# [R] Profile confidence intervals and LR chi-square test Classic List Threaded 5 messages Open this post in threaded view
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## [R] Profile confidence intervals and LR chi-square test

 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: [R] Profile confidence intervals and LR chi-square test

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