informality, the 2010 edition

August 24, 2010
By

(This article was first published on simon jackman's blog » R, and kindly contributed to R-bloggers)

For the last two cycles I’ve done some simple regression analysis of the informal vote.  I saw Possum have his go at it, using a specification that is virtually the same as what I’ve run in the past (2007, 2004).

The 2010 edition follows.  As usual, electorate-level informality in House of Reps voting increases with (a) the number of candidates on the ballot; (b) the percentage of the electorate residing in non-English-speaking households (NESH); (c) does the state have optional preferential voting in their state legislative elections (NSW & QLD); but decreases with (d) percentage of the electorate with tertiary qualifications.

The basic linear spec gets you:

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  4.196338   0.304983  13.759  < 2e-16 ***
OPTRUE       1.618110   0.146803  11.022  < 2e-16 ***
neshp        0.104462   0.005328  19.606  < 2e-16 ***
Nominations  0.126415   0.045005   2.809  0.00566 **
unip        -0.139205   0.010577 -13.162  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.8898 on 145 degrees of freedom
Multiple R-squared: 0.7977,	Adjusted R-squared: 0.7921

Not too shabby for 4 linear, additive predictors.

You can do a little better with semi-parametric terms (thin-plate smoothing splines, via the mgcv package in R) in the NESH and tertiary predictors, and an interaction with OP/non-OP:

Formula:
InformalPercent ~ OPf + s(neshp, by = OPf) + s(unip, by = OPf) +
    Nominations

Parametric coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  4.11470    0.19677   20.91  < 2e-16 ***
OPfTRUE      1.62839    0.11146   14.61  < 2e-16 ***
Nominations  0.11768    0.03362    3.50 0.000636 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Approximate significance of smooth terms:
                    edf Ref.df     F  p-value
s(neshp):OPfFALSE 2.554  3.200 23.78 7.17e-13 ***
s(neshp):OPfTRUE  7.515  8.424 95.63  < 2e-16 ***
s(unip):OPfFALSE  3.057  3.769 26.34 1.81e-15 ***
s(unip):OPfTRUE   2.558  3.170 50.91  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

R-sq.(adj) =  0.895   Deviance explained = 90.8%
GCV score = 0.45629  Scale est. = 0.39945   n = 150

Update: by request, the four smooth terms from the GAM.
PDF

To leave a comment for the author, please follow the link and comment on his blog: simon jackman's blog » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , ,

Comments are closed.