Re: OMEGA matrix

Douglas makes important point in this discussion. That is, the method used to judge parsimony of the model must consider the performance of the model for intended purpose. Consider the parsimony principle: "all things being equal, choose the simpler model". The key is in how to judge the first part of that statement. A model developed based on goodness of fit metrics such as AIC, BIC, or repeated likelihood ratio tests, may be the most parsimonious model for predicting the current data set. This doesn't ensure that the model will be "equal" in performance to more complex models for the purpose of predicting the typical value in an external data set - external cross validation might be required for that conclusion. Further, if the purpose is to develop a model that is a reliable stochastic simulation tool, a simulation-based model checking method should be part of the assessment of "equal" performance when arriving at a parsimonious model. Since most of our modeling goals go far beyond prediction of the current data set, it's necessary to move beyond metrics solely based on objective function and degrees of freedom when selecting a model. In other words, it may be perfectly fine (and even parsimonious) for a model to include more parameters than the likelihood ratio test tells you to, if those parameters improve performance for the intended purpose. Best regards, Marc