The data for this homework first appear in Gentzkow and Shapiro $(2010)$ and summarize the first year of the $109$th Congressional Record $(2005)$ containing all speech in that year for members of the US house and senate$.$ It is stored in the textir package in R in two separate datasets. Use the following $2$ lines of code to load the data.

library$($textir$)$

data$($congress$109)$

The text is already tokenized into bigrams $($two$-$word phrases$)$ after stop$-$word removal and stemming $($using a Porter stemmer$).$ The matrix congress$109$Counts contains the number of times each phrase in a list of $1000$ common bigram and trigrams was used in the $109$th Congress by each of the $529$ members of the House and Senate.

$>$ congress$109$Counts$[$c$("$Barack Obama", "John Boehner"$),995$:$998]$

$2\backslash$times $4$ sparse Matrix of class "dgCMatrix"

stem.cel natural.ga hurricane.katrina trade.agreement

Barack Obama $.1207$

John Boehner $..14.$

The data also contain information about each member of Congress.

$>$ congress$109$Ideology$[1$:$4,]$

name party state chamber repshare cs$1$ cs$2$

Chris Cannon Chris Cannon R UT H $0\mathrm{.}79006210\mathrm{.}5340\mathrm{.}124$

Michael Conaway Michael Conaway R TX H $0\mathrm{.}78360280\mathrm{.}4840\mathrm{.}051$

Spencer Bachus Spencer Bachus R AL H $0\mathrm{.}78129330\mathrm{.}3690\mathrm{.}013$

Mac Thornberry Mac Thornberry R TX H $0\mathrm{.}77765200\mathrm{.}4930\mathrm{.}002$

We will be considering the variable repshare which is the proportion of the two party vote by the members$$ constituents $($districts for members of the house, state for senators$)$ that was captured by the republican candidate $($GW Bush$)$ in the $2004$ presidential election.

Use the following line of code to create a matrix with an indicator for whether each bigram was used or not.

x $<-$ congress$109$Counts$>0$

Then, set the seed to $20,$ load the text$2$vec library, and fit a $10$ topic LDA model.