Hi Claus,
welcome to the wonderful world of collinearity (or multicollinearity, as
some call it)! You have a near linear relationship between some of your
predictors, which can (and in your case does) lead to extreme parameter
estimates, which in some cases almost cancel out (a coefficient of +/-40
on a categorical variable in logistic regression is a lot, and the
intercept and two of the roman parameter estimates almost cancel out)
but which are rather unstable (hence your high p-values).
Belsley, Kuh and Welsch did some work on condition indices and variance
decomposition proportions, and variance inflation factors are quite
popular for diagnosing multicollinearity - google these terms for a bit,
and enlightenment will surely follow.
What can you do? You should definitely think long and hard about your
data. Should you be doing separate regressions for some factor levels?
Should you drop a factor from the analysis? Should you do a categorical
analogue of Principal Components Analysis on your data before the
regression? I personally have never done this, but correspondence
analysis has been recommended as a "discrete alternative" to PCA on this
list, see a couple of books by M. J. Greenacre.
Best of luck!
Stephan
claus orourke schrieb:
Dear list,
I want to perform a logistic regression analysis with multiple
categorical predictors (i.e., a logit) on some data where there is a
very definite relationship between one predicator and the
response/independent variable. The problem I have is that in such a
case the p value goes very high (while I as a naive newbie would
expect it to crash towards 0).
I'll illustrate my problem with some toy data. Say I have the
following data as an input frame:
roman animal colour
1 alpha dog black
2 beta cat white
3 alpha dog black
4 alpha cat black
5 beta dog white
6 alpha cat black
7 gamma dog white
8 alpha cat black
9 gamma dog white
10 beta cat white
11 alpha dog black
12 alpha cat black
13 gamma dog white
14 alpha cat black
15 beta dog white
16 beta cat black
17 alpha cat black
18 beta dog white
In this toy data you can see that roman:alpha and roman:beta are
pretty good predictors of colour
Let's say I perform logistic analysis directly on the raw data with
colour as a response variable:
options(contrasts=c("contr.treatment","contr.poly"))
anal1 <- glm(data$colour~data$roman+data$animal,family=binomial)
then I find that my P values for each individual level coefficient approach 1:
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -41.65 19609.49 -0.002 0.998
data$romanbeta 42.35 19609.49 0.002 0.998
data$romangamma 43.74 31089.48 0.001 0.999
data$animaldog 20.48 13866.00 0.001 0.999
while I expect the p value for roman:beta to be quite low because it
is a good predictor of colour:white
On the other hand, if I then run an anova with a Chi-sq test on the
result model, I find as I would expect that 'roman' is a good
predictor of colour.
anova(anal1,test="Chisq")
Analysis of Deviance Table
Model: binomial, link: logit
Response: data$colour
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL 17 24.7306
data$roman 2 19.3239 15 5.4067 6.366e-05 ***
data$animal 1 1.5876 14 3.8191 0.2077
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Can anyone please explain why my p value is so high for the individual levels?
Sorry for what is likely a stupid question.
Claus
p.s., when I run logistic analysis on data that is more 'randomised'
everything comes out as I expect.
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