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\begin{center}
\LARGE
Psychology 594 \ - \ Fall 2013 \ - \ Instructions for Final\\
\large
Larry Hubert \& Ehsan Bokhari \& Justin Kerm
\end{center}

\small

Your final is expected to be typed. You may turn in a hardcopy version or submit an electronic version via email to \href{mailto:kern4@illinois.edu}{kern4@illinois.edu}.  If you email it, write in the subject line ``Multivariate Take-home Final'' Please do not include any \matlab\ code or output. The instructions below indicate what should be reported in your final for each question.
\begin{enumerate}
	  \item Start by describing the data you selected from Michael Lee's website. Also, indicate
any pre-processing steps that were needed. For example, did you have to convert a
similarity matrix into a dissimilarity matrix? If so, describe the process that was used. NOTE: You may use any dataset except the abstract numbers data (\ttt{abstractnumbers.mat}) and the adolescent drug use data (\ttt{druguse.mat}).
	
	  \begin{enumerate}
	  	
	  	\item Describe how you used the functions (e.g., ``First, I input the abstract numbers dissimilarity
matrix into the \ttt{squareform.m} function to create a vector containing the unique
entries in the dissimilarity matrix. Next, I input this vector of dissimilarities into
the $\dots$ ''). Also, include the figure that is produced by the \ttt{dendrogram.m} function.
		
	  	\item For all of these questions, describe (in your own words) what you are inputting
into each of the functions and what outputs you get from each function. I want to
ensure that you understand what each function is doing. See the below instructions for the additional output that you should report from each function.
		
		  \begin{enumerate}
		
		  	\item \ttt{order.m}: \\ Report the obtained optimal ordering of your objects. \\
		  	
		  				\ttt{ultrafit.m}: \\ Report the variance-accounted-for by the fit ultrametric matrix. \\
		  				
		  				\ttt{ultrafnd.m}: \\ Report the number of random starting permutations that you used and the variance-accounted-for by the best ultrametric matrix.
		  				
				\item \ttt{ultrafnd\_confit.m}: \\ Report the variance-accounted-for by the ultrametric matrix fit to the dissimilarity matrix, the variance-accounted-for by the anti-Robinson matrix fit
to the dissimilarity matrix, and the variance-accounted-for by the ultrametric
matrix fit to the anti-Robinson matrix. \\

							\ttt{ultrafnd\_confnd.m}: \\ Report the same things that you reported for the previous problem. Also,
report the obtained optimal ordering of the objects. \\
				
				\item \ttt{partitionfnd\_averages.m} followed by \ttt{partitionfit.m}: \\ Report the variance-accounted-for by the fit proximity matrix. Also, describe
the three memberships (partitions) that were most influential in forming the
fit proximity matrix (i.e., describe the three input memberships that resulted
in the largest obtained weights).\\

						\ttt{partitionfnd\_diameters.m} followed by \ttt{partitionfit.m}: \\ Report the same things that you reported for the previous problem. \\
						
				\item  \ttt{cent\_ultrafnd confit.m}: \\
Report the variance-accounted-for by the fit proximity matrix. \\

			\ttt{cent\_ultrafnd\_confnd.m}: \\
Report the variance-accounted-for by the fit proximity matrix and the obtained optimal ordering of the objects. \\

	\item \ttt{atreefit.m}: \\
Report the variance-accounted-for by the fit proximity matrix.  \\

		\ttt{atreefnd.m}: \\
Report the number of random starting permutations that you used and the
variance-accounted-for by the best proximity matrix. \\

\ttt{atreedec.m}: \\
There is nothing additional to report here. \\

\ttt{ultraorder.m}: \\
Report the obtained optimal ordering of your objects according to the additive
tree's ultrametric component. \\

\item \ttt{consec\_subsetfit.m}: \\
Report the variance-accounted-for by the fit proximity matrix. Also, describe
the three memberships (partitions) that were most in
influential in forming the fit proximity matrix. \\

\ttt{consec\_subsetfit alter.m}: \\
Report the same things that you reported for the previous problem.
		
	  \end{enumerate}  \end{enumerate}
\item NO SCRIPT FILE. Instead, include the five figures created in the script file, along with a description of each.

\item Report which model (continuous vs.\ categorical) you choose and why. Also, interpret
the chosen model to say a few things about the structure of the Supreme Court.


\end{enumerate}

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