| glmgee {glmtoolbox} | R Documentation |
Fit Generalized Estimating Equations
Description
Produces an object of the class glmgee in which the main results of a Generalized Estimating Equation (GEE) fitted to the data are stored.
Usage
glmgee(
formula,
family = gaussian(),
weights,
id,
waves,
data,
subset,
corstr,
corr,
start = NULL,
scale.fix = FALSE,
scale.value = 1,
toler = 1e-05,
maxit = 50,
trace = FALSE,
...
)
Arguments
formula |
a |
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 |
waves |
an (optional) positive integer-valued variable that is used to identify the order and spacing of observations within clusters. This argument is crucial when there are missing values and gaps in the data. As default, |
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 parameter estimates are obtained by iteratively
solving the estimating equations described by Liang and Zeger (1986).
If the maximum cluster size is 6 and for a cluster of size 4 the value
of waves is set to 2, 4, 5, 6, then it means that the data at
times 1 and 3 are missing, which should be taken into account by
glmgee when the structure of the correlation matrix is assumed
to be "Unstructured", "Stationary-M-dependent", "Non-Stationary-M-dependent"
or "AR-M-dependent". If in this scenario waves is not specified
then glmgee assumes that the available data for this cluster
were taken at times 1, 2, 3 and 4.
A set of standard extractor functions for fitted model objects is
available for objects of class glmgee, including methods to generic functions such as print, summary, model.matrix, estequa,
coef, vcov, logLik, fitted, confint and predict.
In addition, the model may be assessed using functions such as anova.glmgee,
residuals.glmgee, dfbeta.glmgee, cooks.distance.glmgee, localInfluence.glmgee,
tidy.glmgee and glance.glmgee.
The variable selection may be accomplished using the routine
stepCriterion.glmgee.
Value
an object of class glmgee in which the main results of the 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, |
loglik | the value of the quasi-log-likelihood function evaluated at the parameter |
| estimates and the observed data, | |
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, |
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
Liang K.Y., Zeger S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13-22.
Zeger S.L., Liang K.Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42:121-130.
See Also
Examples
###### Example 1: Effect of ozone-enriched atmosphere on growth of sitka spruces
data(spruces)
mod1 <- size ~ poly(days,4) + treat
fit1 <- glmgee(mod1, id=tree, family=Gamma(log), corstr="AR-M-dependent(1)", data=spruces)
summary(fit1, corr.digits=2)
###### Example 2: Treatment for severe postnatal depression
data(depression)
mod2 <- depressd ~ visit + group
fit2 <- glmgee(mod2, id=subj, family=binomial(logit), corstr="AR-M-dependent(1)", data=depression)
summary(fit2, corr.digits=2)
###### Example 3: Treatment for severe postnatal depression (2)
data(depression)
mod3 <- dep ~ visit*group
fit3 <- glmgee(mod3, id=subj, family=gaussian, corstr="AR-M-dependent(1)", data=depression)
summary(fit3, corr.digits=2)
###### Example 4: Dental Clinical Trial
data(rinse)
mod4 <- score/3.6 ~ rinse*time
fit4 <- glmgee(mod4, family=binomial(log), id=subject, corstr="Exchangeable", data=rinse)
summary(fit4, corr.digits=2)
###### Example 5: Shoulder Pain after Laparoscopic Cholecystectomy
data(cholecystectomy)
mod5 <- pain2 ~ treatment + age + time
corstr <- "Stationary-M-dependent(2)"
fit5 <- glmgee(mod5, family=binomial(logit), id=id, corstr=corstr, data=cholecystectomy)
summary(fit5,varest="bias-corrected")
###### Example 6: Guidelines for Urinary Incontinence Discussion and Evaluation
data(GUIDE)
mod6 <- bothered ~ gender + age + dayacc + severe + toilet
fit6 <- glmgee(mod6, family=binomial(logit), id=practice, corstr="Exchangeable", data=GUIDE)
summary(fit6)
###### Example 7: Tests of Auditory Perception in Children with OME
OME <- MASS::OME
mod7 <- cbind(Correct, Trials-Correct) ~ Loud + Age + OME
fit7 <- glmgee(mod7, family = binomial(cloglog), id = ID, corstr = "Exchangeable", data = OME)
summary(fit7, corr=FALSE)
###### Example 8: Epileptic seizures
data(Seizures)
Seizures2 <- within(Seizures, time4 <- ifelse(time==4,1,0))
mod8 <- seizures ~ log(age) + time4 + log(base/4)*treatment
fit8 <- glmgee(mod8, family=poisson(log), id=id, corstr="Exchangeable", data=Seizures2)
summary(fit8)