# GEE Sandwich Variance Estimator Proposed by Liang and Zeger (1986).

### Description

Calculate the GEE original variance estimator proposed by Liang and Zeger (1986).

### Usage

1 | ```
GEE.var.lz(formula,id="subject",family=gaussian,data,corstr="independence")
``` |

### Arguments

`formula` |
an object of class "formula" (or one that can be coerced to that class): a formula expression as for other regression models to be fitted, of the form response ~ predictors. The details of formula specification can be seen in glm() and gee(). |

`id` |
a vector which identifies the clusters. The length of id should be the same as the total number of observations. Data is assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula. |

`family` |
a family object: a list of functions and expressions for defining link and variance functions to be used in the model. This can be a character string naming a family function including "gaussian", "binomial", and "poisson". See family for details of family functions in glm() and gee(). |

`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 glm is called. |

`corstr` |
a character string specifying working correlation structure: "independence", "AR-M","exchangeable", "unstructured" are possible. |

### Details

Fit the model by GEE and calculate the original variance estimator proposed by Liang and Zeger (1986).

### Value

`cov.beta ` |
estimate of the variance for beta |

`cov.var ` |
estimate of the variance-covariance matrix for the variance estimator |

### Author(s)

Ming Wang <mwang@phs.psu.edu>

Maintainer: Zheng Li <zheng.li@outlook.com>

### References

Zeger SL and Liang KY. Longitudinal data analysis for discrete and continuous outcomes. Biometrics 1986: 121-130.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
data(dental)
data_alt <- reshape(dental, direction="long", timevar="Time",
varying=names(dental)[3:6], v.names="response", times=c(8,10,12,14))
data_alt <- data_alt[order(data_alt$subject),]
data_alt$gender <- as.numeric(data_alt$gender)
data_alt$Time <- sqrt(data_alt$Time)
formula <- response~Time+gender
lz.ind <- GEE.var.lz(formula,id="subject",family=gaussian,
data_alt,corstr="independence") ##Independence correlation structure;
lz.exch <- GEE.var.lz(formula,id="subject",family=gaussian,
data_alt,corstr="exchangeable") ##Exchangeable correlation structure;
lz.ar1 <- GEE.var.lz(formula,id="subject",family=gaussian,
data_alt,corstr="AR-M") ##AR-1 correlation structure;
lz.unstr <- GEE.var.lz(formula,id="subject",family=gaussian,
data_alt,corstr="unstructured") ##Unstructured correlation structure;
``` |