onls (version 0.1-1)

confint.onls: Confidence intervals for 'onls' model parameters

Description

Computes confidence intervals for one or more parameters of an onls model. As in MASS:::confint.nls, these are based on profile likelihoods, using onls:::profile.onls and onls:::confint.profile.onls.

Usage

"confint"(object, parm, level = 0.95, ...)

Arguments

object

an object returned from onls.

parm

a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.

level

the confidence level required.

...

additional argument(s) for methods.

Value

A matrix (or vector) with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1 - level)/2 and 1 - (1 - level)/2 in % (by default 2.5% and 97.5%).

Details

Profiling the likelihood uses the following strategy: If $\theta$ is the parameter to be profiled and $\delta$ the vector of remaining parameters, 1) compute the log-likelihood of the model $\mathcal{L}(\theta^{*}, \delta^{*})$ using the converged parameters, 2) compute a lower bound $\theta^{*} - 0.6 \cdot \sigma(\theta^{*})$ for the lower confidence limit, 3) define a grid of values ranging from $\theta^{'}$ to $\theta^{*}$ (e.g., 100 equidistant points), 4) for each grid value $\theta_i$, compute the profile log-likelihood value $\mathcal{L}_1(\theta_i)$ by maximizing $\mathcal{L}(\theta_i, \delta)$ over $\delta$-values by fixing $\theta$ at $\theta_i$, 5) find the confidence level by interpolation of the profile traces obtained from 4).

Examples

## Not run: 
# DNase1 <- subset(DNase, Run == 1)
# DNase1$density <- sapply(DNase1$density, function(x) rnorm(1, x, 0.1 * x))
# mod1 <- onls(density ~ Asym/(1 + exp((xmid - log(conc))/scal)), 
#              data = DNase1, start = list(Asym = 3, xmid = 0, scal = 1))
# confint(mod1)
# ## End(Not run)