if( !require('drc') ){
    install.packages('drc', dependencies=TRUE, repos="http://cran.rstudio.com/")
}
library(drc) # get the dataset vinclozolin

if( !require('nlme') ){
    install.packages('nlme', dependencies=TRUE, repos='http://cran.rstudio.com/')
}
library(nlme)

# I fit a model with all three parameters have randomized effects:
#
fit = nlme(effect ~ d/(1+exp(b*(log(conc)-log(e)))), fixed = list(b~1, d~1, e~1), random=b+d+e~1|exper, start = c(1, 1000, 0.1), data = vinclozolin)
print(summary(fit))

# Fit a model where only two parameters have randomized effects:
#
fit_b_fixed = nlme(effect ~ d/(1+exp(b*(log(conc)-log(e)))), fixed = list(b~1, d~1, e~1), random=d+e~1|exper, start = c(1, 1000, 0.1), data = vinclozolin)
print(summary(fit_b_fixed))

print(anova(fit_b_fixed, fit)) # the restricted model(with a larger RSS)is first