MCDM Approach to Evaluation of Goodness of Fit of Statistical Models

Today, various models with different estimation methods are introduced and used in data modeling. The appropriateness of each method of estimating statistical models in the fit of a dataset is based on a specific goodness-of-fit criterion (or a specific objective function). Also, the goodness-of-fit index of any statistical model (including classical or fuzzy regression models) is defined and formulated according to the structure of that model. Therefore, using and applying only one criterion to compare the goodness-of-fit of a diverse set of statistical models leads to oblique/biased and directional decisions. In fact, such a process leads to prioritization of the models that their objective functions are the same as the evaluation criterion and/or their objective functions are structurally proportional to the evaluation criteria. Therefore, considering only one-criterion to evaluate the goodness-of-fit of the models deprives them of the possibility of a fair and equitable comparison, which is very challenging. Our main goal in this paper is to provide and propose an appropriate framework in the context of multi-criteria decision making to overcome the challenge. In this method, it is possible to aggregate a wide range of evaluation criteria from different point of views to generate a generalized evaluation criterion in order to identify the optimal model.Finally, the proposed approach is employed to rank the fit of 22 different fuzzy regression models.