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Latent variable model for mixed correlated power series and ordinal longitudinal responses with non ignorable missing values. (English) Zbl 1462.62326

Summary: We propose a joint model based on a latent variable for analyzing mixed power series and ordinal longitudinal data with and without missing values. A bivariate probit regression model is used for the missing mechanisms. Random effects are used to take into account the correlation between longitudinal responses. A full likelihood-based approach is used to yield maximum-likelihood estimates of the model parameters. Our model is applied to a medical data set, obtained from an observational study on women where the correlated responses are the ordinal response of osteoporosis of the spine and the power series response of the number of joint damages. Sensitivity analysis is also performed to study the influence of small perturbations of the parameters of the missing mechanisms and overdispersion of the model on likelihood displacement.

MSC:

62H12 Estimation in multivariate analysis
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J02 General nonlinear regression
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