Statistical Models in S by J. M. Chambers, T.J. Hastie

By J. M. Chambers, T.J. Hastie

Statistical types in S extends the S language to slot and learn numerous statistical types, together with research of variance, generalized linear versions, additive types, neighborhood regression, and tree-based versions. The contributions of the 10 authors-most of whom paintings within the facts study division at AT&T Bell Laboratories-represent result of study in either the computational and statistical features of modeling info.

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The following rule specifies which factors should be coded by dummy variables and which should be coded by contrasts in producing the columns of the model matrix: Suppose F; is any factor included in term T;. Let T;(il denote the maryin ofT; for factor F;-that is, the term obtained by dropping F; from T;. We say that T;(j) has appeared in the formula if there is some term T;• for i' < i such that T;t contains all the factors appearing in Ti(j)· The usual case is that T;w itself is one of the preceding terms.

CHAPTER 2. STATISTICAL MODELS 26 Nested terms in a model, on the other hand, arise when the levels of one factor are only meaningful within a particular level for some other factor or combination of factors. For example, suppose we have some geographic data in which the variable state defines the state for each location and the factor county indexes counties within each state. Clearly, county was generated by coding whatever county names appeared for each state, so that level 1 of county means something different in different states.

1 Models and Data A road map models part of the earth's surface, attempting to imitate the rdative position of towns, roads, and other features. We use the map to make inferences about where real features are and how to get to them. Architects use both paper drawings and small-scale physical models to imitate the properties of a building. The appearance and some of the practical characteristics of the actual building can be inferred from the models. Chemists use "wire frame" models of molecules (by either constructing them or displaying them through computer graphics) to imitate theoretical properties of the molecules that, in turn, can be used to predict the behavior of the real objects.

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