11.在lme4中将多个随机效应设定为相关的或相互独立的
#在lme4中,我们可以界定多个自变量的随机斜率之间之间是否相关。
#下面呈现了Model3.10和Model3.11的语句,
#Model3.10的随机效应写在两个单独的括号里,这表示相应的两个随机效应是不相关的,
#Model3.11中,随机效应写在同一个括号里,表示相应的两个随机效应是相关的
- Model3.10 <-
- lmer(geread~cgevocab + cage+(cgevocab + cage|school), Achieve)
- Model3.11 <-
- lmer(geread~cgevocab + cage+ (cgevocab|school) + (cage|school),Achieve)
复制代码
#Model3.10的结果如下
Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod]
Formula: geread ~ cgevocab + cage + (cgevocab + cage | school)
Data: Achieve
REML criterion at convergence: 42995.3
Scaled residuals:
Min 1Q Median 3Q Max
-3.6735 -0.5682 -0.2091 0.3184 4.6840
Random effects:
Groups Name Variance Std.Dev. Corr
school (Intercept) 1.022e-01 0.319698
cgevocab 1.902e-02 0.137918 0.53
cage 2.509e-05 0.005009 -0.28 -0.96
Residual 3.664e+00 1.914181
Number of obs: 10320, groups: school, 160
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.344e+00 3.269e-02 1.442e+02 132.896 <2e-16 ***
cgevocab 5.193e-01 1.435e-02 1.458e+02 36.187 <2e-16 ***
cage -8.882e-03 3.822e-03 2.632e+03 -2.324 0.0202 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) cgevcb
cgevocab 0.367
cage -0.020 -0.048
#Model3.11的结果如下
Linear mixed model fit by REML t-tests use Satterthwaite approximations to degrees of freedom [lmerMod]
Formula: geread ~ cgevocab + cage + (cgevocab | school) + (cage | school)
Data: Achieve
REML criterion at convergence: 42996.5
Scaled residuals:
Min 1Q Median 3Q Max
-3.6937 -0.5681 -0.2081 0.3182 4.6744
Random effects:
Groups Name Variance Std.Dev. Corr
school (Intercept) 2.914e-02 0.1707126
cgevocab 1.919e-02 0.1385421 1.00
school.1 (Intercept) 7.272e-02 0.2696680
cage 7.523e-07 0.0008674 1.00
Residual 3.665e+00 1.9143975
Number of obs: 10320, groups: school, 160
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 4.344e+00 3.264e-02 1.430e+02 133.065 <2e-16 ***
cgevocab 5.192e-01 1.440e-02 1.460e+02 36.063 <2e-16 ***
cage -8.956e-03 3.798e-03 8.039e+03 -2.358 0.0184 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) cgevcb
cgevocab 0.368
cage 0.015 0.033