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Full article: Robust Inference and Modeling of Mean and Dispersion for Generalized Linear Models
Source: amstat.tandfonline.com
Article summary:
1. Generalized Linear Models (GLMs) are a unified way of modeling the mean response when the responses follow an exponential family distribution.
2. To model the dispersion in a GLM framework, Efron proposed the family of double exponential distributions which includes an additional parameter to model the dispersion.
3. Other approaches to model the mean response and the dispersion simultaneously have been proposed in the literature, such as extended quasi-likelihood, pseudo likelihood, double generalized linear models, and dispersion models.
Article analysis:
The article provides a comprehensive overview of Generalized Linear Models (GLMs) and their use for modeling mean response and dispersion. The article is well-structured and clearly explains how GLMs can be used to account for over- or underdispersion in datasets. It also provides an overview of other approaches that have been proposed in the literature for modeling mean response and dispersion simultaneously.
The article is reliable and trustworthy as it provides evidence for its claims by citing relevant research papers from reputable sources. Furthermore, it does not contain any promotional content or partiality towards any particular approach or method mentioned in the article. The article also does not present any risks associated with using GLMs or other approaches mentioned in the article without noting them explicitly.
However, there are some points that could be explored further in order to make this article more comprehensive. For example, while it mentions various approaches that have been proposed for modeling mean response and dispersion simultaneously, it does not provide any comparison between these approaches or discuss their relative merits and drawbacks. Additionally, while it mentions possible link functions for g (the parameter used to model dispersion), it does not provide any discussion on why certain link functions may be more suitable than others depending on the dataset being analyzed or what factors should be taken into consideration when choosing a link function for g. Finally, while it mentions that maximum likelihood inference is sensitive to outliers in data, it does not provide any discussion on how one can identify outliers or what techniques can be used to mitigate their effects on inference results obtained from maximum likelihood estimation methods.
Topics for further research:
Comparison of mean response and dispersion modeling approaches
Choosing a link function for g
Identifying outliers in data
Mitigating effects of outliers on maximum likelihood inference
Advantages and disadvantages of mean response and dispersion modeling approaches
Maximum likelihood estimation methods for GLMs