我正在使用lmer包来构建一个模型，并希望检查随机效应之间的相关性。
首先我构建了一个tibble：
id <- rep(1:6, each=4)
group <- rep(c("A","B"), each=12)
type <- rep(c("pencil", "pencil", "pen", "pen"), times=6)
color <- rep (c ("blue", "red"), times = 12)
dv <- c(-24.3854453, 17.0358639, -15.5174479, 8.6462489, -7.0561166, 3.3524410, 21.6199364, -6.1020999, 13.2464223, 20.3740206, 22.8571793, -6.6159629, 18.7898553, -8.2504319, 17.9571641, 2.9555213, -19.5516738, -0.5845135, 9.6041710, -4.1301420, 4.1740094, -24.2496521, 7.4432948, -0.8290391)
sample_data <- as_tibble(cbind(id, group, type, color, dv)
这是我的样本数据：
id group type color dv
1 A pencil blue 0.05925979
1 A pencil red 4.60326151
1 A pen blue -20.72000620
1 A pen red -15.27612843
2 A pencil blue -0.68719576
2 A pencil red 16.34200026
2 A pen blue 18.23954687
2 A pen red 21.02837383
3 A pencil blue -22.28695974
3 A pencil red -18.36587259
3 A pen blue -15.13952913
3 A pen red 19.95919637
4 B pencil blue -19.52410412
4 B pencil red -3.25912890
4 B pen blue -12.11669400
4 B pen red 15.93333896
5 B pencil blue -17.93575204
5 B pencil red -8.58879605
5 B pen blue 8.89757943
5 B pen red -13.42995221
6 B pencil blue 12.03769124
6 B pencil red -10.28876053
6 B pen blue 7.69523239
6 B pen red -2.94621122
现在我运行我的模型并对其进行总结：
test.model <- lmer(dv ~ 1 + group * type * color + (1 * type * color | id), data = sample_data, REML = FALSE)
summary(test.model)
这是我的输出：
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: dv ~ 1 + group * type * color + (1 * type * color | id)
Data: test
AIC BIC logLik deviance df.resid
204.7 216.5 -92.4 184.7 14
Scaled residuals:
Min 1Q Median 3Q Max
-2.16529 -0.45429 0.09296 0.62406 1.62720
Random effects:
Groups Name Variance Std.Dev.
id (Intercept) 4.975 2.23
Residual 124.228 11.15
Number of obs: 24, groups: id, 6
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) -0.6679 6.5626 23.8937 -0.102 0.9198
groupA -0.6894 9.2809 23.8937 -0.074 0.9414
typepencil -10.3603 9.1005 18.0000 -1.138 0.2699
colorblue 12.3361 9.1005 18.0000 1.356 0.1920
groupA:typepencil 25.3050 12.8700 18.0000 1.966 0.0649 .
groupA:colorblue -1.3256 12.8700 18.0000 -0.103 0.9191
typepencil:colorblue -0.1705 12.8700 18.0000 -0.013 0.9896
groupA:typepencil:colorblue -30.4925 18.2010 18.0000 -1.675 0.1112
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) groupA typpnc colrbl grpA:t grpA:c typpn:
groupA -0.707
typepencil -0.693 0.490
colorblue -0.693 0.490 0.500
grpA:typpnc 0.490 -0.693 -0.707 -0.354
gropA:clrbl 0.490 -0.693 -0.354 -0.707 0.500
typpncl:clr 0.490 -0.347 -0.707 -0.707 0.500 0.500
grpA:typpn: -0.347 0.490 0.500 0.500 -0.707 -0.707 -0.707
我想检查随机效应的相关性，但我看不到通常的"相关性"；Corr"；列(通常出现在"随机效果"下的输出中的"St.Dev."旁边(。它在哪里？
我认为问题源于模型的随机效应部分。您当前拥有：
(1 * type * color | id)
然而，标准公式是：
(1 + type * color | id)
当我运行这个程序时，我得到了一个error，关于观察的数量小于随机效应的数量(这种交互作用使随机效应结构对于样本数据集来说过于复杂(。使用一个不太复杂的随机效应结构(1 + type + color | id)，我可以得到你想要的Corr列：
Linear mixed model fit by maximum likelihood . t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: dv ~ 1 + group * type * color + (1 + type + color | id)
Data: sample_data
AIC BIC logLik deviance df.resid
203.8 221.5 -86.9 173.8 9
Scaled residuals:
Min 1Q Median 3Q Max
-1.5320 -0.7217 0.1363 0.7089 1.3920
Random effects:
Groups Name Variance Std.Dev. Corr
id (Intercept) 130.22 11.411
typepencil 15.49 3.936 0.42
colorred 219.98 14.832 -1.00 -0.37
Residual 41.79 6.464
Number of obs: 24, groups: id, 6
Fixed effects:
Estimate Std. Error df t value Pr(>|t|)
(Intercept) 9.653 7.572 6.888 1.275 0.24368
groupB 2.015 10.708 6.888 0.188 0.85617
typepencil -15.718 5.747 14.358 -2.735 0.01582 *
colorred -11.010 10.059 7.985 -1.095 0.30562
groupB:typepencil 5.187 8.127 14.358 0.638 0.53333
groupB:colorred -1.326 14.226 7.985 -0.093 0.92805
typepencil:colorred 30.663 7.465 11.996 4.108 0.00145 **
groupB:typepencil:colorred -30.492 10.556 11.996 -2.889 0.01362 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) groupB typpnc colrrd grpB:t grpB:c typpn:
groupB -0.707
typepencil -0.174 0.123
colorred -0.922 0.652 0.117
grpB:typpnc 0.123 -0.174 -0.707 -0.083
gropB:clrrd 0.652 -0.922 -0.083 -0.707 0.117
typpncl:clr 0.246 -0.174 -0.649 -0.371 0.459 0.262
grpB:typpn: -0.174 0.246 0.459 0.262 -0.649 -0.371 -0.707
convergence code: 0
Model failed to converge with max|grad| = 0.00237651 (tol = 0.002, component 1)
我仍然得到一个关于模型未能收敛的warning。这可能再次是由于随机效应结构对于您的样本数据集来说过于复杂：lmer(dv ~ 1 + group * type * color + (1 | id), data = sample_data, REML = FALSE)没有给出这样的警告。
希望有帮助吗？