MargCond {MargCond}

Function to fit joint marginal-conditional models for longitudinal multivariate data.

Description

Produces an object of class "MargCond" which is a marginal-conditional multivariate model.

Usage

MargCond(formula, data, ID, tol = 1e-04, max.iter = 50, 
       corstr = "independence", silent = F)

Arguments

formula

a two-sided linear formula object similar to those in lmer.

data

a data frame in which to interpret the variables occuring in the formula.

ID

a vector which identifies the clusters. The length of ID should be the same as the number of observations. Data are assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula.

tol

the tolerance used in the fitting algorithm.

max.iter

the maximum number of iterations for the ES algorithm.

corstr

a character string specifying the correlation structure. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured"

silent

a logical variable controlling whether an indication at each iteration is printed.

Details

The joint marginal-conditional model

Care should be taken when specifying the random effects structure (see the singular models section of https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html). As initial estimates for the expectation-substitution algorithm are taken from the univariate mixed model fits, we recommend that these models be fit separately first and examined to ensure that they are not over parameterized.

Value

An object of class "MargCond" representing the fit.

An object of class "MargCond" is a list containing the following components:

coefficients

a named vector of coefficients.

sigma

a named vector of outcome error standard deviations.

SE

a vector of coefficient, random effect, and error standard deviations.

residuals

the residuals, that is response minus fitted values.

working.correlation

the working correlation returned by the GEE step at convergence.

rand.eff

the random effect covariance matrix.

outcomes

vector of outcome names

Call

the matched call.

v.cov

the scaled covariance matrix of theta

obs

the total number of observations

groups

the total number of clusters

converge

logical indicator of whether the expectation-substitution algorithm converged (i.e. the difference between each element of theta from the previous iteration is smaller than tol, and the number of iterations is less than max.iter).

References

Proudfoot J. A., Faig W., Natarajan L., and Xu R. (2018) A joint marginal-conditional model for multivariate longitudinal data. Statistics in Medicine. https://doi.org/10.1002/sim.7552

See Also

gee, lmer.

Examples

set.seed(2112)
NN = 80
n_times = 1:3

## Simulating some data
simdat <- simDat(n = NN, 
                 fixed_effects = list(c(1, 1, 2), c(1.5, 1, 3)), 
                 rand_effects = list(1, 1),
                 error_var = c(4, 4),
                 error_structure = 'normal',
                 rho = .35,
                 times = n_times,
                 X = cbind(rep(1, NN * length(n_times)), 
                           rnorm(NN * length(n_times), 0, 2), 
                           rbinom(NN * length(n_times), 1, .5)),
                 Z = cbind(rep(1, NN * length(n_times))))
                  
## Adding random missing values
aa <- sample(1:nrow(simdat), 10, replace = TRUE)
bb <- sample(1:7, 10, replace = TRUE)
for (i in 1:length(aa)) {
  simdat[aa[i], bb[i]] <- NA
}

## A fit for this simulated multivariate longitudinal data, 
## including a random intercept and exchangeable correlation 
## structure.
summary(MargCond(c(outcome1, outcome2) ~ X2 + X3 + (1 | ID), 
        data = simdat, ID = simdat$ID, corstr = "exchangeable"))