Abstract
Background: The linear mixed model is one of the common models used to analyze the longitudinal data; it may comprise of Separate (Univariate), joint Bivariate or joint multivariate linear mixed model, which is predicated on the number of response variables incorporated in the analysis. Adjusting for correlation matrix and covariance matrix between and within subjects is one reason why modern longitudinal data analysis techniques are deemed more appropriate than some of the previous methods of analysis. Some studies assume that the correlation between observations is zero. However, it is unlikely that repeated measurements on the same individual will actually be independent. To that end, comparing the different linear mixed models and identifying the appropriate model demonstrates the evolution of patients with CHF.Methods: In this study the separate, bivariate and multivariate linear mixed models were analyzed with different covariance and correlation structures. The parameters in the models were estimated by maximum likelihood estimation and restricted maximum likelihood estimation techniques. The models were compared by AIC, BIC, and Log-likelihood ratio test. Results: The models with unstructured covariance structure for random effects and autoregressive order one for serial correlation structure had small AIC, BIC and -2LL and standard errors. Separate models had high AIC, BIC and -2LL and standard errors than bivariate and multivariate had small AIC, BIC and -2LL and standard errors than all models. Conclusions: Finally, a multivariate linear mixed model with autoregressive order one correlation structure and unstructured covariance structure for random effects, to consider within and between patients’ variations, was considered as the best model to depict the evolution of patients with congestive heart failure.
Covariance Structure Maximum-Likelihood Estimates in Compound Gaussian Noise: Existence and Algorithm Analysis