[R] comparing matched proportions using glm
Corry Gellatly
corry.gellatly at newcastle.ac.uk
Thu Oct 4 21:35:47 CEST 2007
Dear R users,
Is it possible to use a generalized linear model to do a binomial
comparison of one list of proportions with a matched list of proportions
to test for a difference?
So, for example:
list 1 list 2
a1 | b1 a2 | b2
3 | 4 7 | 9
6 | 7 5 | 1
9 | 1 3 | 1
I want to compare list 1 with list 2 and the samples are matched.
Obviously, I could add the columns and do a binomial test, i.e.
prop.test(c(18,15),c(30,26)), however, I have a large dataset so this
would reduce the power of my analysis. I could compare the ratios, i.e.
a1/(a1+b1) compared to a2/(a2+b2) for the samples in each list, however,
this does not account for the difference in sample sizes between samples
in each list.
I have tried a glm where I bind a2 and b2 as the y variable, i.e.
y<-cbind(a2,b2) and also bind a1 and b1 as the x variable, i.e.
y<-cbind(a1,b1) and run <-glm(y~x,binomial)
I get this type of output:
Call:
glm(formula = y ~ x, family = binomial)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.20426 -0.72686 -0.01822 0.68320 4.05035
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.178369 0.186421 0.957 0.339
xa1 0.008109 0.017430 0.465 0.642
xb1 -0.026666 0.018153 -1.469 0.142
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 565.14 on 467 degrees of freedom
Residual deviance: 559.69 on 465 degrees of freedom
AIC: 1883.3
Number of Fisher Scoring iterations: 3
Is this output meaningful? It seems that y is not compared directly with
x, but rather compared with a1 and b1, which is not intended?
I wonder if this is a suitable approach to the problem? I'll be very
grateful for any advice or suggestions.
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