An example
Defining y and x
> y <- c (rpois(10,1), rpois(10,2), rpois(10,3), rpois(10,5))
> y
[1] 0 1 0 2 1 2 0 1 1 0 3 2 2 4 2 3 3 1 1 1 3 0 4 4 2 3 1 4 3 6 3 8 6 3 2 6 5 5 2 8
> x <- gl(4,10)
> x
[1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4
Levels: 1 2 3 4
Fitting a Poisson regression
> f <- glm(y~x, family=poisson)
> summary(f)
Call:
glm(formula = y ~ x, family = poisson)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.44949 -0.90724 0.04533 0.52699 1.52242
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.2231 0.3536 -0.631 0.527945
x2 1.0116 0.4129 2.450 0.014277 *
x3 1.3218 0.3979 3.322 0.000895 ***
x4 1.7918 0.3819 4.692 2.71e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 67.967 on 39 degrees of freedom
Residual deviance: 34.884 on 36 degrees of freedom
AIC: 142.6
Number of Fisher Scoring iterations: 5
Multiple comparisons
> # install.packages("multcomp")
> require(multcomp)
> f.mc <- glht(f, linfct = mcp(x = "Tukey"))
> summary(f.mc)
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: glm(formula = y ~ x, family = poisson)
Linear Hypotheses:
Estimate Std. Error z value Pr(>|z|)
2 - 1 == 0 1.0116 0.4129 2.450 0.06433 .
3 - 1 == 0 1.3218 0.3979 3.322 0.00481 **
4 - 1 == 0 1.7918 0.3819 4.692 < 0.001 ***
3 - 2 == 0 0.3102 0.2807 1.105 0.67729
4 - 2 == 0 0.7802 0.2575 3.030 0.01198 *
4 - 3 == 0 0.4700 0.2327 2.019 0.17303
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported -- single-step method)
> confint(f.mc)
Simultaneous Confidence Intervals
Multiple Comparisons of Means: Tukey Contrasts
Fit: glm(formula = y ~ x, family = poisson)
Quantile = 2.5471
95% family-wise confidence level
Linear Hypotheses:
Estimate lwr upr
2 - 1 == 0 1.01160 -0.04002 2.06322
3 - 1 == 0 1.32176 0.30822 2.33529
4 - 1 == 0 1.79176 0.81905 2.76447
3 - 2 == 0 0.31015 -0.40481 1.02512
4 - 2 == 0 0.78016 0.12436 1.43596
4 - 3 == 0 0.47000 -0.12281 1.06282
> coef(f.mc)
2 - 1 3 - 1 4 - 1 3 - 2 4 - 2 4 - 3
1.0116009 1.3217558 1.7917595 0.3101549 0.7801586 0.4700036
> vcov(f.mc)
2 - 1 3 - 1 4 - 1 3 - 2 4 - 2 4 - 3
2 - 1 1.704542e-01 1.249996e-01 1.249996e-01 -4.545455e-02 -4.545455e-02 9.714451e-17
3 - 1 1.249996e-01 1.583330e-01 1.249996e-01 3.333333e-02 6.938894e-17 -3.333333e-02
4 - 1 1.249996e-01 1.249996e-01 1.458330e-01 -2.775558e-17 2.083333e-02 2.083333e-02
3 - 2 -4.545455e-02 3.333333e-02 -2.775558e-17 7.878788e-02 4.545455e-02 -3.333333e-02
4 - 2 -4.545455e-02 6.938894e-17 2.083333e-02 4.545455e-02 6.628788e-02 2.083333e-02
4 - 3 9.714451e-17 -3.333333e-02 2.083333e-02 -3.333333e-02 2.083333e-02 5.416667e-02
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