Generalized linear hybrid model

Author: Snow Mountain Elephant
Link: https://www.zhihu.com/question/27938684/answer/38730824
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The right to talk about their own understanding.

First of all, the main problem is wrong, GLM generally refers to the generalized linear model, that is, the generalized linear models, rather than the general linear model, that is, generic linear models; GLMM (generalized linear mixed m Odel) is a generalized linear hybrid model.

Generalized linear model GLM is very simple, for example, the efficacy of a drug is related to the dosage of the drug taken. This correlation may be varied, It could be a simple linear relationship (0.1 degrees of fever when you take a pill, two pills fever 0.2 degrees, and so on, this situation is a general linear model, but also may be more complex other relationships, such as exponential relationship (a drug fever 0.1 degrees, two pills fever 0.4 degrees), logarithmic relationship and so on. These complex relationships can generally be transformed into linear relationships through a series of mathematical transformations called generalized linear models. The generalized linear mixed model GLMM is more complex, the GLM request error is random, and glmm the error value is not random, but a certain distribution. For example, we think the effect may be related to the time of the medication, but the correlation is not simply a change in the time of the medication. It is more likely that the degree of random fluctuations in efficacy is related to the duration of the medication. For example, at 10:00 in the morning, everyone is basically in the half full state, at this time take medicine, the same dosage of drugs effect is similar. But at noon, some people have not eaten, some people have eaten, some people drank wine, the result of alcohol and drugs reacted, and some people drank vinegar, vinegar and drugs played another reaction. Obviously, the random error of taking medicine at noon will result in a very large dose. The random error of this effect, rather than the effect itself, changes with time and is distributed in a certain distribution, and must be used in a generalized linear hybrid model.

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