|
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 (). 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: , the residual is , and :level 2: , the residual is , and Thus, the marginal model is, : 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)』 ■ウィキペディアで「Marginal model」の詳細全文を読む スポンサード リンク
|