README.md
In AnestisTouloumis/multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses
multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses
Installation
You can install the release version of multgee:
install.packages("multgee")
The source code for the release version of multgee is available on
CRAN at:
Or you can install the development version of multgee:
# install.packages('devtools')
devtools::install_github("AnestisTouloumis/multgee")
The source code for the development version of multgee is available on
github at:
To use multgee, you should load the package as follows:
library("multgee")
#> Loading required package: gnm
Usage
This package provides a generalized estimating equations (GEE) solver
for fitting marginal regression models with correlated nominal or
ordinal multinomial responses based on a local odds ratios
parameterization for the association structure (see Touloumis, Agresti
and Kateri, 2013).
There are two core functions to fit GEE models for correlated
multinomial responses:
ordLORgee for an ordinal response scale. Options for the marginal
model include cumulative link models or an adjacent categories logit
model,nomLORgee for a nominal response scale. Currently, the only option
is a marginal baseline category logit model.
The main arguments in both functions are:
- an optional data frame (
data),
- a model formula (
formula),
- a cluster identifier variable (
id),
- an optional vector that identifies the order of the observations
within each cluster (
repeated).
The association structure among the correlated multinomial responses is
expressed via marginalized local odds ratios (Touloumis et al., 2013).
The estimating procedure for the local odds ratios can be summarized as
follows: For each level pair of the repeated variable, the available
responses are aggregated across clusters to form a square marginalized
contingency table. Treating these tables as independent, an RC-G(1) type
model is fitted in order to estimate the marginalized local odds ratios.
The LORstr argument determines the form of the marginalized local odds
ratios structure. Since the general RC-G(1) model is closely related to
the family of association models, one can instead fit an association
model to each of the marginalized contingency tables by setting
LORem = "2way" in the core functions.
There are also five useful utility functions:
confint for obtaining Wald–type confidence intervals for the
regression parameters using the standard errors of the sandwich
(method = "robust") or of the model–based (method = "naive")
covariance matrix. The default option is the sandwich covariance
matrix (method = "robust"),waldts for assessing the goodness-of-fit of two nested GEE models
based on a Wald test statistic,vcov for obtaining the sandwich (method = "robust") or model–based
(method = "naive") covariance matrix of the regression parameters,intrinsic.pars for assessing whether the underlying association
structure does not change dramatically across the level pairs of
repeated,gee_criteria for reporting commonly used criteria to select
variables and/or association structure for GEE models.
Example
The following R code replicates the GEE analysis presented in Touloumis
et al. (2013).
data("arthritis")
intrinsic.pars(y, arthritis, id, time, rscale = "ordinal")
#> [1] 0.6517843 0.9097341 0.9022272
The intrinsic parameters do not differ much. This suggests that the
uniform local odds ratios structure might be a good approximation for
the association pattern.
fitord <- ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline),
data = arthritis, id = id, repeated = time)
summary(fitord)
#> GEE FOR ORDINAL MULTINOMIAL RESPONSES
#> version 1.6.0 modified 2017-07-10
#>
#> Link : Cumulative logit
#>
#> Local Odds Ratios:
#> Structure: category.exch
#> Model: 3way
#>
#> call:
#> ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline),
#> data = arthritis, id = id, repeated = time)
#>
#> Summary of residuals:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.5176739 -0.2380475 -0.0737290 -0.0001443 -0.0066846 0.9933154
#>
#> Number of Iterations: 6
#>
#> Coefficients:
#> Estimate san.se san.z Pr(>|san.z|)
#> beta10 -1.84003 0.38735 -4.7504 < 2e-16 ***
#> beta20 0.27712 0.34841 0.7954 0.42639
#> beta30 2.24779 0.36509 6.1568 < 2e-16 ***
#> beta40 4.54824 0.41994 10.8307 < 2e-16 ***
#> factor(time)3 -0.00079 0.12178 -0.0065 0.99485
#> factor(time)5 -0.36050 0.11413 -3.1586 0.00159 **
#> factor(trt)2 -0.50463 0.16725 -3.0173 0.00255 **
#> factor(baseline)2 -0.70291 0.37861 -1.8565 0.06338 .
#> factor(baseline)3 -1.27558 0.35066 -3.6376 0.00028 ***
#> factor(baseline)4 -2.65579 0.41039 -6.4714 < 2e-16 ***
#> factor(baseline)5 -3.99555 0.53246 -7.5040 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Local Odds Ratios Estimates:
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [2,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [3,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [4,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [5,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [6,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [7,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [8,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [9,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [10,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [11,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [12,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#>
#> p-value of Null model: < 0.0001
The 95% Wald confidence intervals for the regression parameters are
confint(fitord)
#> 2.5 % 97.5 %
#> beta10 -2.5992134 -1.08084855
#> beta20 -0.4057572 0.95999854
#> beta30 1.5322296 2.96335073
#> beta40 3.7251701 5.37130863
#> factor(time)3 -0.2394781 0.23790571
#> factor(time)5 -0.5841988 -0.13680277
#> factor(trt)2 -0.8324304 -0.17683500
#> factor(baseline)2 -1.4449754 0.03916401
#> factor(baseline)3 -1.9628588 -0.58829522
#> factor(baseline)4 -3.4601391 -1.85143755
#> factor(baseline)5 -5.0391534 -2.95195213
To illustrate model comparison, consider another model with age and
sex as additional covariates:
fitord1 <- update(fitord, formula = . ~ . + age + factor(sex))
waldts(fitord, fitord1)
#> Goodness of Fit based on the Wald test
#>
#> Model under H_0: y ~ factor(time) + factor(trt) + factor(baseline)
#> Model under H_1: y ~ factor(time) + factor(trt) + factor(baseline) + age + factor(sex)
#>
#> Wald Statistic = 3.8313, df = 2, p-value = 0.1472
gee_criteria(fitord, fitord1)
#> QIC CIC RJC QICu Parameters
#> fitord 1268.444 1268.375 11.0347 1.2779 11
#> fitord1 1279.759 1279.582 13.0885 0.9964 13
According to the Wald test, there is no evidence of no difference
between the two models. The QICu criterion suggest that fitord should
be preferred over fitord1.
Getting help
The statistical methods implemented in multgee are described in
Touloumis et al. (2013). A detailed description of the functionality of
multgee can be found in Touloumis (2015). Note that an updated version
of this paper also serves as a vignette:
browseVignettes("multgee")
How to cite
To cite 'multgee' in publications, please use:
Touloumis A. (2015). "R Package multgee: A Generalized Estimating
Equations Solver for Multinomial Responses." _Journal of Statistical
Software_, *64*(8), 1-14.
<https://www.jstatsoft.org/index.php/jss/article/view/v064i08>.
A BibTeX entry for LaTeX users is
@Article{,
title = {{R} Package {multgee}: A Generalized Estimating Equations Solver for Multinomial Responses},
author = {{Touloumis A.}},
journal = {Journal of Statistical Software},
year = {2015},
volume = {64},
number = {8},
pages = {1-14},
url = {https://www.jstatsoft.org/index.php/jss/article/view/v064i08},
}
To cite the methodology implemented in 'multgee' in publications,
please use:
Touloumis A., Agresti A., Kateri M. (2013). "GEE for multinomial
responses using a local odds ratios parameterization." _Biometrics_,
*69*(3), 633-640. <https://doi.org/10.1111/biom.12054>.
A BibTeX entry for LaTeX users is
@Article{,
title = {GEE for multinomial responses using a local odds ratios parameterization},
author = {{Touloumis A.} and {Agresti A.} and {Kateri M.}},
journal = {Biometrics},
year = {2013},
volume = {69},
number = {3},
pages = {633-640},
url = {https://doi.org/10.1111/biom.12054},
}
References
Touloumis, A. (2015) [R Package multgee: A Generalized Estimating
Equations Solver for Multinomial
Responses](https://www.jstatsoft.org/v064/i08). *Journal of Statistical
Software*, **64**, 1–14.
Touloumis, A., Agresti, A. and Kateri, M. (2013) [GEE for Multinomial
Responses Using a Local Odds Ratios
Parameterization](https://onlinelibrary.wiley.com/doi/10.1111/biom.12054/full).
*Biometrics*, **69**, 633–640.
AnestisTouloumis/multgee documentation built on March 19, 2024, 9:55 p.m.
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multgee: GEE Solver for Correlated Nominal or Ordinal Multinomial Responses
Installation
You can install the release version of multgee:
install.packages("multgee")
The source code for the release version of multgee is available on
CRAN at:
Or you can install the development version of multgee:
# install.packages('devtools')
devtools::install_github("AnestisTouloumis/multgee")
The source code for the development version of multgee is available on
github at:
To use multgee, you should load the package as follows:
library("multgee")
#> Loading required package: gnm
Usage
This package provides a generalized estimating equations (GEE) solver for fitting marginal regression models with correlated nominal or ordinal multinomial responses based on a local odds ratios parameterization for the association structure (see Touloumis, Agresti and Kateri, 2013).
There are two core functions to fit GEE models for correlated multinomial responses:
ordLORgeefor an ordinal response scale. Options for the marginal model include cumulative link models or an adjacent categories logit model,nomLORgeefor a nominal response scale. Currently, the only option is a marginal baseline category logit model.
The main arguments in both functions are:
- an optional data frame (
data), - a model formula (
formula), - a cluster identifier variable (
id), - an optional vector that identifies the order of the observations
within each cluster (
repeated).
The association structure among the correlated multinomial responses is
expressed via marginalized local odds ratios (Touloumis et al., 2013).
The estimating procedure for the local odds ratios can be summarized as
follows: For each level pair of the repeated variable, the available
responses are aggregated across clusters to form a square marginalized
contingency table. Treating these tables as independent, an RC-G(1) type
model is fitted in order to estimate the marginalized local odds ratios.
The LORstr argument determines the form of the marginalized local odds
ratios structure. Since the general RC-G(1) model is closely related to
the family of association models, one can instead fit an association
model to each of the marginalized contingency tables by setting
LORem = "2way" in the core functions.
There are also five useful utility functions:
confintfor obtaining Wald–type confidence intervals for the regression parameters using the standard errors of the sandwich (method = "robust") or of the model–based (method = "naive") covariance matrix. The default option is the sandwich covariance matrix (method = "robust"),waldtsfor assessing the goodness-of-fit of two nested GEE models based on a Wald test statistic,vcovfor obtaining the sandwich (method = "robust") or model–based (method = "naive") covariance matrix of the regression parameters,intrinsic.parsfor assessing whether the underlying association structure does not change dramatically across the level pairs ofrepeated,gee_criteriafor reporting commonly used criteria to select variables and/or association structure for GEE models.
Example
The following R code replicates the GEE analysis presented in Touloumis et al. (2013).
data("arthritis")
intrinsic.pars(y, arthritis, id, time, rscale = "ordinal")
#> [1] 0.6517843 0.9097341 0.9022272
The intrinsic parameters do not differ much. This suggests that the uniform local odds ratios structure might be a good approximation for the association pattern.
fitord <- ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline),
data = arthritis, id = id, repeated = time)
summary(fitord)
#> GEE FOR ORDINAL MULTINOMIAL RESPONSES
#> version 1.6.0 modified 2017-07-10
#>
#> Link : Cumulative logit
#>
#> Local Odds Ratios:
#> Structure: category.exch
#> Model: 3way
#>
#> call:
#> ordLORgee(formula = y ~ factor(time) + factor(trt) + factor(baseline),
#> data = arthritis, id = id, repeated = time)
#>
#> Summary of residuals:
#> Min. 1st Qu. Median Mean 3rd Qu. Max.
#> -0.5176739 -0.2380475 -0.0737290 -0.0001443 -0.0066846 0.9933154
#>
#> Number of Iterations: 6
#>
#> Coefficients:
#> Estimate san.se san.z Pr(>|san.z|)
#> beta10 -1.84003 0.38735 -4.7504 < 2e-16 ***
#> beta20 0.27712 0.34841 0.7954 0.42639
#> beta30 2.24779 0.36509 6.1568 < 2e-16 ***
#> beta40 4.54824 0.41994 10.8307 < 2e-16 ***
#> factor(time)3 -0.00079 0.12178 -0.0065 0.99485
#> factor(time)5 -0.36050 0.11413 -3.1586 0.00159 **
#> factor(trt)2 -0.50463 0.16725 -3.0173 0.00255 **
#> factor(baseline)2 -0.70291 0.37861 -1.8565 0.06338 .
#> factor(baseline)3 -1.27558 0.35066 -3.6376 0.00028 ***
#> factor(baseline)4 -2.65579 0.41039 -6.4714 < 2e-16 ***
#> factor(baseline)5 -3.99555 0.53246 -7.5040 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Local Odds Ratios Estimates:
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [2,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [3,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [4,] 0.000 0.000 0.000 0.000 1.919 1.919 1.919 1.919 2.484 2.484 2.484 2.484
#> [5,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [6,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [7,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [8,] 1.919 1.919 1.919 1.919 0.000 0.000 0.000 0.000 2.465 2.465 2.465 2.465
#> [9,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [10,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [11,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#> [12,] 2.484 2.484 2.484 2.484 2.465 2.465 2.465 2.465 0.000 0.000 0.000 0.000
#>
#> p-value of Null model: < 0.0001
The 95% Wald confidence intervals for the regression parameters are
confint(fitord)
#> 2.5 % 97.5 %
#> beta10 -2.5992134 -1.08084855
#> beta20 -0.4057572 0.95999854
#> beta30 1.5322296 2.96335073
#> beta40 3.7251701 5.37130863
#> factor(time)3 -0.2394781 0.23790571
#> factor(time)5 -0.5841988 -0.13680277
#> factor(trt)2 -0.8324304 -0.17683500
#> factor(baseline)2 -1.4449754 0.03916401
#> factor(baseline)3 -1.9628588 -0.58829522
#> factor(baseline)4 -3.4601391 -1.85143755
#> factor(baseline)5 -5.0391534 -2.95195213
To illustrate model comparison, consider another model with age and
sex as additional covariates:
fitord1 <- update(fitord, formula = . ~ . + age + factor(sex))
waldts(fitord, fitord1)
#> Goodness of Fit based on the Wald test
#>
#> Model under H_0: y ~ factor(time) + factor(trt) + factor(baseline)
#> Model under H_1: y ~ factor(time) + factor(trt) + factor(baseline) + age + factor(sex)
#>
#> Wald Statistic = 3.8313, df = 2, p-value = 0.1472
gee_criteria(fitord, fitord1)
#> QIC CIC RJC QICu Parameters
#> fitord 1268.444 1268.375 11.0347 1.2779 11
#> fitord1 1279.759 1279.582 13.0885 0.9964 13
According to the Wald test, there is no evidence of no difference
between the two models. The QICu criterion suggest that fitord should
be preferred over fitord1.
Getting help
The statistical methods implemented in multgee are described in
Touloumis et al. (2013). A detailed description of the functionality of
multgee can be found in Touloumis (2015). Note that an updated version
of this paper also serves as a vignette:
browseVignettes("multgee")
How to cite
To cite 'multgee' in publications, please use:
Touloumis A. (2015). "R Package multgee: A Generalized Estimating
Equations Solver for Multinomial Responses." _Journal of Statistical
Software_, *64*(8), 1-14.
<https://www.jstatsoft.org/index.php/jss/article/view/v064i08>.
A BibTeX entry for LaTeX users is
@Article{,
title = {{R} Package {multgee}: A Generalized Estimating Equations Solver for Multinomial Responses},
author = {{Touloumis A.}},
journal = {Journal of Statistical Software},
year = {2015},
volume = {64},
number = {8},
pages = {1-14},
url = {https://www.jstatsoft.org/index.php/jss/article/view/v064i08},
}
To cite the methodology implemented in 'multgee' in publications,
please use:
Touloumis A., Agresti A., Kateri M. (2013). "GEE for multinomial
responses using a local odds ratios parameterization." _Biometrics_,
*69*(3), 633-640. <https://doi.org/10.1111/biom.12054>.
A BibTeX entry for LaTeX users is
@Article{,
title = {GEE for multinomial responses using a local odds ratios parameterization},
author = {{Touloumis A.} and {Agresti A.} and {Kateri M.}},
journal = {Biometrics},
year = {2013},
volume = {69},
number = {3},
pages = {633-640},
url = {https://doi.org/10.1111/biom.12054},
}
References
Touloumis, A. (2015) [R Package multgee: A Generalized Estimating
Equations Solver for Multinomial
Responses](https://www.jstatsoft.org/v064/i08). *Journal of Statistical
Software*, **64**, 1–14.
Touloumis, A., Agresti, A. and Kateri, M. (2013) [GEE for Multinomial
Responses Using a Local Odds Ratios
Parameterization](https://onlinelibrary.wiley.com/doi/10.1111/biom.12054/full).
*Biometrics*, **69**, 633–640.
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