gnm: Generalized Nonlinear Models.

Description

gnm is used to fit generalized nonlinear models, specified by giving a symbolic description of the "linear" predictor and a description of the error distribution.

Usage

gnm(
  formula,
  family = gaussian(),
  offset = NULL,
  weights = NULL,
  data,
  subset = NULL,
  start = NULL,
  toler = 1e-05,
  maxit = 50,
  trace = FALSE,
  ...
)

Value

an object of class gnm in which the main results of the model fitted to the data are stored, i.e., a list with components including

`coefficients`	a vector containing the parameter estimates,

`fitted.values`	a vector containing the estimates of \(\mu_1,\ldots,\mu_n\),

`start`	a vector containing the starting values used,

`prior.weights`	a vector containing the case weights used,

`offset`	a vector containing the offset used,

`terms`	an object containing the terms objects,

`loglik`	the value of the log-likelihood function avaliated at the parameter estimates,

`estfun`	a vector containing the estimating functions evaluated at the parameter estimates
	and the observed data,

`formula`	the formula,

`converged`	a logical indicating successful convergence,

`model`	the full model frame,

`y`	the response vector,

`family`	an object containing the family object used,

`linear.predictors`	a vector containing the estimates of \(g(\mu_1),\ldots,g(\mu_n)\),

`R`	a matrix with unscaled estimate of the variance-covariance
	matrix of model parameters,

`call`	the original function call.

Arguments

formula: a formula expression which is a symbolic description of the "linear" predictor of the model to be fitted to the data.
family: a description of the error distribution and link function to be used in the model. For gnm this can be a character string naming a family function, a family function or the result of a call to a family function. As default, family is set to gaussian(identity).
offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases.
weights: an (optional) vector of "prior weights" to be used in the fitting process. The length of weights should be the same as the number of observations.
data: an (optional) data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which gnm is called.
subset: an (optional) vector specifying a subset of observations to be used in the fitting process.
start: an (optional) vector of starting values for the parameters in the "linear" predictor.
toler: an (optional) positive value which represents the convergence tolerance. The convergence is reached when the maximum of the absolute relative differences between the values of the parameters in the "linear" predictor in consecutive iterations of the fitting algorithm is lower than toler. As default, toler is set to 0.00001.
maxit: an (optional) integer value which represents the maximum number of iterations allowed for the fitting algorithm. As default, maxit is set to 50.
trace: an (optional) logical variable. If TRUE, output is produced for each iteration of the estimating algorithm.
...: further arguments passed to or from other methods.

Details

A set of standard extractor functions for fitted model objects is available for objects of class gnm, including methods to the generic functions such as summary, model.matrix, estequa, coef, vcov, logLik, fitted, confint, AIC, BIC and predict. In addition, the model fitted to the data may be assessed using functions such as adjR2.gnm, anova.gnm, residuals.gnm, dfbeta.gnm, cooks.distance.gnm, localInfluence.gnm and envelope.gnm.

Examples

Run this code

###### Example 1: The effects of fertilizers on coastal Bermuda grass
data(Grass)
fit1 <- gnm(Yield ~ b0 + b1/(Nitrogen + a1) + b2/(Phosphorus + a2) + b3/(Potassium + a3),
            family=gaussian(inverse), start=c(b0=0.1,b1=13,b2=1,b3=1,a1=45,a2=15,a3=30), data=Grass)
summary(fit1)

###### Example 2: Assay of an Insecticide with a Synergist
data(Melanopus)
fit2 <- gnm(Killed/Exposed ~ b0 + b1*log(Insecticide-a1) + b2*Synergist/(a2 + Synergist),
            family=binomial(logit), weights=Exposed, start=c(b0=-3,b1=1.2,a1=1.7,b2=1.7,a2=2),
		   data=Melanopus)
summary(fit2)

###### Example 3: Developmental rate of Drosophila melanogaster
data(Drosophila)
fit3 <- gnm(Duration ~ b0 + b1*Temp + b2/(Temp-a), family=Gamma(log),
            start=c(b0=3,b1=-0.25,b2=-210,a=55), weights=Size, data=Drosophila)
summary(fit3)

###### Example 4: Radioimmunological Assay of Cortisol
data(Cortisol)
fit4 <- gnm(Y ~ b0 + (b1-b0)/(1 + exp(b2+ b3*lDose))^b4, family=Gamma(identity),
            start=c(b0=130,b1=2800,b2=3,b3=3,b4=0.5), data=Cortisol)
summary(fit4)

###### Example 5: Age and Eye Lens Weight of Rabbits in Australia
data(rabbits)
fit5 <- gnm(wlens ~ b1 - b2/(age + b3), family=Gamma(log),
            start=c(b1=5.5,b2=130,b3=35), data=rabbits)
summary(fit5)

###### Example 6: Calls to a technical support help line
data(calls)
fit6 <- gnm(calls ~ SSlogis(week, Asym, xmid, scal), family=poisson(identity), data=calls)
summary(fit6)

###### Example 7: Growth of Paramecium aurelium
data(paramecium)
fit7 <- gnm(Number ~ exp(alpha - exp(beta - gamma*Days)), family=poisson(log),
            start=c(alpha=1.85,beta=0.7,gamma=0.35), data=paramecium)
summary(fit7)