Some aspects of complex statistical dependencies - Kartsonaki, C (2014)
In the first part parametric models for which the likelihood is intractable are discussed. A method for fitting such models when simulation from the model is possible is presented, which gives estimates that are linear functions of a possibly large set of candidate features. A combination of simulations based on a fractional design and sets of discriminant analyses is used to find an optimal estimate of the parameter vector and its covariance matrix. The procedure is an alternative to Approximate Bayesian Computation and Indirect Inference methods. A way of assessing goodness of fit is briefly described. In the second part the aim is to give a relationship between the effect of one or more explanatory variables on the response when adjusting for an intermediate variable and when not. This relationship is examined mainly for the cases in which the response depends on the two variables via a logistic regression or a proportional hazards model. Some of the theoretical results are illustrated using a set of data on prostate cancer. Then matched pairs with binary outcomes are discussed, for which two methods of analysis are described and compared.