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\input{plots/t-Roptions}


\title[glm2]{After Fitting Regressions}


\author{Paul E. Johnson\inst{1} \and \inst{2}}


\institute[K.U.]{\inst{1}Department of Political Science\and \inst{2}Center for
Research Methods and Data Analysis, University of Kansas}


\date[2012]{2012}

\makebeamertitle



\AtBeginSubsection[]{

  \frame<beamer>{

    \frametitle{Outline}

    \tableofcontents[currentsection,currentsubsection]

  }

}



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\begin{frame}
  \titlepage
\end{frame}



\begin{frame}
\frametitle{Outline}

\tableofcontents{}

\end{frame}

%==================================================

\section{Methods}
\begin{frame}[containsverbatim]
  \frametitle{Methods: Things To Do ``To'' a Regression Object}





\input{plots/t-glm10}

\begin{description}
  \item [pres04] Kerry,  Bush
  \item [partyid]  Factor with 7 levels, SD $\rightarrow$ SR
  \item [sex]    Male, Female
  \item [owngun] Yes, No
\end{description}
\end{frame}

\begin{frame}[containsverbatim]
  \frametitle{Just for the Record, The Data Preparation Steps Were $\ldots$}

\input{plots/t-gssdata10}
\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{First, Find Out What You Got}


\input{plots/t-glm12}

\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{Understanding attributes}
  \begin{itemize}
  \item If  you see \$, it means you have an S3 object
  \item That means you can just ``take'' values out of the object with
    the dollar sign operator using commands like

\input{plots/t-glm15}

\item That "crude" approach is discouraged. We should instead use
    "extractor methods"

    \texttt{coefficients(bush1)}

  \item Challenge: finding/remembering the extractor functions.
  \end{itemize}
\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{Just Making Sure About the Object's Class}

  \begin{itemize}
  \item Ask the object what class it is from

\input{plots/t-methods05}

  \end{itemize}
\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{ Ask What Methods Apply to a ``glm'' Object}

\input{plots/t-methods10}

\end{frame}



\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{Check methods for ``lm'' class}

\input{plots/t-012}

\end{frame}




\begin{frame}[containsverbatim]
  \frametitle{Do You Wonder How ``They'' Do ``That''?}
  \begin{itemize}

    \item At some point, you realize that the help page is not
      detailed enough.  You may need to see the Actual Code

    \item Darth said ``Use the Source, Luke!''

      If you want to know ``what a function does'', the
      best option is to download the ACTUAL SOURCE CODE and read it!
    \end{itemize}
\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{Can See Some Code Within an R Session}
  \begin{itemize}
  \item In the ``old days'', you could easily see a function's
      ``code'' by typing its name (i.e., omit the parentheses).

      Ex: q used to show all of the steps in shutting down.

    \item Today, in R 2.11, when I type q I see:

\begin{Schunk}\begin{Soutput}
> q
function (save = "default", status = 0, runLast = TRUE)
.Internal(quit(save, status, runLast))
<environment: namespace:base>
  \end{Soutput}
\end{Schunk}

\end{itemize}
\end{frame}

\begin{frame}[containsverbatim]
  \frametitle{Some Functions Still Show Their Code}
  \begin{itemize}

   \item Some very informative examples. Try:
      \begin{itemize}
        \item \texttt{ > lm \#(or stats::lm)}
        \item \texttt{ > glm \#(or stats::glm)}
        \item \texttt{ > termplot}
      \end{itemize}

    \item Generic method output not so useful. Try:
      \begin{itemize}
      \item \texttt{ > predict}
      \item \texttt{ > plot}
      \end{itemize}

    \end{itemize}
  \end{frame}


\begin{frame}
  \frametitle{Looking Into the Class Hierarchy}
  \begin{itemize}

  \item In many cases, you can only find what you need if you give
      the ``function'' name and the name of the ``class'' separated by
      a period.

   \item Try:
      \begin{itemize}
      \item \texttt{ > predict.lm }

      \item \texttt{ > predict.glm}
      \end{itemize}

    \item Many methods are inside ``namespaces'' and you can't see
      their code without some extra effort.
      \begin{itemize}
      \item namespace::method will often be useful

      \item Three colons needed for ``hidden methods''

        stats:::weights.glm
      \end{itemize}

    \item Many times I have doublechecked this detailed posting by
      Prof. Brian Ripley on this question:

      \url{http://tolstoy.newcastle.edu.au/R/help/05/09/12506.html}

    \end{itemize}

\end{frame}

% ______________________________

\section{Interrogate Models}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{The First Method Used is usually \texttt{summary()}}

\input{plots/t-sum20}

\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{Summary Object}

  Create a Summary Object
\input{plots/t-sum30}

 My deviance is

\input{plots/t-sum40}

\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{The coef Enigma}

  \begin{itemize}
  \item \texttt{coef()} is the same as \texttt{coefficients()}

  \item Note the Bizarre Truth:
    \begin{enumerate}
    \item that the ``coef'' function returns
something different when it is applied to a model object
\input{plots/t-sum45}

Than is returned from a summary object.

\input{plots/t-sum50}
\end{enumerate}
\end{itemize}
\end{frame}






\begin{frame}[containsverbatim]
  \frametitle{\texttt{anova()}}
  \begin{itemize}
    \item You can apply \texttt{anova()} to just one model
    \item That gives a ``stepwise'' series of comparisons (not very useful)

\input{plots/t-anova10}
\end{itemize}
\end{frame}

% _____________________________

\begin{frame}
  \frametitle{But anova Very Useful to Compare 2 Models}

  Here's the basic procedure:

  \begin{enumerate}
  \item Fit 1 big model, ``mod1''
  \item Exclude some variables to create a smaller model, ``mod2''
  \item Run \texttt{anova()} to compare:

      anova(mod1, mod2, test=''Chisq'')

   \item If resulting test statistic is far from 0, it means the big
     model really is better and you should keep those variables in there.
   \end{enumerate}

   Quick Reminder:

   \begin{itemize}
   \item In an OLS model, this is would be an F test for the
     hypothesis that the coefficients for omitted parameters are all
     equal to 0.
   \item In a model estimated by maximum likelihood, it is a
     likelihood ratio test with df= number of omitted parameters.
   \end{itemize}
 \end{frame}


% ______________________________

\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{But there's an anova ``Gotcha''}


%<<>>=
%anova(bush0, bush1, test="Chisq")
%@

\begin{Schunk}
  \begin{Soutput}
> anova(bush0, bush1, test="Chisq")
Error in anova.glmlist(c(list(object), dotargs),
  dispersion = dispersion,  :
  models were not all fitted to the same size of dataset
\end{Soutput}
\end{Schunk}

  What the Heck?
\end{frame}

% _____________________________

\begin{frame}
  \frametitle{\texttt{anova()} Gotcha, cont.}
  \begin{itemize}
    \item Explanation: Listwise Deletion of Missing Values causes this.

      Missings cause sample sizes to differ when variables change.

    \item One Solution: Fit both models on same data.
    \begin{enumerate}
      \item Fit the ``big model'' (one with most variables)


mod1 <- glm(y~ x1+ x2 + x3 + $\ldots$, data=dat, family=binomial)


      \item Fit the ``smaller Model'' with the data extracted from
        the fit of the previous model (mod1\$model) as the data frame

mod2 <- glm(y~  x3 + $\ldots$, data=mod1\$model, family=binomial)

     \item After that, anova() will work

     \end{enumerate}

     \item Hasten to add: more elaborate treatment of missingness is
       often called for.

   \end{itemize}
\end{frame}

\begin{frame}[containsverbatim]
  \frametitle{Example anova()}
  \begin{itemize}


  \item Here's the big model
\input{plots/t-glm30}

 \item Here's the small model
\input{plots/t-glm31}

 \end{itemize}
 \end{frame}


%___________________________________


\begin{frame}[containsverbatim]
  \frametitle{\texttt{anova()}: The Big Reveal!}
  \begin{itemize}

  \item anova:
\input{plots/t-glmanova10}

  \item Conclusion: the big model is not statistically significantly
    better than the small model
  \item Same as: Can't reject the null hypothesis that $\beta_j$=0 for
    all omitted parameters
 \end{itemize}
\end{frame}


\begin{frame}
  \frametitle{Interesting Use of anova}
  \begin{itemize}
    \item Consider the fit for ``polviews'' in bush3 (recall
      ``extremely liberal'' is the reference category, the intercept)
    \end{itemize}


\begin{tabular}{l|ccccccc}
\hline
label:& lib. & slt. lib. & mod. & sl. con. & con. & extr. con. \tabularnewline
\hline
mle($\hat{\beta}$): & 0.41 & 1.3  & 1.8* & 2.5* & 2.6* & 3.1*\tabularnewline
\hline
se: & 0.88 & 0.83 & 0.79 & 0.83 & 0.84 & 1.2\tabularnewline
\hline
\end{tabular}

* $p \leq 0.05$

\begin{itemize}
\item I wonder: are all ``conservatives'' the same? Do we really
  need separate parameter estimates for those respondents?
\end{itemize}

\end{frame}

%______________________________

\begin{frame}[containsverbatim]
  \frametitle{Use \texttt{anova()} To Test the Recoding}

  \begin{enumerate}
    \item Make a New Variable for the New Coding
\input{plots/t-glmanova20}
\end{enumerate}

\begin{itemize}
  \item Effect is to set slight and extreme conservatives into the
    conservative category
  \end{itemize}

\end{frame}

%_________________________________

\begin{frame}[containsverbatim]
  \frametitle{Better Check newpolv}


\input{plots/t-glmanova30}

\end{frame}

%_________________________________

\begin{frame}[containsverbatim]
  \frametitle{Neat anova thing, cont.}

  \begin{enumerate}
  \item Fit a new regression model, replacing polviews with newpolv


\input{plots/t-glmanova40}
 \item Use \texttt{anova()} to test:

\input{plots/t-glmanova50}
\end{enumerate}
\begin{itemize}
\item Apparently, all conservatives really are alike :)
\item A similar test for liberals is left to the reader!
\end{itemize}
\end{frame}


%_______________________________________________


\begin{frame}[containsverbatim]
  \frametitle{\texttt{drop1} Relieves Tedium}

  \begin{itemize}
  \item \texttt{drop1()} repeats the \texttt{anova()} procedure,
    removing each variable one-at-a-time.

\input{plots/t-029}

   \item Recall ``Chisq'' $\Leftrightarrow$ L.L.R test.
   \end{itemize}
 \end{frame}




\begin{frame}[containsverbatim]
  \frametitle{Termplot: Plotting The Linear Predictor}


\input{plots/t-termplot10}
\includegraphics[width=10cm]{plots/t-termplot10}
\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{Termplot: Some of the Magic is Lost on a Logistic Model}


\input{plots/t-termplot20}
\includegraphics[width=10cm]{plots/t-termplot20}
\end{frame}



\begin{frame}[containsverbatim]
  \frametitle{Termplot: But If You Had Some Continuous Data, Watch Out!}

\input{plots/t-termplot30}
\includegraphics[width=10cm]{plots/t-termplot30}
\end{frame}




\begin{frame}[containsverbatim]
  \frametitle{\texttt{termplot()} works because $\ldots$}

  \begin{itemize}
  \item termplot doesn't make calculations, it uses the
    ``\texttt{predict}'' method associated with a model object.
  \item \texttt{predict} is a generic method, it doesn't do any work either!
  \item Actual work gets done by methods for models,
    \texttt{predict.lm} or  \texttt{predict.glm}.
  \item You can leave out the ``terms'' option, termplot will
    cycle through all of the predictors in the model.
  \end{itemize}
\end{frame}

\begin{frame}[containsverbatim]
  \frametitle {Why Termplot is Not the End of the Story}
  \begin{itemize}
  \item Termplot draws $X\hat{\beta}$, the linear predictor.
  \item Maybe we want predicted probabilities instead.
  \item Maybe we want predictions for certain case types: \texttt{ termplot} allows the predict implementation to decide which
    values of the inputs will be used.
  \item A regression expert will quickly conclude that a really
    great graph may require direct use of the \texttt{predict}
    method for the model object.
  \end{itemize}
\end{frame}


% _____________________________________________

\begin{frame}
  \frametitle{\texttt{predict()} with newdata}

  \begin{itemize}
    \item If you run this:

      \texttt{predict(bush5)}

    R calculates $X\hat{\beta}$, a ``linear predictor'' value for each row in your dataframe

  \item See ``\texttt{?predict.glm}.''

  \item We ask for predicted probabilities like so

    \texttt{predict(bush5, type="response")}

    and you still get one prediction for each line in the data.
  \end{itemize}
\end{frame}



\begin{frame}
  \frametitle{Use predict to calculate with ``for example'' values}
  \begin{itemize}
  \item Create ``example'' dataframes and get probabilities for
    hypothetical cases.

    \texttt{ > mydf <- \# Pretend there are some commands \\ \#to
      create an example data frame}

  \item Run that new example data frame through the predict function
    \texttt{ > predict(bush5, newdata=mydf, type="response"}

   \end{itemize}
 \end{frame}





\begin{frame}[containsverbatim]
  \frametitle{Create the New Data Frame}

\footnotesize{
\input{plots/t-predict10}
}

\end{frame}

\begin{frame}[containsverbatim]
  \frametitle{Make Table of Predicted Probabilities}

\input{plots/t-predict20}

\input{plots/t-predict30}
\end{frame}

\begin{frame}
  \frametitle{Or Perhaps You Would Like A Figure?}


\includegraphics[width=10cm]{plots/t-pred90}
\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{How Could You Make That Figure?}

  \input{plots/t-pred90}
\end{frame}

%===================================================


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{Covariance of $\hat{\beta}$}
\input{plots/t-038}

These will match the ``SE'' column in the summary of bush1
\input{plots/t-039}
\end{frame}



\begin{frame}[containsverbatim]
  \frametitle{Heteroskedasticity-consistent Standard Errors?}

  Variants of the
  Huber-White ``heteroskedasticity-consistent'' (slang: robust)
  covarance matrix are available in ``car'' and ``sandwich''.

  \begin{itemize}

    \item  hccm() in car works for linear models only

    \item vcovHC in the ``sandwich'' package returns a matrix of
      estimates. One should certainly read ?vcovHC and the associated literature.

\input{plots/t-040}
\end{itemize}
\end{frame}


\begin{frame}[containsverbatim]
  \frametitle{The heteroskedasticity consistent standard errors of the $\hat{\beta}$  are:}

\input{plots/t-041}
\end{frame}



\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{Compare those:}

\begin{columns}
  \column{3cm}

The HC and ordinary standard errors are almost identical:
  \column{8cm}
\input{plots/t-042}
\includegraphics{plots/t-042}
\end{columns}

\end{frame}


\begin{frame}[containsverbatim]
\frametitle{Tons of Diagnostic Information}

  Run plot() on the model object for a quick view.

  Example: plot(myolsmod)




\end{frame}

\begin{frame}[plain]

\includegraphics[width=10cm]{plots/t-diag09}

\end{frame}


\begin{frame}[plain]
  \frametitle{Tough to read the glm plot, IMHO$\ldots$}

\includegraphics[width=10cm]{plots/t-diag10}

\end{frame}




\begin{frame}[containsverbatim,allowframebreaks]
   \frametitle{\texttt{influence()} Function Digs up the Diagnostics}

\input{plots/t-046}
\end{frame}

\begin{frame}[containsverbatim,allowframebreaks]
 \frametitle{\texttt{influence.measures()} A bigger collection of influence measures}

 From influence.measures, DFBETAS for each parameter, DFFITS, covariance ratios, Cook's distances and the diagonal elements of the hat matrix.


\input{plots/t-047}

     Can get component columns directly with ‘dfbetas’, ‘dffits’, ‘covratio’ and ‘cooks.distance’.
\end{frame}




\begin{frame}[containsverbatim,allowframebreaks]
 \frametitle{But if You Want dfbeta, Not dfbetas, Why Not Ask?}


\input{plots/t-048}

      I wondered what dfbetas does. You can see for yourself. Look at
      the code. Run:

\begin{Schunk}\begin{Soutput}
    >  stats:::dfbetas.lm
  \end{Soutput}
\end{Schunk}

\end{frame}



% > influencePlot(bush1)

% opens up an interactive plot--user left-clicks on
% the observations return their row number
% \end{frame}

% ===================================================
\section{Output}

\begin{frame}[containsverbatim]
  \frametitle{You Will Want to Use \LaTeX{}     After You See This}

  \begin{itemize}
    \item How do you get regression tables out of your project?
    \item Do you go through error-prone copying, pasting, typing,
      tabling, etc?
    \item What if your software could produce a finished
      publishable table?
    \end{itemize}
  \end{frame}

\input{plots/t-049}

\begin{frame}[containsverbatim]
  \frametitle{}
  \begin{itemize}
    \item Years ago, I wrote a function ``outreg''





    \item This command:

\input{plots/t-output10}
   \item Produces the output on the next slide
  \end{itemize}
\end{frame}

\begin{frame}[plain,containsverbatim]


\input{plots/t-output40}
\end{frame}




\begin{frame}[containsverbatim]
  \frametitle{Polish that up}

  \begin{itemize}
    \item you can beautify the variable labels, either by specifying
      them in the outreg command or editing the table output.
    \item outreg produces Latex that looks like this in the R session output.

\input{plots/t-output41}

\end{itemize}
\end{frame}


\begin{frame}
  \frametitle{Push Several Models Into One Wide Table}

\input{plots/t-output50}

  Sorry, I had to split this manually across 3 slides :(

\end{frame}


\begin{frame}[plain,allowframebreaks]


\footnotesize{
\input{plots/t-output51}
}
\end{frame}

%__________________________________


\begin{frame}
  \frametitle {R Packages for Producing Regression Output}

  \begin{itemize}
  \item memisc: works well, further from final form than outreg

  \item xtable: incomplete output, but latex or HTML works

  \item apsrtable: very similar to outreg

  \item Hmisc ``latex'' function

  \end{itemize}
\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]

\input{plots/t-output70}


\end{frame}

\begin{frame}[containsverbatim]
  \frametitle{If you Can't Shake the MS Word ``Habit''}

  The best you can do is HTML output, which you can copy paste-special
  into a document.

\input{plots/t-output80}
\end{frame}

\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{memisc mtable is nice for comparing models (except for
    verbosity of parameter labels)}

\input{plots/t-059}
\end{frame}


\begin{frame}[containsverbatim,allowframebreaks]
  \frametitle{memisc toLatex}

\footnotesize{
\input{plots/t-output84}
}
\end{frame}

\begin{frame}
  \frametitle{Relable Levels to Truncate Output}

  \begin{itemize}
    \item We could have to edit that output A LOT


    \item Hack the Labels down
\input{plots/t-061}

    \item Re-run the models

\input{plots/t-062}
\end{itemize}
\end{frame}

%___________________________

\begin{frame}[containsverbatim,allowframebreaks,plain]

\footnotesize{
\input{plots/t-output85}
}



\end{frame}


%===================================================
\end{document}
