Parsimonious models are simple models with great explanatory predictive power. They explain data with a minimum number of parameters, or predictor variables. The idea us according to the law of briefness. The law states that you should use no more “things” than necessary; In the case of parsimonious models, those “things” are parameters.
There is generally a tradeoff between goodness of fit and parsimony: low parsimony models (i.e. models with many parameters) tend to have a better fit than high parsimony models. This is not usually a good thing; adding more parameters usually results in a good model fit for the data at hand, but that same model will likely be useless for predicting other data sets.
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