Modeling, Model Selection and Multimodel Inference

"A model is a representation of the world, but it is rarely a perfect representation. There will always be some differences between the model and the world, that is some error. If we could build a perfect copy, it would not be a model, it would be a duplicate."

"DATA = MODEL + ERROR"

From "Applying Regression and Correlation" by Miles, J. and Shevlin, M. (2001)

"This book is about making valid inferences from scientific data when a meaningful analysis depends on a model of the information in the data."

"There are many studies to understand our world; models are important because of the parameters in them and relationships expressed between and among variables. These parameters have relevant, useful interpretations, even when they relate to quantities that are not directly observable. Science would be very limited without such unobservables as constructs in models."

"We do not believe that model selection should be treated as an activity that precedes the analysis; rather, model selection is a critical and integral aspect of scientific data analysis that leads to valid inference."

"Often, one first develops a global model (or set of models) and then derives several other plausible candidate (sub)models postulated to represent good approximations to information at hand. This forms the set of candidate models."

"... selection of an estimated "best approximating model" from the a priori set of candidate models."

"Modeling is an art as well as a science and is directed toward finding a good approximating model of the information in empirical data as the basis for statistical inference from those data."

From "Model Selection and Multimodel Inference" by Burnham, K. P. and Anderson, D. R. (2002)