High Dimensional Multivariate Mixed Models for Binary Questionnaire Data

Abstract

Questionnaires that are used to measure the effect of an intervention often consist of different sets of items, each set possibly measuring another concept. Mixed models with set-specific random effects are a flexible tool to model the different sets of items jointly. However, computational problems typically arise as the number of sets increases. This is especially true when the random-effects distribution cannot be integrated out analytically, as with mixed models for binary data. A pairwise modelling strategy, in which all possible bivariate mixed models are fitted and where inference follows from pseudolikelihood theory, has been proposed as a solution. This approach has been applied to assess the effect of physical activity on psychocognitive functioning, the latter measured by a battery of questionnaires. Copyright 2006 Royal Statistical Society.

A joint modeling and estimation method for multivariate longitudinal data with mixed types of responses to analyze physical activity data generated by accelerometers

“…For joint modeling approach, most of the current multivariate methods focus on 1 or 2 types of outcomes. 3 For example, Fieuws and Verbeke 4 and Fieuws et al 5 respectively discuss the methods to handle multiple normal and binary outcomes, Gueorguieva and Agresti 6 develop a modeling strategy for one normal and one binary responses, and Buu et al 7 propose a joint model for one count and one binary variables to handle zero-inflated count data. These models are limited in practice.…”

“…4 For models of nonlinear variables, large-dimensional integration problems are more difficult to handle in the presence of multiple random effects. For example, the maximum likelihood approach using Monte Carlo or Gauss-Hermite quadrature is computationally extremely difficult for the integration of 7 random effects in Fieuws et al 5 For our accelerometer data, we respectively set a random intercept and a random slope for 8 variables. Therefore, our model involves 2 × 8 = 16 dimensional random effects, and it exceeds the limit for maximum likelihood.…”

Bayesian inference for joint modelling of longitudinal continuous, binary and ordinal events

“…Geys et al 17 utilised the Plackett-Dale approach to deal with such bivariate outcomes, which was later extended to ordinal and continuous outcomes by Faes et al 18 On the other hand, the generalised linear mixed models are also commonly used in analysing combined continuous and binary/ordinal outcomes in longitudinal or clustered data, and PROC NLMIXED in SAS may help to calculate the estimates of parameters. Fieuws and Verbeke et al 19,20 proposed pairwise fitting methods for multivariate longitudinal profiles, of which the types of outcomes are usually only binary and/or continuous. Jorgensen et al 21 proposed a class of state-space models for multivariate longitudinal data with mixed types where the outcomes may have different distributions.…”

On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes

“…[1][2][3] More recently, the approach has been extended to multivariate nonlinear models for outcomes with normal residuals 4,5 and multivariate generalized linear models. [6][7][8][9][10][11][12][13] We describe a multivariate generalized linear mixed model for multiple outcomes which may be nonnormal and differently distributed and evaluate random coefficient associations among the outcomes, beginning with simple correlation coefficients discussed by others. 7,[9][10][11][12][13] A series of extensions and novel contributions follow that together inform procedures for estimating and testing random coefficient associations.…”