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> 
> # Data from table 2.6 in Agresti
> # we compare logistic regression and Poisson regression and show that they
> # are the same
> 
> victim <- factor(rep(c("white", "black"), each = 2))
> defendant <- factor(rep(c("white", "black"), times = 2))
> deathpenalty <- matrix(c(53, 11, 0, 4, 414, 37, 16, 139),
+         ncol = 2, dimnames = list(NULL, c("yes", "no")))
> 
> data.frame(victim, defendant, deathpenalty)
  victim defendant yes  no
1  white     white  53 414
2  white     black  11  37
3  black     white   0  16
4  black     black   4 139
> 
> # logistic regression (binomial glm with logit link)
> # same analysis as was done in mcmc-too.R
> 
> bout <- glm(deathpenalty ~ victim + defendant, family = binomial)
> summary(bout)

Call:
glm(formula = deathpenalty ~ victim + defendant, family = binomial)

Deviance Residuals: 
       1         2         3         4  
 0.02660  -0.06232  -0.60535   0.09379  

Coefficients:
               Estimate Std. Error z value Pr(>|z|)    
(Intercept)     -3.5961     0.5069  -7.094 1.30e-12 ***
victimwhite      2.4044     0.6006   4.003 6.25e-05 ***
defendantwhite  -0.8678     0.3671  -2.364   0.0181 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 22.26591  on 3  degrees of freedom
Residual deviance:  0.37984  on 1  degrees of freedom
AIC: 19.3

Number of Fisher Scoring iterations: 4

> 
> # Now try to do the same thing assuming cells are independent poisson
> # have to stretch data out into a vector
> 
> resp <- as.vector(deathpenalty)
> 
> # then have to make all the predictors twice as long
> victim <- rep(victim, times = 2)
> defendant <- rep(defendant, times = 2)
> deathpenalty <- factor(rep(colnames(deathpenalty), each = 4))
> 
> data.frame(victim, defendant, deathpenalty, resp)
  victim defendant deathpenalty resp
1  white     white          yes   53
2  white     black          yes   11
3  black     white          yes    0
4  black     black          yes    4
5  white     white           no  414
6  white     black           no   37
7  black     white           no   16
8  black     black           no  139
> 
> pout <- glm(resp ~ deathpenalty + victim + defendant, family = poisson)
> summary(pout)

Call:
glm(formula = resp ~ deathpenalty + victim + defendant, family = poisson)

Deviance Residuals: 
       1         2         3         4         5         6         7         8  
  2.4276   -1.0165   -4.7949   -0.2614    4.3420   -9.7343  -10.6526   12.0733  

Coefficients:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)      3.70160    0.10103   36.64   <2e-16 ***
deathpenaltyyes -2.18737    0.12789  -17.10   <2e-16 ***
victimwhite      1.17526    0.09073   12.95   <2e-16 ***
defendantwhite   0.92774    0.08548   10.85   <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: 1225.08  on 7  degrees of freedom
Residual deviance:  402.84  on 4  degrees of freedom
AIC: 448.88

Number of Fisher Scoring iterations: 6

> 
> 
> proc.time()
   user  system elapsed 
  0.127   0.010   0.214