Summary
グループ構造のあるデータに対して適用される統計モデリングの枠組み。正規分布に従うグループレベルの誤差を加えることで、グループ間の違いを考慮しながら説明変数の効果(偏回帰係数)を推定する。
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function “lmer”
確率分布:正規分布
パッケージ:lme4
その他:なし
# sample data plot: points are colored by group
Col <- rainbow(10)
plot(Y ~ X, data = dat1, pch = 21, bg = Col[dat1$groupID], col = NA)
# run lmer
fit <- lmer(Y ~ X + (1|factor(dat1$groupID)), data = dat1)
summary(fit)
## Linear mixed model fit by REML ['lmerMod'] ## Formula: Y ~ X + (1 | factor(dat1$groupID)) ## Data: dat1 ## ## REML criterion at convergence: -92.5 ## ## Scaled residuals: ## Min 1Q Median 3Q Max ## -2.18657 -0.65569 -0.01559 0.47664 2.59009 ## ## Random effects: ## Groups Name Variance Std.Dev. ## factor(dat1$groupID) (Intercept) 0.52432 0.7241 ## Residual 0.01156 0.1075 ## Number of obs: 100, groups: factor(dat1$groupID), 10 ## ## Fixed effects: ## Estimate Std. Error t value ## (Intercept) 0.900439 0.230086 3.913 ## X 0.102362 0.003581 28.584 ## ## Correlation of Fixed Effects: ## (Intr) ## X -0.086
function “glmer”
確率分布:ポアソン分布、二項分布、ガンマ分布など
パッケージ:lme4
その他:なし
Poisson
# sample data plot: points are colored by group
Col <- rainbow(10)
plot(Y ~ X, data = dat2, pch = 21, bg = Col[dat2$groupID], col = NA)
# run glmer
fit <- glmer(Y ~ X + (1|factor(dat2$groupID)), data = dat2, family = poisson)
summary(fit)
## Generalized linear mixed model fit by maximum likelihood (Laplace ## Approximation) [glmerMod] ## Family: poisson ( log ) ## Formula: Y ~ X + (1 | factor(dat2$groupID)) ## Data: dat2 ## ## AIC BIC logLik deviance df.resid ## 481.7 489.5 -237.8 475.7 97 ## ## Scaled residuals: ## Min 1Q Median 3Q Max ## -1.72217 -0.65979 -0.05568 0.56604 2.67057 ## ## Random effects: ## Groups Name Variance Std.Dev. ## factor(dat2$groupID) (Intercept) 1.187 1.09 ## Number of obs: 100, groups: factor(dat2$groupID), 10 ## ## Fixed effects: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 0.61515 0.35750 1.721 0.0853 . ## X 0.20356 0.01223 16.638 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Correlation of Fixed Effects: ## (Intr) ## X -0.218
Binomial
# sample data plot: points are colored by group
Col <- rainbow(10)
plot(Y ~ X, data = dat3, pch = 21, bg = Col[dat3$groupID], col = NA)
# run glmer
fit <- glmer(Y ~ X + (1|factor(dat3$groupID)), data = dat3, family = poisson)
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = ## control$checkConv, : Model failed to converge with max|grad| = 0.00493791 ## (tol = 0.001, component 1)
summary(fit)
## Generalized linear mixed model fit by maximum likelihood (Laplace ## Approximation) [glmerMod] ## Family: poisson ( log ) ## Formula: Y ~ X + (1 | factor(dat3$groupID)) ## Data: dat3 ## ## AIC BIC logLik deviance df.resid ## 359.2 367.0 -176.6 353.2 97 ## ## Scaled residuals: ## Min 1Q Median 3Q Max ## -1.4552 -0.7819 -0.2008 0.4063 2.2327 ## ## Random effects: ## Groups Name Variance Std.Dev. ## factor(dat3$groupID) (Intercept) 0.08707 0.2951 ## Number of obs: 100, groups: factor(dat3$groupID), 10 ## ## Fixed effects: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) -0.86604 0.21124 -4.10 4.14e-05 *** ## X 0.33065 0.02421 13.66 < 2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Correlation of Fixed Effects: ## (Intr) ## X -0.858 ## convergence code: 0 ## Model failed to converge with max|grad| = 0.00493791 (tol = 0.001, component 1)
function “glmer.nb”
確率分布:負の二項分布
パッケージ:lme4
その他:なし
# sample data plot: points are colored by group
Col <- rainbow(10)
plot(Y ~ X, data = dat4, pch = 21, bg = Col[dat4$groupID], col = NA)
# run glmer.nb
fit <- glmer.nb(Y ~ X + (1|factor(dat4$groupID)), data = dat4, family = poisson)
summary(fit)
## Generalized linear mixed model fit by maximum likelihood (Laplace ## Approximation) [glmerMod] ## Family: Negative Binomial(1.4135) ( log ) ## Formula: Y ~ X + (1 | factor(dat4$groupID)) ## Data: dat4 ## ## AIC BIC logLik deviance df.resid ## 910.1 920.5 -451.0 902.1 96 ## ## Scaled residuals: ## Min 1Q Median 3Q Max ## -1.1658 -0.7114 -0.2650 0.4356 2.8117 ## ## Random effects: ## Groups Name Variance Std.Dev. ## factor(dat4$groupID) (Intercept) 1.166 1.08 ## Number of obs: 100, groups: factor(dat4$groupID), 10 ## ## Fixed effects: ## Estimate Std. Error z value Pr(>|z|) ## (Intercept) 0.69477 0.41093 1.691 0.0909 . ## X 0.47894 0.03663 13.075 <2e-16 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Correlation of Fixed Effects: ## (Intr) ## X -0.510
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