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\begin{frame}
\frametitle{Data analysis using R}
\begin{itemize}
\item We store a ``rectangular'' data set (columns correspond to
variables, rows to observations or cases) as a \Emph{data frame}.
Typical column types are \code{numeric}, \code{factor}
(categorical data) and \code{ordered} (ordered categories).
\item R has a wealth of graphics functions. Use them. I
particularly like the functions available in the \code{lattice}
package.
\item We specify models using \code{formula} and \code{data}
arguments. Typically we assign the fitted model to a name and use
\Emph{extractor} functions to access parts of the fitted model or
functions like \code{summary} and \code{print} to display some of
the information about the fit.
\item In many cases there are graphical functions to display
information about the fit or characteristics extracted from the
fit.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Fitting linear mixed models}
\begin{itemize}
\item The formula for a linear mixed model consists of several
\Emph{terms} separated by `\code{+}' symbols.
\item A random effects term, which is usually enclosed in
parentheses, contains the `\code{|}' symbol. The expression to
the right, which is usually the name of a variable, is evaluated
as the grouping factor. The expression to the left, frequently
`\code{1}' indicating a simple scalar random effect for each
level, is evaluated as a model matrix.
\item Remember that `\code{(x|f)}' is equivalent to
`\code{(1+x|f)}'. If we want to suppress the intercept we use
`\code{(0+x|f)}' or `\code{(x-1|f)}'.
\item An interaction of a random-effects factor, `\code{f}' and a
fixed-effects factor, `\code{g}' can be modelled as
\code{g + (1|f:g) + (1:f)} or as \code{g + (0+g|f)}. The second
is more difficult to fit than is the first.
\end{itemize}
\end{frame}
\begin{frame}
\frametitle{Fitting generalized linear mixed models}
\begin{itemize}
\item To fit a generalized linear mixed model we specify a
\code{family} in addition to the formula and data arguments.
\item The family includes definitions of the link function, the
inverse link function and the variance function.
\item For Bernoulli (binary) data we use the \code{binomial} family
for which the canonical link function is the logit. Some people
prefer the probit link. Usually the fit with probit is very
similar to the fit with logit.
\item For count data we use the \code{poisson} family for which the
canonical link is the logarithm.
\end{itemize}
\end{frame}