| wglmgee {glmtoolbox} | R Documentation |
Fit Weighted Generalized Estimating Equations
Description
Produces an object of the class wglmgee in which the main results of a Weighted Generalized Estimating Equation (WGEE) fitted to the data are stored.
Usage
wglmgee(
formula,
level = c("observations", "clusters"),
family = gaussian(),
weights,
id,
data,
subset,
corstr,
corr,
start = NULL,
scale.fix = FALSE,
scale.value = 1,
toler = 1e-05,
maxit = 50,
trace = FALSE,
...
)
Arguments
formula |
an |
level |
an (optional) character string which allows to specify the weighted GEE method. The available options are: "observations" and "clusters" for Observation- and Cluster-specified Weighted GEE, respectively. As default, level is set to "observations". |
family |
an (optional) |
weights |
an (optional) vector of positive "prior weights" to be used in the fitting process. The length of |
id |
a vector which identifies the subjects or clusters. The length of |
data |
an (optional) |
subset |
an (optional) vector specifying a subset of observations to be used in the fitting process. |
corstr |
an (optional) character string which allows to specify the working-correlation structure. The available options are: "Independence", "Unstructured", "Stationary-M-dependent(m)", "Non-Stationary-M-dependent(m)", "AR-M-dependent(m)", "Exchangeable" and "User-defined", where m represents the lag of the dependence. As default, |
corr |
an (optional) square matrix of the same dimension of the maximum cluster size containing the user specified correlation. This is only appropriate if |
start |
an (optional) vector of starting values for the parameters in the linear predictor. |
scale.fix |
an (optional) logical variable. If TRUE, the scale parameter is fixed at the value of |
scale.value |
an (optional) numeric value at which the scale parameter should be fixed. This is only appropriate if |
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 |
maxit |
an (optional) integer value which represents the maximum number of iterations allowed for the fitting algorithm. As default, |
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
The values of the multivariate response variable measured on n subjects or clusters,
denoted by y_{i}=(y_{i1},\ldots,y_{in_i})^{\top} for i=1,\ldots,n, are assumed to be
realizations of independent random vectors denoted by Y_{i}=(Y_{i1},\ldots,Y_{in_i})^{\top}
for i=1,\ldots,n. The random variables associated to the i-th subject or
cluster, Y_{ij} for j=1,\ldots,n_i, are assumed to satisfy
\mu_{ij}= E(Y_{ij}),Var(Y_{ij})=\frac{\phi}{\omega_{ij}}V(\mu_{ij})
and Corr(Y_{ij},Y_{ik})=r_{jk}(\rho),
where \phi>0 is the dispersion parameter,
V(\mu_{ij}) is the variance function, \omega_{ij}>0 is a known weight, and
\rho=(\rho_1,\ldots,\rho_q)^{\top} is a parameter vector.
In addition, \mu_{ij} is assumed to be dependent on the regressors vector x_{ij}
by g(\mu_{ij})=z_{ij} + x_{ij}^{\top}\beta, where g(\cdot) is the link function,
z_{ij} is a known offset and \beta=(\beta_1,\ldots,\beta_p)^{\top} is
a vector of regression parameters. The probabilities Pr[T_{ij}=1|T_{i,j-1}=1,x_{i1},\ldots,x_{ij},Y_{i1},\ldots,Y_{i,j-1}]
are estimated by using a logistic model whose covariates are given by z_{1},\ldots,z_{r}. Then, those
probabilities are used to computed the weights to be included in the parameter estimation algorithm.
A set of standard extractor functions for fitted model objects is available for objects of class glmgee,
including methods to the generic functions such as print, summary, model.matrix, estequa,
coef, vcov, fitted, confint and predict. The input data are assumed to be ordered
in time within each cluster.
Value
an object of class wglmgee in which the main results of the weighted GEE model fitted to the data are stored, i.e., a list with components including
coefficients | a vector with the estimates of \beta_1,\ldots,\beta_p, |
fitted.values | a vector with the estimates of \mu_{ij} for i=1,\ldots,n and j=1,\ldots,n_i, |
start | a vector with the starting values used, |
iter | a numeric constant with the number of iterations, |
prior.weights | a vector with the values of \omega_{ij} for i=1,\ldots,n and j=1,\ldots,n_i, |
offset | a vector with the values of z_{ij} for i=1,\ldots,n and j=1,\ldots,n_i, |
terms | an object containing the terms objects, |
estfun | a vector with the estimating equations evaluated at the parameter |
| estimates and the observed data, | |
formula | the formula, |
levels | the levels of the categorical regressors, |
contrasts | an object containing the contrasts corresponding to levels, |
converged | a logical indicating successful convergence, |
model | the full model frame, |
y | a vector with the values of y_{ij} for i=1,\ldots,n and j=1,\ldots,n_i, |
family | an object containing the family object used, |
linear.predictors | a vector with the estimates of g(\mu_{ij}) for i=1,\ldots,n and j=1,\ldots,n_i, |
R | a matrix with the (robust) estimate of the variance-covariance, |
corr | a matrix with the estimate of the working-correlation, |
corstr | a character string specifying the working-correlation structure, |
level | a character string specifying the weighted GEE method, |
id | a vector which identifies the subjects or clusters, |
sizes | a vector with the values of n_i for i=1,\ldots,n, |
call | the original function call, |
References
Fitzmaurice G.M., Laird N.M., Ware J.H. (2011). Applied Longitudinal Analysis. 2nd ed. John Wiley & Sons.
Preisser J.S., Lohman K.K., Rathouz P.J. (2002). Performance of Weighted Estimating Equations for Longitudinal Binary Data with Drop-Outs Missing at Random. Statistics in Medicine 21:3035–3054.
Robins J.M., Rotnitzky A., Zhao L.P. (1995) Analysis of Semiparametric Regression Models for Repeated Outcomes in the Presence of Missing Data. Journal of the American Statistical Association 90:122–129.
See Also
Examples
###### Example: Amenorrhea rates over time
data(amenorrhea)
amenorrhea2 <- within(amenorrhea,{
Ctime <- factor(Time)
Ctime <- relevel(Ctime,ref="1")
ylag1 <- c(0,amenorrhea[-length(ID)])
ylag1 <- ifelse(Time==0,0,ylag1)})
mod <- amenorrhea ~ poly(Time,2) + Dose | Ctime + Dose + ylag1
### Observation-specified Weighted GEE
fit1 <- wglmgee(mod, family=binomial, data=amenorrhea2, id=ID,
corstr="AR-M-dependent(1)", level="observations")
summary(fit1)
### Cluster-specified Weighted GEE
fit2 <- wglmgee(mod, family=binomial, data=amenorrhea2, id=ID,
corstr="Exchangeable", level="clusters")
summary(fit2)