[R] comparing strength of association instead of strength of evidence?

[Weiwei Shi]

Dear all:
I still need some further help since I think the question itself might
be very interesting (i hope so:) :
the question is on chisq.test, my concern is which criteria should be
used here to evaluate the independence. The reason i use this old
subject of the email is, b/c I think the problem here is about how to
look at p.value, which evaluate the strength of evidence instead of
association. If i am wrong, please correct me.

the result looks like this:
   index   word.comb     id in.class0 in.class1      p.value odds.ratio
1      1  TOTAL|LAID 54|241         2         4 0.0004997501 0.00736433
2      2 THEFT|RECOV  52|53     40751       146 0.0004997501 4.17127643
3      3  BOLL|ACCID  10|21     36825      1202 0.0004997501 0.44178546
4      4  LAB|VANDAL   8|55     24192       429 0.0004997501 0.82876099
5      5 VANDAL|CAUS  55|59       801        64 0.0004997501 0.18405918
6      6    AI|TOTAL   9|54      1949        45 0.0034982509 0.63766766
7      7    AI|RECOV   9|53      2385        61 0.0004997501 0.57547012
8      8 THEFT|TOTAL  52|54     33651       110 0.0004997501 4.56174408

the target is to look for best subset of word.comb to differentiate
between class0 and class1. p.value is obtained via
p.chisq.sim[i] <- as.double(chisq.test(tab, sim=TRUE, B=myB)$p.value)
and B=20000 (I increased B and it won't help. the margin here is
class0=2162792
class1=31859
)

So, in conclusion, which one I should use first, odds.ratio or p.value
to find the best subset.

I read some on feature selection in text categorization (A comparative
study on feature selection in text categorization might be a good
ref.). Anyone here has other suggestions?

thanks,

weiwei


On 6/24/05, Gabor Grothendieck <ggrothendieck at gmail.com> wrote:
> On 6/24/05, Kjetil Brinchmann Halvorsen <kjetil at acelerate.com> wrote:
> > Weiwei Shi wrote:
> >
> > >Hi,
> > >I asked this question before, which was hidden in a bunch of
> > >questions. I repharse it here and hope I can get some help this time:
> > >
> > >I have 2 contingency tables which have the same group variable Y. I
> > >want to compare the strength of association between X1/Y and X2/Y. I
> > >am not sure if comparing p-values IS the way  even though the
> > >probability of seeing such "weird" observation under H0 defines
> > >p-value and it might relate to the strength of association somehow.
> > >But I read the following statement from Alan Agresti's "An
> > >Introduction to Categorical Data Analysis" :
> > >"Chi-squared tests simply indicate the degree of EVIDENCE for an
> > >association....It is sensible to decompose chi-squared into
> > >components, study residuals, and estimate parameters such as odds
> > >ratios that describe the STRENGTH OF ASSOCIATION".
> > >
> > >
> > >
> > Here are some things you can do:
> >
> >  > tab1<-array(c(11266, 125, 2151526, 31734), dim=c(2,2))
> >
> >  > tab2<-array(c(43571, 52, 2119221, 31807), dim=c(2,2))
> >  > library(epitools) # on CRAN
> >  > ?odds.ratio
> > Help for 'odds.ratio' is shown in the browser
> >  > library(help=epitools) # on CRAN
> >  > tab1
> >      [,1]    [,2]
> > [1,] 11266 2151526
> > [2,]   125   31734
> >  > odds.ratio(11266, 125, 2151526, 31734)
> > Error in fisher.test(tab) : FEXACT error 40.
> > Out of workspace.                 # so this are evidently for tables
> > with smaller counts
> >  > library(vcd) # on CRAN
> >
> >  > ?oddsratio
> > Help for 'oddsratio' is shown in the browser
> >  > oddsratio( tab1)  # really is logodds ratio
> > [1] 0.2807548
> >  > plot(oddsratio( tab1) )
> >  > library(help=vcd) # on CRAN  Read this for many nice functions.
> >  > fourfoldplot(tab1)
> >  > mosaicplot(tab1)     # not really usefull for this table
> >
> > Also has a look at function Crosstable in package gmodels.
> >
> > To decompose the chisqure you can program yourselves:
> >
> > decomp.chi <- function(tab) {
> >        rows <-  rowSums(tab)
> >        cols <-   colSums(tab)
> >        N <-   sum(rows)
> >         E <- rows %o% cols / N
> >         contrib <- (tab-E)^2/E
> >         contrib }
> >
> >
> >  > decomp.chi(tab1)
> >          [,1]         [,2]
> > [1,] 0.1451026 0.0007570624
> > [2,] 9.8504915 0.0513942218
> >  >
> >
> > So you can easily see what cell contributes most to the overall chisquared.
> >
> > Kjetil
> >
> >
> >
> >
> >
> > >Can I do this "decomposition" in R for the following example including
> > >2 contingency tables?
> > >
> > >
> > >
> > >>tab1<-array(c(11266, 125, 2151526, 31734), dim=c(2,2))
> > >>tab1
> > >>
> > >>
> > >      [,1]    [,2]
> > >[1,] 11266 2151526
> > >[2,]   125   31734
> > >
> > >
> > >
> > >>tab2<-array(c(43571, 52, 2119221, 31807), dim=c(2,2))
> > >>tab2
> > >>
> > >>
> > >      [,1]    [,2]
> > >[1,] 43571 2119221
> > >[2,]    52   31807
> > >
> 
> 
> Here are a few more ways of doing this using chisq.test,
> glm and assocplot:
> 
> > ## chisq.test ###
> 
> > tab1.chisq <- chisq.test(tab1)
> 
> > # decomposition of chisq
> > resid(tab1.chisq)^2
>           [,1]         [,2]
> [1,] 0.1451026 0.0007570624
> [2,] 9.8504915 0.0513942218
> 
> > # same
> > with(tab1.chisq, (observed - expected)^2/expected)
>           [,1]         [,2]
> [1,] 0.1451026 0.0007570624
> [2,] 9.8504915 0.0513942218
> 
> 
> > # Pearson residuals
> > resid(tab1.chisq)
>            [,1]        [,2]
> [1,]  0.3809234 -0.02751477
> [2,] -3.1385493  0.22670294
> 
> > # same
> > with(tab1.chisq, (observed - expected)/sqrt(expected))
>            [,1]        [,2]
> [1,]  0.3809234 -0.02751477
> [2,] -3.1385493  0.22670294
> 
> 
> > ### glm ###
> > # Pearson residuals via glm
> 
> > tab1.df <- data.frame(count = c(tab1), A = gl(2,2), B = gl(2,1,4))
> > tab1.glm <- glm(count ~ ., tab1.df, family = poisson())
> > resid(tab1.glm, type = "pearson")
>           1           2           3           4
>  0.38092339 -3.13854927 -0.02751477  0.22670294
> > plot(tab1.glm)
> 
> > ### assocplot ###
> > # displaying Pearson residuals via an assocplot
> > assocplot(t(tab1))
> 


-- 
Weiwei Shi, Ph.D

"Did you always know?"
"No, I did not. But I believed..."
---Matrix III