generalized linear model GLM R reduced Model update

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一般化線型モデル generalized linear model; GLM

一般化線型モデル generalized linear model; GLM

Rを使ったデータ処理 （尤度比検定） reduced. Model <- update( poisson. Reg. Result, ~. - L ) #poisson.

Rを使ったデータ処理 （尤度比検定） reduced. Model <- update( poisson. Reg. Result, ~. - L ) #poisson. Reg. Resultから変数Lを除いたモデルの当てはめを行い、 #結果をreduced. Model に入れる。 summary( reduced. Model ) #reduced. Model の要約の出力 #null devianceとresidual devianceが等しくなっている anova( reduced. Model, poisson. Reg. Result, test = "Chi" ) #poisson. Reg. Result、 reduced. Modelの対数尤度の差→尤度比検定 Model 1: offspring. Shoot. Number ~ 1 Model 2: offspring. Shoot. Number ~ L Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 6 7. 1843 2 5 0. 9616 1 6. 2227 0. 0126 2つのモデルに含ま れている変数の数 2つのモデルのresidual devianceと両者の差（この 差が尤度比検定統計量） χ2分布と比較して出したpvalue

例2 ロジスティック回帰 データ準備・グラフ描き survival <- c( rep( 0, 8 ), 1, rep( 0, 3

例2 ロジスティック回帰 データ準備・グラフ描き survival <- c( rep( 0, 8 ), 1, rep( 0, 3 ), 1, 1, 0, 0, 1, 0, rep( 1, 12 ) ) size <- 1: 30 plot( size, survival, xlab = "Size", ylab = "Survival", type = "p" )

Summaryの中身 • • • Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -5. 0527

Summaryの中身 • • • Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -5. 0527 1. 8696 -2. 703 0. 00688 ** size 0. 3487 0. 1219 2. 861 0. 00422 ** --Signif. codes: 0 ‘***’ 0. 001 ‘**’ 0. 01 ‘*’ 0. 05 ‘. ’ 0. 1 ‘ ’ 1 • (Dispersion parameter for binomial family taken to be 1) • • • Null deviance: 41. 455 Residual deviance: 18. 407 AIC: 22. 407 on 29 on 28 degrees of freedom – Null deviance：定数項のみのモデルと飽和したモデル（すべての応答 変数が残差なく説明されるよう、応答変数の個数だけ説明変数を使 ったモデル）の対数尤度の差に-2をかけたもの – Residual deviance：指定したモデルと飽和したモデルの対数尤度の差 に-2をかけたもの Null Deviance 対数尤度に-2を かけたもの Residual Deviance 飽和したモデルの Deviance 指定したモデルの Deviance 定数項のみのモデル のDeviance

Rを使ったデータ処理 （尤度比検定） reduced. Model <- update( logistic. Reg. Result , ~. - size )

Rを使ったデータ処理 （尤度比検定） reduced. Model <- update( logistic. Reg. Result , ~. - size ) #logistic. Reg. Resultから変数sizeを除いたモデルの当てはめを行い、 #結果をreduced. Model に入れる。 summary( reduced. Model ) #reduced. Model の要約の出力 #null devianceとresidual devianceが等しくなっている anova( reduced. Model, logistic. Reg. Result, test = "Chi" ) #logistic. Reg. Result、 reduced. Modelの対数尤度の差→尤度比検定 Model 1: Model 2: Resid. 1 2 survival ~ 1 survival ~ size Df Resid. Dev Df Deviance 29 41. 455 28 18. 407 1 23. 048 2つのモデルに含ま れている変数の数 Pr(>Chi) 2つのモデルのresidual devianceと両者の差（この 差が尤度比検定統計量） 1. 58 e-06 *** χ2分布と比較して出したpvalue

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