We consider the application of Markov chain Monte Carlo (MCMC) estimation methods to random-effects models and in particular the family of discrete time survival models. Survival models can be used in many situations in the medical and social sciences and we illustrate their use through two examples that differ in terms of both substantive area and data structure. A multilevel discrete time survival analysis involves expanding the data set so that the model can be cast as a standard multilevel binary response model. For such models it has been shown that MCMC methods have advantages in terms of reducing estimate bias. However, the data expansion results in very large data sets for which MCMC estimation is often slow and can produce chains that exhibit poor mixing. Any way of improving the mixing will result in both speeding up the methods and more confidence in the estimates that are produced. The MCMC methodological literature is full of alternative algorithms designed to improve mixing of chains and we describe three reparameterization techniques that are easy to implement in available software. We consider two examples of multilevel survival analysis: incidence of mastitis in dairy cattle and contraceptive use dynamics in Indonesia. For each application we show where the reparameterization techniques can be used and assess their performance.
These findings suggest modafinil as a well-tolerated and potentially effective agent in combination with fluoxetine in the management of patients with major depression.
Multivariate circular observations, i.e. points on a torus arise frequently in fields where instruments such as compass, protractor, weather vane, sextant or theodolite are used. Multivariate wrapped models are often appropriate to describe data points scattered on p−dimensional torus. However, the statistical inference based on such models is quite complicated since each contribution in the loglikelihood function involves an infinite sum of indices in Z p , where p is the dimension of the data. To overcome this problem, for moderate dimension p, we propose two estimation procedures based on Expectation-Maximisation and Classification Expectation-Maximisation algorithms. We study the performance of the proposed techniques on a Monte Carlo simulation and further illustrate the advantages of the new procedures on three real-world data sets.
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