cglm (version 1.1)

cglm: Estimates the ratio of the regression coefficients and the dispersion parameter in conditional generalized linear models for clustered data.

Description

cglm estimates the ratio of the regression coefficients and the dispersion parameter in conditional generalized linear models. This is of particular interest in the so-called case-time-control design.

Usage

cglm(method, formula, data, id, link, ...)

Arguments

method

a string specifying the desired estimation method; either "ts" for two-step estimation, or "cml" for conditional maximum likelihood estimation.

formula

a symbolic description of the model to be fitted.

data

a data frame containing the variables in the model.

id

a string containing the name of the cluster identification variable.

link

a string specifying the desired link function. This argument is not used when method="cml".

…

optional arguments passed on to the nleqslv function or the optim function, which are used to solve the estimating equations when method="ts" and method="cml", respectively. See the help pages for nleqslv and optim.

Value

An object of class "cglm" is a list containing

call

the matched call.

coefficients

the ratio of the estimated coefficients and the estimated dispersion parameter.

var

the variance-covariance matrix.

convergence

was a solution found to the estimating equations?

Details

Let \(y_{ij}\) and \(x_{ij}\) be the outcome and covariate(s) for subject \(j\) in cluster \(i\), respectively. Consider the conditional generalized linear model $$p(y_{ij}|i,x_{ij})=\textrm{exp}\left[\frac{\theta_{ij}y_{ij}-A(\theta_{ij})}{\phi}+k(y_{ij},\phi)\right]$$ where $$\theta_{ij}=\eta\{E(y_{ij}|x_{ij})\}=b_i+\beta x_{ij}.$$ cglm estimates the ratio $$\beta / \phi.$$ This ratio is of particular interest in so-called case-time-control designs; see Sjolander (2016) and Sjolander and Ning (2018) for details. Two estimation methods are allowed; the two-step method proposed by Sjolander (2016) and the conditional maximum likelihood method proposed by Sjolander and Ning (2018).

References

Sjolander A. (2017). The case-time-control method for non-binary exposures. Sociological Methodology 47(1), 182-211.

Sjolander A., Ning Y. (2018). A general and robust estimation method for the case-time-control design. Sociological Methodology 49(1), 349-365.

Examples

# NOT RUN {
data(teenpov)

fit.ide <- cglm(method="ts", formula=hours~nonpov+inschool+spouse+age+mother, 
  data=teenpov, id="ID", link="identity")
summary(fit.ide)

fit.log <- cglm(method="ts", formula=hours~nonpov+inschool+spouse+age+mother, 
  data=teenpov, id="ID", link="log")
summary(fit.log)

fit.cglm <- cglm(method="cml", formula=hours~nonpov+inschool+spouse+age+mother,
  data=teenpov, id="ID")
summary(fit.cglm)

# }