library(ggplot2)
library(knitr)
library(rmdformats)
library(lme4)
## Loading required package: Matrix
ggplot(sleepstudy, aes(x = Days, y = Reaction)) +
geom_point()+
geom_smooth(method = "lm")
## `geom_smooth()` using formula 'y ~ x'
ggplot(aes(Days, Reaction), data = sleepstudy) + geom_point() +
geom_smooth(method = "lm")+
facet_wrap(~ Subject) +
xlab("length") + ylab("test score")
## `geom_smooth()` using formula 'y ~ x'
lm1<-lm (Reaction ~ Days * Subject, sleepstudy)
summary(lm1)
##
## Call:
## lm(formula = Reaction ~ Days * Subject, data = sleepstudy)
##
## Residuals:
## Min 1Q Median 3Q Max
## -106.397 -10.692 -0.177 11.417 132.510
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 244.193 15.042 16.234 < 2e-16 ***
## Days 21.765 2.818 7.725 1.74e-12 ***
## Subject309 -39.138 21.272 -1.840 0.067848 .
## Subject310 -40.708 21.272 -1.914 0.057643 .
## Subject330 45.492 21.272 2.139 0.034156 *
## Subject331 41.546 21.272 1.953 0.052749 .
## Subject332 20.059 21.272 0.943 0.347277
## Subject333 30.826 21.272 1.449 0.149471
## Subject334 -4.030 21.272 -0.189 0.850016
## Subject335 18.842 21.272 0.886 0.377224
## Subject337 45.911 21.272 2.158 0.032563 *
## Subject349 -29.081 21.272 -1.367 0.173728
## Subject350 -18.358 21.272 -0.863 0.389568
## Subject351 16.954 21.272 0.797 0.426751
## Subject352 32.179 21.272 1.513 0.132535
## Subject369 10.775 21.272 0.507 0.613243
## Subject370 -33.744 21.272 -1.586 0.114870
## Subject371 9.443 21.272 0.444 0.657759
## Subject372 22.852 21.272 1.074 0.284497
## Days:Subject309 -19.503 3.985 -4.895 2.61e-06 ***
## Days:Subject310 -15.650 3.985 -3.928 0.000133 ***
## Days:Subject330 -18.757 3.985 -4.707 5.84e-06 ***
## Days:Subject331 -16.499 3.985 -4.141 5.88e-05 ***
## Days:Subject332 -12.198 3.985 -3.061 0.002630 **
## Days:Subject333 -12.623 3.985 -3.168 0.001876 **
## Days:Subject334 -9.512 3.985 -2.387 0.018282 *
## Days:Subject335 -24.646 3.985 -6.185 6.07e-09 ***
## Days:Subject337 -2.739 3.985 -0.687 0.492986
## Days:Subject349 -8.271 3.985 -2.076 0.039704 *
## Days:Subject350 -2.261 3.985 -0.567 0.571360
## Days:Subject351 -15.331 3.985 -3.848 0.000179 ***
## Days:Subject352 -8.198 3.985 -2.057 0.041448 *
## Days:Subject369 -10.417 3.985 -2.614 0.009895 **
## Days:Subject370 -3.709 3.985 -0.931 0.353560
## Days:Subject371 -12.576 3.985 -3.156 0.001947 **
## Days:Subject372 -10.467 3.985 -2.627 0.009554 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 25.59 on 144 degrees of freedom
## Multiple R-squared: 0.8339, Adjusted R-squared: 0.7936
## F-statistic: 20.66 on 35 and 144 DF, p-value: < 2.2e-16
library(car)
## Loading required package: carData
## Registered S3 methods overwritten by 'car':
## method from
## influence.merMod lme4
## cooks.distance.influence.merMod lme4
## dfbeta.influence.merMod lme4
## dfbetas.influence.merMod lme4
Anova(lm1)
## Anova Table (Type II tests)
##
## Response: Reaction
## Sum Sq Df F value Pr(>F)
## Days 162703 1 248.4234 < 2.2e-16 ***
## Subject 250618 17 22.5093 < 2.2e-16 ***
## Days:Subject 60322 17 5.4178 3.272e-09 ***
## Residuals 94312 144
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
summary(fm1)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Reaction ~ Days + (Days | Subject)
## Data: sleepstudy
##
## REML criterion at convergence: 1743.6
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.9536 -0.4634 0.0231 0.4634 5.1793
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 612.10 24.741
## Days 35.07 5.922 0.07
## Residual 654.94 25.592
## Number of obs: 180, groups: Subject, 18
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 251.405 6.825 36.838
## Days 10.467 1.546 6.771
##
## Correlation of Fixed Effects:
## (Intr)
## Days -0.138
fitF <- lmer(Reaction ~ Days + (1 | Subject), sleepstudy)
summary(fitF)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Reaction ~ Days + (1 | Subject)
## Data: sleepstudy
##
## REML criterion at convergence: 1786.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2257 -0.5529 0.0109 0.5188 4.2506
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 1378.2 37.12
## Residual 960.5 30.99
## Number of obs: 180, groups: Subject, 18
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 251.4051 9.7467 25.79
## Days 10.4673 0.8042 13.02
##
## Correlation of Fixed Effects:
## (Intr)
## Days -0.371
anova(fm1,fitF)
## refitting model(s) with ML (instead of REML)
## Data: sleepstudy
## Models:
## fitF: Reaction ~ Days + (1 | Subject)
## fm1: Reaction ~ Days + (Days | Subject)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## fitF 4 1802.1 1814.8 -897.04 1794.1
## fm1 6 1763.9 1783.1 -875.97 1751.9 42.139 2 7.072e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
plot(fm1)
qqnorm(resid(fm1))
qqline(resid(fm1))
fm2 <- lmer(Reaction ~ 1 + (Days | Subject), sleepstudy)
summary(fm2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: Reaction ~ 1 + (Days | Subject)
## Data: sleepstudy
##
## REML criterion at convergence: 1769.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.0449 -0.4486 0.0089 0.4819 5.2186
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 651.6 25.53
## Days 142.2 11.93 -0.18
## Residual 654.9 25.59
## Number of obs: 180, groups: Subject, 18
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 257.76 6.76 38.13
anova(fm1,fm2)
## refitting model(s) with ML (instead of REML)
## Data: sleepstudy
## Models:
## fm2: Reaction ~ 1 + (Days | Subject)
## fm1: Reaction ~ Days + (Days | Subject)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## fm2 5 1785.5 1801.4 -887.74 1775.5
## fm1 6 1763.9 1783.1 -875.97 1751.9 23.537 1 1.226e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RShowDoc("lmerperf", package = "lme4")