A joint model for multivariate mixed ordinal and continuous outcomes with potentially non-random missing values in both types of responses is proposed. A full likelihood-based approach is used to obtain maximum likelihood estimates of the model parameters. Some modified Pearson residuals are also introduced where the correlation between responses are taken into account. The joint modelling of responses with the possibility of missing values requires caution since the interpretation of the fitted model highly depends on the missing mechanism assumptions that are unexaminable in a fundamental sense. A common way to investigate the influence of perturbations of model components on the key results of the analysis is to compare the results derived from the original and perturbed models using an influence maximal normal curvatures. For This, influence of a small perturbation of elements of the covariance structure of the model on maximal normal curvature is also studied. To illustrate the utility of the proposed model, a large data set excerpted from the British Household Panel Survey (BHPS) is analyzed. For these data, the simultaneous effects of some covariates on life satisfaction, income and the amount of money spent on leisure activities per month as three mixed correlated responses are explored.
Samani, Ehsan B. and Ganjali, M.
A Multivariate Latent Variable Model for Mixed – Data from Continuous and Ordinal Responses with Possibility of Missing Responses,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 5,
2, Article 17.
Available at: https://digitalcommons.pvamu.edu/aam/vol5/iss2/17