various choices of variance functions
- function in 2.2 to illustrate the the effect of the assumed variance function (using the identity link for all functions)
x <- 1:3 y <- c(1,2,9) glm(y~x,family=gaussian(link=identity))
Call: glm(formula = y ~ x, family = gaussian(link = identity))
Coefficients:
(Intercept) x
-4 4
Degrees of Freedom: 2 Total (i.e. Null); 1 Residual
Null Deviance: 38
Residual Deviance: 6 AIC: 16.59
glm(y~x,family=poisson(link=identity))
Call: glm(formula = y ~ x, family = poisson(link = identity))
Coefficients:
(Intercept) x
-2.4 3.2
Degrees of Freedom: 2 Total (i.e. Null); 1 Residual
Null Deviance: 9.052
Residual Deviance: 1.69 AIC: 14.36
glm(y~x,family=Gamma(link=identity))
Call: glm(formula = y ~ x, family = Gamma(link = identity))
Coefficients:
(Intercept) x
-1.799 2.744
Degrees of Freedom: 2 Total (i.e. Null); 1 Residual
Null Deviance: 2.537
Residual Deviance: 0.4385 AIC: 14.6
glm(y~x,family=inverse.gaussian(link=identity))
Call: glm(formula = y ~ x, family = inverse.gaussian(link = identity))
Coefficients:
(Intercept) x
-1.370 2.353
Degrees of Freedom: 2 Total (i.e. Null); 1 Residual
Null Deviance: 0.8611
Residual Deviance: 0.1181 AIC: 13.48
model on page 16 to illustrate the use of an offset
- data can be downloaded here as zip http://stata-press.com/data/hh3/glmext3.zip or here as tar.Z http://stata-press.com/data/hh3/glmext3.tar.Z
- first build the model
require(foreign) medpar <- read.dta("glmext3/medpar.dta") m <- glm(los ~ hmo + white + type2 + type3, data=medpar, family=poisson(link="log")) summary(m)
Warnmeldung:
In read.dta("glmext3/medpar.dta") :
Faktorbeschriftungen von Stata-5-Dateien können nicht gelesen werden
Call:
glm(formula = los ~ hmo + white + type2 + type3, family = poisson(link = "log"),
data = medpar)
Deviance Residuals:
Min 1Q Median 3Q Max
-5.3063 -1.8259 -0.6319 1.0081 15.3827
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 2.33293 0.02721 85.744 < 2e-16 ***
hmo -0.07155 0.02394 -2.988 0.00281 **
white -0.15387 0.02741 -5.613 1.99e-08 ***
type2 0.22165 0.02105 10.529 < 2e-16 ***
type3 0.70948 0.02614 27.146 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 8901.1 on 1494 degrees of freedom
Residual deviance: 8142.7 on 1490 degrees of freedom
AIC: 13868
Number of Fisher Scoring iterations: 5
- Wald test whether the coefficient on white is equal to -0.2
require(survey) regTermTest(m,test.terms = "white",null=-0.2,method="Wald")
Wald test for white
in glm(formula = los ~ hmo + white + type2 + type3, family = poisson(link = "log"),
data = medpar)
F = 2.831664 on 1 and 1490 df: p= 0.092632
- define model with offset variable white=-0.2
- do the likelihood-ratio test
m1 <- glm(los ~ hmo + type2 + type3 + offset(-0.2*white), data=medpar, family=poisson(link="log")) anova(m1,m,test="Chisq")
Analysis of Deviance Table Model 1: los ~ hmo + type2 + type3 + offset(-0.2 * white) Model 2: los ~ hmo + white + type2 + type3 Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 1491 8145.5 2 1490 8142.7 1 2.8657 0.09049 . --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
