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")