mmmgee.test {mmmgee} | R Documentation |
Hypothesis Tests for Linear Contrasts in Multiple Marginal GEE Models
Description
Global hypothesis tests, multiple testing procedures and simultaneous confidence intervals for multiple linear contrasts of regression coefficients in a single generalized estimating equation (GEE) model or across multiple GEE models.
Usage
mmmgee.test(x, L, r = NULL, statistic = c("wald", "score"),
type = c("maximum", "quadratic"), asymptotic = TRUE,
biascorr = FALSE, closed.test = FALSE, conf.int = FALSE,
conf.level = 0.95, alternative = c("undirected", "greater", "less"),
denomDF = NULL, scaled.F = FALSE, maxit = 20, tol = 10^(-8), ...)
Arguments
x |
a |
L |
a contrast matrix defining a contrast for the stacked vector of regression coefficients of the marginal models, or a list of contrast matrices.
In the latter case, the list must contain one matrix for each model listed in |
r |
right hand side vector of the null hypothesis or a list of vectors resembling the right hand side of the null hypothesis. If not specified, |
statistic |
either |
type |
either |
asymptotic |
logical, if |
biascorr |
logical indicating whether the Mancl and DeRouen Bias correction should be used when estimating the joint covariance matrix via |
closed.test |
logical, if |
conf.int |
logical. If |
conf.level |
the nominal simultaneous coverage probability of the confidence intervals. |
alternative |
one of |
denomDF |
Defaults to |
scaled.F |
logical. If |
maxit |
maximal number of iterations to be passed to |
tol |
tolerance limit for the convergence criterion to be passed to |
... |
additional arguments that are passed to |
Details
The null hypothesis is where
L
is a contrast matrix,
the stacked vector of regression coefficients rom the marginal models and
r
a real values right hand side vector.
L
can be specified as matrix or, if it is a block diagonal matrix with each block corresponding to
a contrast for one marginal GEE model, as list of the matrices on the diagonal. The right hand side r
can be speficied as vector or as list of
vectors each corresponding to the part of the right hand side vector for one model.
When choosing statistic="wald"
and type="maximum"
, the maximum of the standardized entries of is used as test statistic and the
p-value is calculated from a multivariate normal or t-distribution (depending on
asymptotic
being TRUE
or FALSE
) with correlation matrix
estimated for . For the t-distribution, denominator degrees of freedom are used as specified in
denomDF
.
When choosing statistic="wald"
and type="quadratic"
, a quadratic form of and the inverse of the estimated covariance matrix
of
is used as test statistic and the p-value is calculated from a
chi-squared distribution or an F-distribution (depending on
asymptotic
being TRUE
or FALSE
).
With statistic="score"
, generalized score tests are calculated by replacing by the first order approximation
where
is the stacked estimating equation (the score) and
is the negative inverse of the matrix
of first derivatives of
, both evaluated at the location of constrained estimates for
under the null hypothesis.
Analogous to the Wald statistic, a maximum-type and a quadratic form score test are available. For the score test the option
asymptotic
is ignored
and the reference distribution is multivariate normal or chi-squared.
Value
A list with class mmmgeetest
containing the following components, if required:
test
Contains a data frame with the test statistic, degrees of freedom (depending in the type of test) and the p-value. If closed test was required, a further data frame is reported with estimates, right hand side vector, unadjusted p-values and adjusted p-values for each line of
.
hypothesis
A list containing the contrast matrix
and the right hand side vector
.
conf.int
The simultaneous confidence intervals.
denomDF
The type and value of the denominator degrees of freedom used in the procedure.
mmmgee
The
mmmgee
object containing in particular the estimated covariance matrix for the coefficents of the models inx
. Seemmmgee
.
Note
A single value for the denominator degrees of freedom is calculated for the covariance matrix estimate across all contrasts. In the closed testing procedure, this value is used for the degrees of freedom associated with the covariance matrix of any subset of contrasts.
Usual linear models or generalized linear models can be regarded as special case of GEE models and can be included in the analysis framework.
Note however that mmmgee.test
always uses the robust sandwich covariance matrix estimate, even if the calculation of the sandwich covariance was suppressed
in the model objects in x
.
Author(s)
Robin Ristl, robin.ristl@meduniwien.ac.at
References
Dennis D. Boos. On generalized score tests. The American Statistician, 1992, 46(4):327-333.
Lloyd A. Mancl, Timothy A. DeRouen. A covariance estimator for GEE with improved small sample properties. Biometrics, 2001, 57(1):126-134.
See Also
Examples
data(keratosis)
m1<-geem2(clearance~trt,id=id,data=keratosis,family=binomial,corstr="independence")
m2<-geem2(pain~trt,id=id,data=keratosis[keratosis$lesion==1,],family=gaussian,corstr="independence")
L1<-L2<-diag(1,4)[-1,]
mmmgee.test(x=m1,L=list(L1),statistic="wald",type="maximum")
mmmgee.test(x=m1,L=list(L1),statistic="score",type="maximum")
mmmgee.test(x=list(m1,m2),L=list(L1,L2),type="maximum",asymptotic=FALSE,biascorr=TRUE)
mmmgee.test(x=list(m1,m2),L=list(L1,L2),type="maximum",closed.test=TRUE)
mmmgee.test(x=list(m1,m2),L=list(L1,L2),type="maximum",asymptotic=FALSE,
alternative="less",conf.int=TRUE,denomDF=40)
mmmgee.test(x=list(m1,m2),L=list(L1,L2),type="quadratic",asymptotic=TRUE)
mmmgee.test(x=list(m1,m2),L=list(L1,L2),statistic="score",type="quadratic")
mmmgee.test(x=list(m1,m2),L=list(L1,L2),statistic="score",type="maximum")
#
## Not run:
data(datasim)
mod1<-geem2(Y.lin~gr.lang+x1,id=id,data=datasim,family="gaussian",corstr="exchangeable")
mod2<-geem2(Y.poi~gr.lang+x2,id=id,data=datasim,family="poisson",corstr="exchangeable")
mod3<-geem2(Y.bin~gr.lang+x3,id=id,data=datasim,family="binomial",corstr="exchangeable")
Li<-matrix(c(0,1,0),nrow=1)
mmmgee.test(list(mod1,mod2,mod3),L=list(Li,Li,Li),statistic="Wald",type="maximum",
biascorr=TRUE,asymptotic=FALSE,closed.test=TRUE)
mmmgee.test(list(mod1,mod2,mod3),L=list(Li,Li,Li),statistic="score",closed.test=TRUE)
## End(Not run)