# Example: Dose-response study

The data reports the death of adult flour beetles after the exposure to gaseous carbon disulfide at various dosages. The data is in a group-level form.

``````beetles2 <- read.table("beetles2.dat", header = T)
beetles2``````

## 2.1 Group-level data V.S. ungrouped data

``````alive <- beetles2\$n - beetles2\$dead
data <- matrix(append(beetles2\$dead, alive), ncol = 2)
logdose <- beetles2\$logdose
n <- beetles2\$n
fit.probit <- glm(data ~ logdose, family = binomial(link = probit))
summary(fit.probit)``````
``````##
## Call:
## glm(formula = data ~ logdose, family = binomial(link = probit))
##
## Deviance Residuals:
##     Min       1Q   Median       3Q      Max
## -1.5627  -0.4848   0.7647   1.0530   1.3149
##
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -34.956      2.649  -13.20   <2e-16 ***
## logdose       19.741      1.488   13.27   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
##     Null deviance: 284.202  on 7  degrees of freedom
## Residual deviance:   9.987  on 6  degrees of freedom
## AIC: 40.185
##
## Number of Fisher Scoring iterations: 4``````

Residual deviance is \(9.99\) (with p-value \(0.125\) from the likelihood ratio test, after comparing with the group-level saturated model)

Now letâ€™s check the ungrouped data

``````Beetles <- read.table("Beetles.dat", header = T)
Beetles``````
``````fit.probit2 <- glm(y ~ x, family = binomial(link = probit), data = Beetles)
summary(fit.probit2)``````
``````##
## Call:
## glm(formula = y ~ x, family = binomial(link = probit), data = Beetles)
##
## Deviance Residuals:
##     Min       1Q   Median       3Q      Max
## -2.5638  -0.6263   0.1597   0.4478   2.3883
##
## Coefficients:
##             Estimate Std. Error z value Pr(>|z|)
## (Intercept)  -34.956      2.649  -13.20   <2e-16 ***
## x             19.741      1.488   13.27   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
##     Null deviance: 645.44  on 480  degrees of freedom
## Residual deviance: 371.23  on 479  degrees of freedom
## AIC: 375.23
##
## Number of Fisher Scoring iterations: 6``````

Residual deviance is \(371.23\). The log-likelihood ratio test here for the residual deviance is invalid.