Generalized Estimating Equations by Andreas Ziegler (auth.)

By Andreas Ziegler (auth.)

Generalized estimating equations became more and more renowned in biometrical, econometrical, and psychometrical purposes simply because they triumph over the classical assumptions of records, i.e. independence and normality, that are too restrictive for plenty of problems.

Therefore, the most objective of this booklet is to offer a scientific presentation of the unique generalized estimating equations (GEE) and a few of its extra advancements. in this case, the emphasis is wear the unification of assorted GEE ways. this is often performed by means of varied estimation ideas, the pseudo greatest chance (PML) process and the generalized approach to moments (GMM).

The writer info the statistical beginning of the GEE method utilizing extra normal estimation recommendations. The booklet may well consequently be used as foundation for a path to graduate scholars in records, biostatistics, or econometrics, and may be valuable to practitioners within the comparable fields.

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N let xi be a p × 1 vector of fixed and/or stochastic independent variables. Furthermore, let the T dimensional dependent variable y i given xi be T dimensionally normally distributed, specifically, y i |xi ∼ NT (µi , Σ). , g = id, is chosen as the link function and if B = (β 1 , . . , β T ) ∈ IRp×T is the matrix comprising the parameters of interest, one obtains the multivariate linear regression model by letting µi = η i = B xi . This model can also be formulated in standard notation by letting X i = xi ⊗ IT , which is of dimension T × T p, and the T p × 1 parameter vector β = (β 1 , .

2002). 44 4 Maximum likelihood method The key assumption of ML estimation is the correct specification of the true conditional density f (y i |X i )||β 0 ) in the parameter of interest β 0 . This assumption includes that the link function, the functional form of the independent variables and the independent variables, are all correctly specified. If the distribution f is misspecified, we can still apply the standard ML approach. Under mild regularity conditions, there exists an ML estimator ˆ even under the misspecified model, which is termed a quasi ML (QML) β estimator because quasi is an ML estimator.

J can be repaJ rameterized via β1 = κ21 , β2 = κ21 + κ22 , up to βK = j=1 κ2j . 4 Maximum likelihood estimation in linear exponential families ML estimation is a very general approach, and it is simplified substantially in linear exponential families. We consider n independently but not necessarily identically distributed T -dimensional random vectors y 1 , . . , y n with densities (or probability mass functions for discrete distributions) belonging to the simple linear exponential family f (y i ||ϑ, Ψ ) = exp ϑ y i + bi (y i , Ψ ) − di (ϑ, Ψ ) .

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