R help - Mar 2009 - Interaction term not significant when using glm???

Dear all,

I have a dataset where the interaction is more than obvious, but I was asked
to give a p-value, so I ran a logistic regression using glm. Very funny, in
the outcome the interaction term is NOT significant, although that's
completely counterintuitive. There are 3 variables : spot (binary response),
constr (gene construct) and vernalized (growth conditions). Only for the FLC
construct after vernalization, the chance on spots should be lower. So in
the model one would suspect the interaction term to be significant.

Yet, only the two main terms are significant here. Can it be my data is too
sparse to use these models? Am I using the wrong method?

# data generation
testdata <-
matrix(c(rep(0:1,times=4),rep(c("FLC","FLC","free","free"),times=2),
  rep(c("no","yes"),each =4),3,42,1,44,27,20,3,42),ncol=4)
colnames(testdata)
<-c("spot","constr","vernalized","Freq")
testdata <- as.data.frame(testdata)

# model
T0fit <- glm(spot~constr*vernalized, weights=Freq, data=testdata,
family="binomial")
anova(T0fit)

Kind regards
Joris

	[[alternative HTML version deleted]]

I think the interaction is not so strong anymore if you do what glm
does: use a logit transformation.
testdata <-
matrix(c(rep(0:1,times=4),rep(c("FLC","FLC","free","free"),times=2),
  rep(c("no","yes"),each =4),3,42,1,44,27,20,3,42),ncol=4)
colnames(testdata)
<-c("spot","constr","vernalized","Freq")
testdata <- as.data.frame(testdata)
testdata$Freq <- as.numeric(as.character(testdata$Freq))
testdata$spot <- as.numeric(as.character(testdata$spot))

T2 <-
reshape(testdata,v.names='Freq',timevar='spot',idvar=names(testdata)[c(2,3)],direction='wide')
T2$Prop <- T2$Freq.0/(T2$Freq.0+T2$Freq.1)
plot(log(T2$Prop/(1-T2$Prop)),x=interaction(T2$constr,T2$vernalized))

Kees

joris meys wrote:
> Dear all,
>
> I have a dataset where the interaction is more than obvious, but I was
asked
> to give a p-value, so I ran a logistic regression using glm. Very funny, in
> the outcome the interaction term is NOT significant, although that's
> completely counterintuitive. There are 3 variables : spot (binary
response),
> constr (gene construct) and vernalized (growth conditions). Only for the
FLC
> construct after vernalization, the chance on spots should be lower. So in
> the model one would suspect the interaction term to be significant.
>
> Yet, only the two main terms are significant here. Can it be my data is too
> sparse to use these models? Am I using the wrong method?
>
> # data generation
> testdata <-
>
matrix(c(rep(0:1,times=4),rep(c("FLC","FLC","free","free"),times=2),
>   rep(c("no","yes"),each
=4),3,42,1,44,27,20,3,42),ncol=4)
> colnames(testdata)
<-c("spot","constr","vernalized","Freq")
> testdata <- as.data.frame(testdata)
>
> # model
> T0fit <- glm(spot~constr*vernalized, weights=Freq, data=testdata,
> family="binomial")
> anova(T0fit)
>
> Kind regards
> Joris
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

On Fri, 6 Mar 2009, joris meys wrote:
> Dear all,
>
> I have a dataset where the interaction is more than obvious, but I was
asked
> to give a p-value, so I ran a logistic regression using glm. Very funny, in
> the outcome the interaction term is NOT significant, although that's
> completely counterintuitive. There are 3 variables : spot (binary
response),
> constr (gene construct) and vernalized (growth conditions). Only for the
FLC
> construct after vernalization, the chance on spots should be lower. So in
> the model one would suspect the interaction term to be significant.
>
> Yet, only the two main terms are significant here. Can it be my data is too
> sparse to use these models? Am I using the wrong method?
The point estimate for the interaction term is large: 1.79, or an odds ratio of
nearly 6.

The data are very strongly overdispersed (variance is 45 times larger than it
should be), so they don't fit a binomial model well. If you used a
quasibinomial model you would get no statistical significance for any of the
terms.

I would say the problem is partly combination of the overdispersion and the
sample size.  It doesn't help that the situation appears to be a difference
between the FLC:yes cell and the other three cells, a difference that is spread
out over the three parameters.

      -thomas

> # data generation
> testdata <-
>
matrix(c(rep(0:1,times=4),rep(c("FLC","FLC","free","free"),times=2),
>  rep(c("no","yes"),each
=4),3,42,1,44,27,20,3,42),ncol=4)
> colnames(testdata)
<-c("spot","constr","vernalized","Freq")
> testdata <- as.data.frame(testdata)
>
> # model
> T0fit <- glm(spot~constr*vernalized, weights=Freq, data=testdata,
> family="binomial")
> anova(T0fit)
>
> Kind regards
> Joris
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle