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In statistics, separation is a phenomenon associated with models for dichotomous or categorical outcomes, including logistic and probit regression. Separation occurs if the predictor (or a linear combination of some subset of the predictors) is associated with only one outcome value when the predictor is greater than some constant. For example, if the predictor ''X'' is continuous, and the outcome ''y'' = 1 for all observed ''x'' > 2. If the outcome values are perfectly determined by the predictor (e.g., ''y'' = 0 when ''x'' ≤ 2) then the condition "complete separation" is said to obtain. If instead there is some overlap (e.g., ''y'' = 0 when ''x'' < 2, but ''y'' has observed values of 0 and 1 when ''x'' = 2) then "quasi-complete separation" obtains. A 2 × 2 table with an empty cell is an example of quasi-complete separation. This observed form of the data is important because it causes problems with estimated regression coefficients. Loosely, a parameter in the model "wants" to be infinite, if complete separation is observed. If quasi-complete separation is the case, the likelihood is maximized at a very large but not infinite value for that parameter. Computer programs will often output an arbitrarily large parameter estimate with a very large standard error. Methods to fit these models include exact logistic regression and "Firth" logistic regression, a bias-reduction method based on a penalized likelihood. ==References== *Albert, A. and Anderson, J.A. (1984). “On the Existence of Maximum Likelihood Estimates in Logistic Regression Models.” Biometrika 71: 1-10. *Heinze, G. and Schemper, M. (2002). "A Solution to the Problem of Separation in logistic regression". ''Statistics in Medicine,'' 21, 2409 - 2419. *Heinze, G. and Ploner, M. (2003). "Fixing the nonconvergence bug in logistic regression with SPLUS and SAS". ''Computer Methods and Programs in Biomedicine'', 71, 181-187. *Heinze, G. (2006). "A comparative investigation of methods for logistic regression with separated or nearly separated data". ''Statistics in Medicine'', 25, 4216-4226. 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「Separation (statistics)」の詳細全文を読む スポンサード リンク
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