New PDF release: A generalized moverstayer model for panel data

By Cook R. J., Kalbfleisch J. D.

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This unit deviance is regular because it is twice continuously differentiable. t. μ are, respectively, ∂2d ∂d = 2. = −2(y − μ), and ∂μ ∂μ2 It follows that the unit variance function is V (μ) = 2 2 = 1. 2 (Poisson Distribution). 2, express the Poisson density with mean parameter μ as follows: p(y; μ) = μy −μ e , y ∈ {0, 1, . }; μ ∈ Ω = (0, ∞), y! or equivalently p(y; μ) = 1 exp{y log μ − μ}. y! 28 2 Dispersion Models Note that the exponent {y log μ − μ} is not a deviance function because it does not equal to zero when y = μ.

To avoid the difficulty of specifying a full probability model, the second approach takes a compromise; that is, it only specifies the first two moments of the data distribution. This approach constitutes the minimal requirements for a quasi-likelihood inference procedure. Although the resulting estimation is less efficient than the MLE, it enjoys the robustness against model misspecifications on higher moments. This quasi-likelihood inference would be the choice when robustness appears to be more appealing than efficiency in a given data analysis.

The dispersion models provide a rich class of one-dimensional parametric distributions for various data types, including those commonly considered in the GLM analysis. In effect, error distributions in the GLMs form a special subclass of the dispersion models, which are the exponential dispersion models. This means that the GLMs considered in this chapter, as well as in the entire book, encompass a wider scope of GLMs than those outlined in McCullagh and Nelder’s (1989) book. Two special examples are the von Mises distribution for directional (circular or angular) data and the simplex distribution for compositional (or proportional) data, both of which are the dispersion models but not the exponential dispersion models.

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A generalized moverstayer model for panel data by Cook R. J., Kalbfleisch J. D.

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