Flexible Marginalized Models for Binary Correlated Outcomes.
binaryMM: Fitting Flexible Marginalized Models for Binary Correlated Outcomes
The binaryMM package allows users to fit marginalized transition and latent variables (mTLV) models for binary correlated data. You can install the development version from GitHub with:
install.packages("devtools")
devtools::install_github("ChiaraDG/binaryMM")
Examples
Fitting Marginalized Models
The function mm allows users to fit marginalized models with a transition and/or a latent term. Users specify the marginal mean model with mean.formula, the transition component of the dependence model with t.formula and the latent variable component of the dependence model with lv.formula. The model below specifies both a transition and a latent variable term in the dependence model:
mod.mtlv <- mm(mean.formula = thought ~ month*gender + month*age,
t.formula = ~1, lv.formula = ~1,
data = madras, id = id)
Results from the model above can be displayed using the summaryfunction:
#>
#> Class:
#> MMLong
#>
#> Call:
#> mm(mean.formula = thought ~ month * gender + month * age, lv.formula = ~1,
#> t.formula = ~1, id = id, data = madras)
#>
#> Information Criterion:
#> AIC BIC logLik Deviance
#> 680.1283 699.7631 -332.0642 664.1283
#>
#> Marginal Mean Parameters:
#> Estimate Model SE Chi Square Pr(>Chi)
#> (Intercept) 1.327440 0.434588 9.3299 0.002255
#> month -0.367564 0.077443 22.5268 2.072e-06
#> gender -0.282497 0.402015 0.4938 0.482241
#> age -0.732176 0.436180 2.8177 0.093228
#> month:gender -0.111740 0.078306 2.0362 0.153591
#> month:age 0.117705 0.080870 2.1184 0.145536
#>
#> Association Parameters:
#> Estimate Model SE Chi Square Pr(>Chi)
#> gamma:(Intercept) 2.511119 0.303963 68.2486 <2e-16
#> log(sigma):(Intercept) 0.074494 0.244870 0.0925 0.761
#>
#> Number of clusters: 86
#> Maximum cluster size: 12
#> Convergence status (nlm code): 1
#> Number of iterations: 50
User can speficy a dependence model with a transition term only with the code below:
mod.mt <- mm(mean.formula = thought ~ month*gender + month*age,
t.formula = ~1, lv.formula = NULL,
data = madras, id = id)
summary(mod.mt)
#>
#> Class:
#> MMLong
#>
#> Call:
#> mm(mean.formula = thought ~ month * gender + month * age, t.formula = ~1,
#> id = id, data = madras)
#>
#> Information Criterion:
#> AIC BIC logLik Deviance
#> 688.3789 705.5594 -337.1895 674.3789
#>
#> Marginal Mean Parameters:
#> Estimate Model SE Chi Square Pr(>Chi)
#> (Intercept) 1.183683 0.444318 7.0971 0.007721
#> month -0.342857 0.081841 17.5501 2.798e-05
#> gender -0.141884 0.416152 0.1162 0.733147
#> age -0.649770 0.449183 2.0925 0.148021
#> month:gender -0.143788 0.081853 3.0859 0.078975
#> month:age 0.111555 0.085896 1.6867 0.194040
#>
#> Association Parameters:
#> Estimate Model SE Chi Square Pr(>Chi)
#> gamma:(Intercept) 3.16583 0.23014 189.23 < 2.2e-16
#>
#> Number of clusters: 86
#> Maximum cluster size: 12
#> Convergence status (nlm code): 1
#> Number of iterations: 22
Generate Outcome Data under a Marginalized Model Framework
The function GenerateBinayY in the binaryMM package allows users to generate outcome data under a marginalized model framework. The code below shows how the data can be generated. Note that the output of GenerateBinayY is the longitudinal outcome vector.
set.seed(1)
N = 100
nclust = sample( seq(10,10), N, replace=TRUE)
id = rep(seq(N), nclust)
Xe = rep(rbinom(N,size=1,prob=.5), nclust) # binary exposure
time = unlist( sapply( as.list(nclust), function(ZZ) seq(ZZ)-1 ) )
data = data.frame(id, time, Xe)
data = data[order(data$id, data$time),]
Y = GenBinaryY(mean.formula=~time*Xe, lv.formula=~1, t.formula=~1,
beta=c(-2.5, 0.25, 0.25, 0.1), sigma=1, gamma=1, id=id, data=data, q=20, Yname = "binY")