By James S. Hodges

ISBN-10: 143986683X

ISBN-13: 9781439866832

ISBN-10: 1439866848

ISBN-13: 9781439866849

''This ebook covers a variety of statistical versions, together with hierarchical, hierarchical generalized linear, linear combined, dynamic linear, smoothing, spatial, and longitudinal. It offers a framework for expressing those richly parameterized versions jointly in addition to instruments for exploring and analyzing the result of becoming the versions to facts. It extends the traditional conception of linear types and illustrates theRead more...

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**Extra resources for Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects**

**Sample text**

They are too disparate and they are developing too quickly. Having made that unsexy concession, there does seem to be a good place to start. Many of the new methods are now undergoing a process of unification analogous to the unifications that produced generalized linear models and, even earlier, the projection theory of linear models. The unification of models with random effects — so far — consists of a few competing syntaxes for expressing a large class of models and a method for fitting models expressed in each syntax.

To answer this question, each eGFR was compared separately to iGFR, using the following analysis. I describe the simplest analysis; variants included a covariate describing steroid use and analyses of subsets of subjects. The dataset included two observations (“cases”) per subject per annual visit, one for iGFR and one for eGFR. The mixed linear model fit a straight line in time (visit number) for each combination of a subject and a GFR method (iGFR or eGFR). For each subject these four quantities — a slope and intercept for each method — were treated as an iid draw from a 4-variate normal distribution.

Examples of this unification include Robinson (1991) and Ruppert et al. (2003). This class of models is rich enough to be interesting and close enough to single-error-term linear models to allow many insights and methods to be borrowed or adapted. A theory of richly parameterized linear models needs more than a syntax and a computing method. It needs to explain things that happen when these models are used to analyze data, to provide ways to detect problems, and when possible, to show how to mitigate or avoid those problems.

### Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects by James S. Hodges

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