drc (version 0.8-2)

logit: The logit function

Description

'logit' provides a very general way of specifying logit dose-response functions for binomial data.

Usage

logit(lowerc = c(-Inf, -Inf, -Inf, -Inf), upperc = c(Inf, Inf, Inf, Inf), 
fixed = c(NA, NA, 0, 1), names = c("a", "b", "c", "d"), 
useDer = FALSE, logTrans = TRUE)

Arguments

lowerc

numeric vector. The lower bound on parameters. Default is minus infinity.

upperc

numeric vector. The upper bound on parameters. Default is plus infinity.

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed.

names

a vector of character strings giving the names of the parameters (should not contain ":"). The default is reasonable (see under 'Usage'). The order of the parameters is: b, c, d, e, f (see under 'Details').

useDer

logical. If TRUE derivatives are supplied, otherwise they are not supplied. Not yet implemented!

logTrans

logical. If TRUE (default) the logarithm of the dose is used in the linear predictor.

Value

• The value returned by the 'logistic' is a list with the following components
• fct
  The dose response function.
• ssfct
  The self starter function.
• deriv1
  The first derivative.
• deriv2
  The second derivative.
• lowerc
  The lower bounds on the parameters.
• upperc
  The upper bounds on the parameters.
• edfct
  The ED function.
• sifct
  The SI function (not yet available).

Details

The default arguments yields the five-parameter logistic function given by the expression $$f(x) = c + (d - c) inverse logit (a + b \log(x))$$

References

Finney, D. J. (1971) Probit Analysis, Cambridge: Cambridge University Press.

See Also

Special cases of the function 'logistic' are l3, l4 and l5.

Examples

## Example dataset from Finney (1971) - example 19
logdose <- c(2.17, 2,1.68,1.08,-Inf,1.79,1.66,1.49,1.17,0.57)
n <- c(142,127,128,126,129,125,117,127,51,132)
r <- c(142,126,115,58,21,125,115,114,40,37)
treatment <- factor(c("w213","w213","w213","w213","control","w214","w214","w214","w214","w214"))
finney_ex19 <-data.frame(logdose, n, r, treatment)

## Fitting logistic regression model
model1 <- multdrc(r/n~logdose, treatment, logDose=10, weights=n, fct=logit(), data=finney_ex19[-5,])
anova(model1)
summary(model1)

## Fitting extended logistic regression model (lower limit above 0 is estimated)
model2 <- multdrc(r/n~logdose, treatment, logDose=10, weights=n, 
fct=logit(fixed=c(NA,NA,NA,1)), cm="control", 
collapse=data.frame(treatment,treatment,1), data=finney_ex19)
anova(model2)
summary(model2)

rm(logdose, n, r, treatment, finney_ex19, model1, model2)