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Marginal model : ウィキペディア英語版
Marginal model
In statistics, marginal models (Heagerty & Zeger, 2000) are a technique for obtaining regression estimates in multilevel modeling, also called hierarchical linear models.
People often want to know the effect of a predictor/explanatory variable ''X'', on a response variable ''Y''. One way to get an estimate for such effects is through regression analysis.
==Why the name marginal model?==
In a typical multilevel model, there are level 1 & 2 residuals (R and U variables). The two variables form a joint distribution for the response variable (Y_). In a marginal model, we collapse over the level 1 & 2 residuals and thus ''marginalize'' (see also conditional probability) the joint distribution into a univariate normal distribution. We then fit the marginal model to data.
For example, for the following hierarchical model,
:level 1: Y_ = \beta_ + R_, the residual is R_, and var(R_) = \sigma^2
:level 2: \beta_ = \gamma_ + U_, the residual is U_, and var(U_) = \tau_0^2
Thus, the marginal model is,
:Y_ \sim N(\gamma_,(\tau_0^2+\sigma^2))
This model is what is used to fit to data in order to get regression estimates.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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