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\section*{Second Mini-Project, 36-401, Spring 1998}

\subsection*{Description of the problem}

What factors affect childrens' perceptions of themselves, their life
goals, etc?  Chase and Dummer (Chase, M. A., and Dummer, G. M. (1992),
{\em The Role of Sports as a Social Determinant for Children},
Research Quarterly for Exercise and Sport, 63, 418--424) surveyed
school children in Michigan to find out. 


The subjects consist of 478 students in grades 4--6 from three school
districts in Ingham and Clinton Counties, Michigan.  Chase and Dummer
stratified their sample, selecting students from urban, suburban, and
rural school districts with approximately 1/3 of their sample coming
from each district. Students indicated whether good grades, athletic
ability, or popularity was most important to them.  They also ranked
four factors: grades, sports, looks, and money, in order of their
importance for popularity. The questionnaire also asked for gender,
grade level, and other demographic information.

An extract of the data suitable for log-linear modeling is contained
in the data file {\tt catkids.dat} in \www{\tt mp2}.  The data looks
like this
\begin{verbatim}
   Gender Grade  Race Urban  Goals Resp 
 1    boy     4 Other Rural Grades    0
 2   girl     4 Other Rural Grades    0
 3    boy     5 Other Rural Grades    0
 4   girl     5 Other Rural Grades    1
 5    boy     6 Other Rural Grades    0
 6   girl     6 Other Rural Grades    2
\end{verbatim}
where the variable names are:
\begin{itemize}
\item {\tt Gender} is the gender of the child (boy/girl)
\item {\tt Grade} is the child's grade in school (4/5/6)
\item {\tt Race} is the child's race (White/Other)
\item {\tt Urban} is the location of the school district (Urban,
Suburban or Rural)
\item {\tt Goals} are the child's goals (Grades/Popular/Sports)

and

\item{\tt Resp} is the number of children with each combination of the
other factors.
\end{itemize}

\subsection*{Your mission}

Your mission is to explore and analyze these data, and write up a
report of your conclusions.  The main questions to keep in mind are:
\begin{itemize}
\item Which factors listed above are related to each other?  What are
the conditional independence relationships among the variables?
\item Which factors seem to influence the ``Goals'' of the child?
\item How do childrens' goals change depending on gender? race? urban
setting? grade in school?
\item Is there a causal story to tell about these variables?
\end{itemize}
You may use either (or both) of log-linear modeling and logistic
regression, as well as any appropriate EDA, residual diagnostics, etc.
For the log-linear modeling, please:
\begin{itemize}
\item Since the authors tried to stratify their sampling on ``Urban'',
assume that the totals for Urban are fixed.
\item In your final models please try to obey both
\begin{itemize}
\item {\em the hierarchy principle} (including an
interaction forces you to include all lower-order interactions and
main effects for the same variable); and
\item {\em the graphical principle} (if every ($n-1)$-way interaction
among $n$ variables is in the model, tnen also put the $n$-way
interaction in the model)
\end{itemize}
\end{itemize}
If you also decide to do some logistic regression, 
\begin{itemize}
\item Note that logistic regression will require a reformulation of the data
(see problems 2 and 3 on the third set of finger exercises for an
example of such a reformulation).
\item Try to obey the hierarchy principle in your final models
\end{itemize}

\subsection*{On Writeups}

A good generic outline for project reports is:
\begin{enumerate}\parsep=0pt\parskip=0pt\itemsep=0pt\setcounter{enumi}{-1}
\item Executive summary (state background, problem, and conclusions in
one page or less);
\item Description of problem, problem background, and data;
\item Summary of analyses performed (what, why, how, results);
\item Conclusions;
\item Technical Appendices;
\item Bibliography and Credits
\end{enumerate}
Parts 1--3 should have as little technical material as you can
possibly get away with: a few well-chosen graphs, the names of the
techniques you applied and what parts of the data were used, and
perhaps one or two parameter estimates or $p$-values is the most you
should think about.  Part 4 should contain the ``story'' of your
technical analyses.  However, it should be possible to understand what
you've done from parts 1--3, without looking at part 4 at all.

You are welcome to discuss this problem with each other, but I would
like a list of people you discussed this with (in and out of class),
as well as a list of any outside sources you consulted (books, Web
pages, etc.) in Part 5 of your report.

\subsection*{Timeline, Deadines}

I would like this to be a ``miniproject'', not a full-blown project.
So I would like to discuss with you your progress after a week or so,
probably in class, and then I would like you to hand in your final
reports a week later.  So the deadlines are:
\begin{itemize}\parsep=0pt\parskip=0pt\itemsep=0pt
\item {\em Thu Mar 19.} I will take questions in class on the data,
the project, etc.
\item {\em Tue Mar 31.} Bring a draft of Part 4 of your report to
class for me to check, in class.
\item {\em Tue Apr 6.} Bring your final reports to class.
\end{itemize}


\subsection*{Appendix: the full data set}

The file {\tt kids.dat} in \www{\tt mp2} is a more complete version of
the data set.  It looks like this

\begin{verbatim}
   Gender Grade Age  Race Urban.Rural School   Goals Grades Sports Looks Money 
 1    boy     5  11 White       Rural    Elm  Sports      1      2     4     3
 2    boy     5  10 White       Rural    Elm Popular      2      1     4     3
 3   girl     5  11 White       Rural    Elm Popular      4      3     1     2
 4   girl     5  11 White       Rural    Elm Popular      2      3     4     1
\end{verbatim}
The variable names are
\begin{enumerate}\parsep=0pt\parskip=0pt\itemsep=0pt
    \item Gender: Boy or girl
    \item Grade: 4, 5 or 6
    \item Age: Age in years 
    \item Race: White, Other 
    \item Urban/Rural: Rural, Suburban, or Urban school district 
    \item School: Brentwood Elementary, Brentwood Middle, Ridge, Sand,
      Eureka, Brown, Main, Portage, Westdale Middle
    \item Goals: Student's choice in the personal goals question where
      options were 1 = Make Good Grades, 2 = Be Popular, 3 = Be Good
      in Sports
    \item Grades: Rank of "make good grades" (1=most important for
      popularity, 4=least important)
    \item Sports: Rank of "being good at sports" (1=most important for
      popularity, 4=least important)
    \item Looks: Rank of "being handsome or pretty" (1=most important
      for popularity, 4=least important)
    \item Money: Rank of "having lots of money" (1=most important for
      popularity, 4=least important)
\end{enumerate}

You may find it useful to go back to this data set, and perhaps
produce a different extract of the data for your particular analyses.
You may also find that there are interesting questions using the full
data set which simply can't be answered with the more compact data set
{\tt catkids.dat}.  (For example we could build a logistic regression
model for the outcome ``Grades ranked first as a determinant of
popularity''; this can be done with {\tt kids.dat} but not with
{\tt catkids.dat}).  

Please feel free to work with either data set {\tt catkids.dat} and.or
{\tt kids.dat} depending on where your investigations lead you.


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