is certainly true is that if the data set is changed in any way, whether by omitting observations, taking logs, or anything else, model selection must be explored again, as the results previously obtained might not be appropriate for the new form of the data.
Although best subsets algorithms and modern computing power have made automatic model selection more feasible than it once was, they are still limited computationally to a maximum of roughly predictors. In recent years, it has become more common for a data analyst to be faced with data sets with hundreds or thousands of predictors, making such methods infeasible. Recent work has focused on alternatives to least squares called regularization methods, which can (possibly) be viewed as effectively variable selectors, and are feasible for very large numbers of predictors. These methods are discussed further in Chapter 14.
KEY TERMS
A modified version of the Akaike Information Criterion () that guards against overfitting in small samples. It is used to compare models when performing model selection.Best subsets regressionA procedure that generates the best‐fitting models for each number of predictors in the model.Chow testA statistical (partial ‐)test for determining whether a single regression model can be used to describe the regression relationships when two groups are present in the data.CollinearityWhen predictor variables in a regression fit are highly correlated with each other.Constant shift modelRegression models that have different intercepts but the same slope coefficients for the predicting variables for different groups in the data.Indicator variableA variable that takes on the values or , indicating whether a particular observation belongs to a certain group or not.Interaction effectWhen the relationship between a predictor and the target variable differs depending on the group in which an observation falls.Linear restrictionA linear condition on the regression coefficients that defines a special case (subset) of a larger unrestricted model.Mallows'A criterion used for comparing several competing models to each other. It is designed to estimate the expected squared prediction error of a model.Model selection uncertaintyThe variability in results that comes from the fact that model selection is an iterative process, arrived at after examination of several models, and therefore the final model chosen is dependent on the particular sample drawn from the population. Significance levels, confidence intervals, etc., are not exact, as they depend on a chosen model that is itself random. This should be recognized when interpreting results.OverfittingIncluding redundant or noninformative predictors in a fitted regression.Partial‐test‐test used to compare the fit of an unrestricted model to that of a restricted model (defined by a linear restriction), in order to see if the restricted model is adequate to describe the relationship in the data.Pooled modelA single model fit to the data that ignores group classification.ReplicabilityThe finding that a scientific experiment or modeling process obtains a consistent result when it is repeated.UnderfittingOmitting informative essential variables in a fitted regression.Variance inflation factorA statistic giving the proportional increase in the variance of the sample regression coefficient for a particular predictor due to the linear association of the predictor with other predictors.
Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal, WebMoney, Яндекс.Деньги, QIWI Кошелек, бонусными картами или другим удобным Вам способом.
is certainly true is that if the data set is changed in any way, whether by omitting observations, taking logs, or anything else, model selection must be explored again, as the results previously obtained might not be appropriate for the new form of the data.
