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Abstract: The improvement of the convergence rate of the parameter estimation process is dealt with in the context of disease mapping when generalized linear mixed models are used. Two transformations of the random effects covariance matrix parameters are proposed with the aim of forcing the resulting estimates into their domain. The increased convergence rate using these transformations is shown through a simulation study. The approach is illustrated with reference to Scottish lip cancer data and insulin-dependent diabetes mellitus data from Catalonia. Both datasets suffer problems of convergence which are solved using the transformed parameters. [Copyright &y& Elsevier]