[R] Profile confidence intervals and LR chi-square test
Inman, Brant A. M.D.
Inman.Brant at mayo.edu
Tue Nov 14 00:41:08 CET 2006
System: R 2.3.1 on Windows XP machine.
I am building a logistic regression model for a sample of 100 cases in
dataframe "d", in which there are 3 binary covariates: x1, x2 and x3.
----------------
> summary(d)
y x1 x2 x3
0:54 0:50 0:64 0:78
1:46 1:50 1:36 1:22
> fit <- glm(y ~ x1 + x2 + x3, data=d, family=binomial(link=logit))
> summary(fit)
Call:
glm(formula = y ~ x1 + x2 + x3, family = binomial(link = logit),
data = d)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6503 -1.0220 -0.7284 0.9965 1.7069
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.3772 0.3721 -1.014 0.3107
x11 -0.8144 0.4422 -1.842 0.0655 .
x21 0.9226 0.4609 2.002 0.0453 *
x31 1.3347 0.5576 2.394 0.0167 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 137.99 on 99 degrees of freedom
Residual deviance: 120.65 on 96 degrees of freedom
AIC: 128.65
Number of Fisher Scoring iterations: 4
> exp(fit$coef)
(Intercept) x11 x21 x31
0.6858006 0.4429233 2.5157321 3.7989873
---------------
After reading the appropriate sections in MASS4 (7.2 and 8.4 in
particular), I decided to estimate the 95% confidence intervals for the
odds ratios using the profile method implemented in the "confint"
function. I then used the "anova" function to perform the deviance
chi-square tests for each covariate.
---------------
> ci <- confint(fit); exp(ci)
Waiting for profiling to be done...
2.5 % 97.5 %
(Intercept) 0.3246680 1.413684
x11 0.1834819 1.048154
x21 1.0256096 6.314473
x31 1.3221533 12.129210
> anova(fit, test='Chisq')
Analysis of Deviance Table
Model: binomial, link: logit
Response: y
Terms added sequentially (first to last)
Df Deviance Resid. Df Resid. Dev P(>|Chi|)
NULL 99 137.989
x1 1 5.856 98 132.133 0.016
x2 1 5.271 97 126.862 0.022
x3 1 6.212 96 120.650 0.013
----------------
My question relates to the interpretation of the significance of
variable x1. The OR for x1 is 0.443 and its profile confidence interval
is 0.183-1.048. If a type I error rate of 5% is assumed, this result
would tend to suggest that x1 is NOT a significant predictor of y.
However, the deviance chi-square test has a P-value of 0.016, which
suggests that x1 is indeed a significant predictor of y. How do I
reconcile these two differing messages? I do recognize that the upper
bound of the confidence interval is pretty close to 1, but I am certain
that some journal reviewer will point out the problem as inconsistent.
Brant Inman
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