# [R] exponential distribution

From: Antonio Gasparrini <Antonio.Gasparrini_at_lshtm.ac.uk>
Date: Sun, 08 Jun 2008 13:13:51 +0100

I've tried to solve the Es. 12, cap 4 of "Introduction to GLM" by Annette Dobson. It's about the relationship between survival time of leukemia patients and blood cell count. I tried to fit a model with exponential distribution, first by glm (family gamma and then dispersion parameter fixed to 1) and then with survreg.
They gave me the same point estimates but the standard errors are slightly different. I checked the results building the routine manually, and it seems that the glm results are the correct one.

#######################################################
data <- data.frame(y=c(65,156,100,134,16,108,121,4,39,143,56,26,22,1,1,5,65),  x=c(3.36,2.88,3.63,3.41,3.78,4.02,4.00,4.23,3.73,3.85,3.97,4.51,  4.54,5.00,5.00,4.72,5.00))

model2 <- survreg(Surv(y) ~ x, data, dist="exponential") summary(model2)

```X <- model.matrix(model1)
y <- as.vector(data\$y)
b <- as.matrix(c(1,1))  # STARTING VALUES
```
iter <- matrix(0,7,2)
iter[1,] <- b
for (i in 2:7) {
``` W <- diag(rep(1,length(y)))
z <- X%*%b + (y-exp(X%*%b))*1/exp(X%*%b)
b <- solve(t(X)%*%W%*%X) %*% (t(X)%*%W%*%z)
```
iter[i,] <- b
}
summary(model1,dispersion=1)\$coef
summary(model2)
iter[nrow(temp),]
sqrt(diag(solve(t(X)%*%W%*%X)))
#######################################################

Antonio Gasparrini
Public and Environmental Health Research Unit (PEHRU) London School of Hygiene & Tropical Medicine Keppel Street, London WC1E 7HT, UK
Office: 0044 (0)20 79272406 - Mobile: 0044 (0)79 64925523 http://www.lshtm.ac.uk/people/gasparrini.antonio ( http://www.lshtm.ac.uk/pehru/ )

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