g", "p", "smooth")}.  Repeat this plot using \code{"r"}
  instead of \code{"smooth"} to add a reference (or ``regression'')
  line.
\begin{center}
\includegraphics{figs/ex2-xyplot}
\end{center}

\item The negative correlation between \code{mathkind} and \code{mathgain} 
\begin{Schunk}
\begin{Sinput}
> with(classroom, cor(mathkind, mathgain))
\end{Sinput}
\begin{Soutput}
[1] -0.4870136
\end{Soutput}
\end{Schunk}
  is not surprising because \code{mathgain} is the grade 1 score minus
  the kindergarten score.  Create a new variable \code{math1} which is
  the sum of \code{mathkind} and \code{mathgain}
\begin{Schunk}
\begin{Sinput}
> classroom <- within(classroom, math1 <- mathkind + mathgain)
> with(classroom, cor(mathkind, math1))
\end{Sinput}
\begin{Soutput}
[1] 0.6311802
\end{Soutput}
\end{Schunk}
  and plot \code{math1} versus \code{mathkind}.  The version shown
  below uses the optional argument \code{aspect="iso"} to ensure that a
  unit change on the x axis corresponds to a unit change on the y axis.
\begin{center}
\includegraphics{figs/ex2-xyplot1}
\end{center}

\item Create a multi-panel scatterplot of \code{math1} versus
  \code{mathkind} with separate panels for males and females.
\begin{center}
\includegraphics{figs/ex2-xyplot2}
\end{center}
\item Create a multi-panel scatterplot of \code{math1} versus
  \code{mathkind} with separate panels for minority and non-minority
  students.
\begin{center}
\includegraphics{figs/ex2-xyplot3}
\end{center}
\item Create a multi-panel scatterplot of \code{math1} versus
  \code{mathkind} classified according to \code{sex} and \code{minority}
\begin{center}
\includegraphics{figs/ex2-xyplot4}
\end{center}
\item Consider only the students in school 11.  The study includes
  students from nine different classrooms in that school.
\begin{Schunk}
\begin{Sinput}
> xtabs(~classid, classroom, schoolid == 11, drop = TRUE)
\end{Sinput}
\begin{Soutput}
classid
 86 113 131 172 195 201 233 285 293 
  5   3   2   4   4   5   1   3   4 
\end{Soutput}
\end{Schunk}
  Create a dot-plot of the \code{mathgain} by classroom for students
  in school 11 only.
  \begin{center}
\includegraphics{figs/ex2-dotplot1}
  \end{center}
  Repeat the plot reordering the classrooms according to increasing
  mean gain and joining the classroom averages.
  \begin{center}
\includegraphics{figs/ex2-dotplot2}
  \end{center}
\end{enumerate}
\end{document}

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