Introduction to the Modeling and Analysis of Complex Systems

2.4. WHAT ARE GOOD MODELS? 212.4 What Are Good Models?You can create various kinds of models for a system, but useful ones have several importantproperties. Here is a very brief summary of what a good model should look like:A good model is simple, valid, and robust.Simplicity of a model is really the key essence of what modeling is all about. Themain reason why we want to build a model is that we want to have a shorter, simplerdescription of reality. As the famous principle of Occam’s razor says, if you have twomodels with equal predictive power, you should choose the simpler one. This is not atheorem or any logically proven fact, but it is a commonly accepted practice in science.Parsimony is good because it is economical (e.g., we can store more models within thelimited capacity of our brain if they are simpler) and also insightful (e.g., we may finduseful patterns or applications in the models if they are simple). If you can eliminate anyparameters, variables, or assumptions from your model without losing its characteristicbehavior, you should.Validity of a model is how closely the model’s prediction agrees with the observedreality. This is of utmost importance from a practical viewpoint. If your model’s predictiondoesn’t reasonably match the observation, the model is not representing reality and isprobably useless. It is also very important to check the validity of not only the predictionsof the model but also the assumptions it uses, i.e., whether each of the assumptionsused in your model makes sense at its face value, in view of the existing knowledge aswell as our common sense. Sometimes this “face validity” is more important in complexsystems modeling, because there are many situations where we simply can’t conduct aquantitative comparison between the model prediction and the observational data. Evenif this is the case, you should at least check the face validity of your model assumptionsbased on your understanding about the system and/or the phenomena.Note that there is often a trade-off between trying to achieve simplicity and validity of amodel. If you increase the model complexity, you may be able to achieve a better fit to theobserved data, but the model’s simplicity is lost and you also have the risk of overfitting—that is, the model prediction may become adjusted too closely to a specific observation atthe cost of generalizability to other cases. You need to strike the right balance betweenthose two criteria.Finally, robustness of a model is how insensitive the model’s prediction is to minor variationsof model assumptions and/or parameter settings. This is important because thereare always errors when we create assumptions about, or measure parameter values from,