Earthworm toxicity test

The dataset was obtained from a toxicity test using earthworms, and it contains the number of earthworms remaining in a container that was contaminated with a toxic substance (not disclosed) at various doses; so the number of earthworms not migrating to the neighbouring uncontaminated container.

data(earthworms)

Format

A data frame with 35 observations on the following 3 variables.

dose

a numeric vector of dose values

number

a numeric vector containing counts of remaining earthworms in the container

total

a numeric vector containing total number of earthworms put in the containers

Details

At dose 0 around half of the earthworms is expected be in each of the two containers. Thus it is not appropriate to fit an ordinary logistic regression with log(dose) as explanatory variable to these data as it implies an upper limit of 1 at dose 0 and in fact this model does not utilise the observations at dose 0 (see the example section below).

Source

The dataset is kindly provided by Nina Cedergreen, Faculty of Life Sciences, University of Copenhagen, Denmark.

Examples

# NOT RUN {
library(drc)

## Fitting a logistic regression model
earthworms.m1 <- drm(number/total~dose, weights = total, data = earthworms,
fct = LL.2(), type = "binomial")
modelFit(earthworms.m1)  # a crude goodness-of-fit test

## Fitting an extended logistic regression model 
##  where the upper limit is estimated
earthworms.m2 <- drm(number/total~dose, weights = total, data = earthworms,
fct = LL.3(), type = "binomial")
modelFit(earthworms.m2)  # goodness-of-fit test
# improvement not visible in test!!!

## Comparing model1 and model2 
## (Can the first model be reduced to the second model?)
anova(earthworms.m1, earthworms.m2)
# }