Helped so much. Many thanks to PaigeMiller (2014.10.13), and also to lvm (2014.10.13), for the comments extremely valuable. The word “distribution” is very expressive surely. To avoid unnecessary proliferation of nomenclature, acronym GdLM proposed for GLIM in SAS purposely in this question may be read, case to case, Gd_distribution, or Gd(distribution), or furthermore, Gd(link-function&distribution), etc., linear model, or linear mixed model, etc. Any linear model is built of the linear component, direct or anyway-linked, fixed or random factor effect, fluctuation, and the probabilistic distribution behind a random or fluctuation element. These components are classified to fixed and random groups to be basis of the analysis. Among various linear models, the Goodnight’s old classical GLM seems to be the unique prototype of models. I like to stick it to understand it enough. Tadao SHIBAYAMA (2014.10.15).
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