lcx: Estimate LCx for a toxin
In ahproctor/LC50: Estimate LC50 in the presence of additional stressors

Description Usage Arguments Details Value See Also

Estimate LCx from survival data in the presence of additional stressors and non-ignorable control mortality.

lcx(formula, concentration, group, data, start = NULL, link = c("probit",
  "logit"), lethal = 50, quasi = FALSE, common.background = FALSE,
  rate.shrink = 0, optim.control = list())

lcx.fit(X, Y, conc, group, alpha, beta, gamma, link, lethal, quasi = FALSE,
  common.background = FALSE, rate.shrink = 0, optim.control = list())

`formula`	A formula relating log LCx to covariates describing the additional stressors.
`concentration`	The name of variable that is the concentration of the toxin.
`group`	A factor distinguishing treatment groups for the additional stressors.
`data`	Dataframe containing the variables in the model.
`start`	Starting values used to initialize the model. If `start=NULL` these parameters are determined by `lcx.initialize`.
`link`	The link function for survival fractions.
`lethal`	The level of lethality (ie "x") to be estimated.
`quasi`	Should a quasibinomial model be fitted?
`common.background`	Should a common background survival be estimated for each treatment group?
`rate.shrink`	The shrinkage penalty for the rate parameters.
`optim.control`	Control parameters for `optim`.
`X`	A design matrix.
`Y`	A two column matrix of responses.
`conc`	A vector of toxin concentrations.
`alpha`	The vector of starting rate parameters.
`beta`	The vector of starting coefficients.
`gamma`	The vector of background survival parameters.

The details of the model are described in the package vignette.

lcx.fit is the workhorse function: it is not normally called directly but can be more efficient when the response vector, design matrix and family have already been calculated.

lcx returns an object of class inheriting from "lcx". See later in this section.

The function summary (i.e., link{summary.lcx}) can be used to obtain or print a summary of the results and the function anova (i.e., anova.lcx) to produce an analysis of deviance table for the tests of additional stressor effects.

An LCx model has several sets of coefficients, the generic accessor function coef returns only the beta coefficients.

An object of class "lcx" is a list containing at least the following components:

`logLik`	the maximized log likelihood.
`aic`	Akaike's information criteria.
`alpha`	a vector of rate coefficients.
`alpha.cov`	covariance of the rate coefficients.
`beta`	a named vector of lcx model coefficients.
`beta.cov`	covariance of the lcx model coefficients.
`gamma`	a vector of background survival coefficients.
`gamma.cov`	covariance of the background survival coefficients.
`coefficients`	a named vector of lcx model coefficients.
`cov.unscaled`	covariance of the lcx model coefficients.
`loglcx`	a named vector of log lcxs for the treatment groups.
`loglcx.cov`	covariance of the lcxs for the treatment groups.
`concentration`	a vector of toxin concentrations.
`group`	a factor distinguishing treatment groups.
`x`	a design matrix relating log lcx to factors describing the additional stressors.
`y`	a two column matrix of responses, giving the survivals and mortalities.
`fitted.values`	the fitted probability of survival.
`residuals`	the deviance residuals for the fit.
`deviance`	the deviance for the fit.
`df.residual`	the residual degrees of freedom.
`dispersion`	the dispersion.
`null.deviance`	the deviance of the null model, which fits a single mortality rate to all data.
`df.null`	the degrees of freedom for the null model.
`optim`	the result of the call to `optim`.
`link`	the link function.
`lethal`	the modelled level of lethality.
`quasi`	is the dispersion estimated.
`common.background`	is background mortality common.
`rate.shrink`	the shrinkage penalty.
`xlevels`	a record of the levels of the factors used in fitting.
`contrasts`	the contrasts used.
`call`	the matched call.
`terms`	the terms object used.
`model`	the model frame.