logitnr | R Documentation |
Link function for logistic regression models with a (fixed/known) natural response parameter.
logitnr(nrp = 0)
nrp |
Natural response parameter in [0,1). |
The logit link function with a natural response parameter is defined as log((E(Y) - \pi)/(1 - E(Y))
and inverse link function E(Y) = \pi + (1 - \pi)/(1 + exp(-\eta))
, where 0 \le \pi < 1
is the natural response parameter. Note that the usual logit link function is a special case where \pi = 0
. The link function implies a lower asymptote of \pi
for E(Y)
as \eta
approaches negative infinity.
User-specified starting values for the regression parameters may be required in cases where \pi
is substantially larger than zero. One strategy is to obtain these from a model with a smaller value \pi
.
logitnnr
# obtain starting values with the natural response parameter set to 0
tmp <- glm(cbind(total-y, y) ~ density + species,
family = binomial(link = logitnr(0)), data = rotifer)
# use starting values with a fixed natural response parameter of 0.1
glm(cbind(total-y, y) ~ density + species,
family = binomial(link = logitnr(0.1)), data = rotifer, start = coef(tmp))
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