我正在使用ezANOVA来执行对具有主题内变量和主题间变量的实验设计的分析。我成功实现了ezANOVA，如下所示：
structure(list(Sub = structure(c(3L, 3L, 3L, 4L, 4L, 4L, 1L,
1L, 1L, 2L, 2L, 2L), .Label = c("A7011", "A7022", "B13", "B14"
), class = "factor"), Depvariable = c(0.375, 0.066667, 0.15,
0.275, 0.025, 0.78333, 0.24167, 0.058333, 0.14167, 0.19167, 0.5,
0), Group = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L), .Label = c("A", "B"), class = "factor"), WithinFactor = c(0.6,
0, -0.3, 0.6, 0, -0.3, 0.6, 0, -0.3, 0.6, 0, -0.3)), .Names = c("Sub",
"Depvariable", "Group", "WithinFactor"), row.names = c(NA, 12L
), class = "data.frame")
mod.ez<-ezANOVA(data,
dv = .(Depvariable),
wid = .(Sub), # subject
within = .(WithinFactor),
between=.(Group),
type=3,
detailed=TRUE,
return_aov=TRUE)
我坚持检查残差的正态分布的过程。
我尝试了以下方法：
shapiro.test(as.numeric(residuals(mod.ez$aov)))
但是我收到以下错误
shapiro.test（as.numeric（residuals（mod.ez $ aov）））中的错误：
样本数量必须在3到5000之间
如果我呼叫
residuals(mod.ez$aov)，则结果为NULL。我也选择了lmer，其中残差的检查似乎很简单
plot(fitted(model_lmer), residuals(model_lmer))
但是，由于ezANOVA还已经实现了球形度的测试和校正，因此我想坚持下去，并找到一种方法来检查假设残差的正态性。
任何帮助，不胜感激
最佳答案
步骤：
完整的例子
首先，您的代码的完整版本为：
library(ez)
data <- structure(list(Sub = structure(c(3L, 3L, 3L, 4L, 4L, 4L, 1L,
1L, 1L, 2L, 2L, 2L), .Label = c("A7011", "A7022", "B13", "B14"
), class = "factor"), Depvariable = c(0.375, 0.066667, 0.15,
0.275, 0.025, 0.78333, 0.24167, 0.058333, 0.14167, 0.19167, 0.5,
0), Group = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L,
1L, 1L), .Label = c("A", "B"), class = "factor"), WithinFactor = c(0.6,
0, -0.3, 0.6, 0, -0.3, 0.6, 0, -0.3, 0.6, 0, -0.3)), .Names = c("Sub",
"Depvariable", "Group", "WithinFactor"), row.names = c(NA, 12L
), class = "data.frame")
mod.ez <- ezANOVA(
data,
dv = .(Depvariable),
wid = .(Sub), # subject
within = .(WithinFactor),
between = .(Group),
type = 3,
detailed = TRUE,
return_aov = TRUE)
如何探索复杂的R结构
其次，如果您找不到残差（等等），那么一个问题是：ezANOVA的结果是否实际上包含残差？还是它剔除了信息？对于此类问题，我喜欢使用以下功能：
wtf_is <- function(x) {
# For when you have no idea what something is.
# https://stackoverflow.com/questions/8855589
cat("1. typeof():\n")
print(typeof(x))
cat("\n2. class():\n")
print(class(x))
cat("\n3. mode():\n")
print(mode(x))
cat("\n4. names():\n")
print(names(x))
cat("\n5. slotNames():\n")
print(slotNames(x))
cat("\n6. attributes():\n")
print(attributes(x))
cat("\n7. str():\n")
print(str(x))
}
从而：
wtf_is(mod.ez)
在ezANOVA输出中寻找残差
输出很长。我们正在寻找长度为12的列表（因为您有12个数据点），或者看起来像残差或预测值的列表。部分输出是：
[...]
7. str():
List of 2
$ ANOVA:'data.frame': 3 obs. of 9 variables:
[...]
$ aov :List of 4
..$ (Intercept) :List of 9
[...]
..$ Sub :List of 9
[...]
.. ..$ residuals : Named num [1:3] 0.102 -0.116 0.164
.. .. ..- attr(*, "names")= chr [1:3] "2" "3" "4"
[...]
.. ..$ fitted.values: Named num [1:3] -1.39e-17 1.28e-01 9.03e-02
.. .. ..- attr(*, "names")= chr [1:3] "2" "3" "4"
..$ Sub:WithinFactor:List of 9
[...]
.. ..$ residuals : Named num [1:4] 0.00964 0.00964 0.23081 -0.23081
.. .. ..- attr(*, "names")= chr [1:4] "5" "6" "7" "8"
[...]
.. ..$ fitted.values: Named num [1:4] 0.0804 -0.0804 -0.0444 -0.0444
.. .. ..- attr(*, "names")= chr [1:4] "5" "6" "7" "8"
[...]
..$ Within :List of 6
[...]
.. ..$ residuals : num [1:4, 1] 0.3286 0.1098 -0.4969 0.0564
.. .. ..- attr(*, "dimnames")=List of 2
.. .. .. ..$ : chr [1:4] "9" "10" "11" "12"
.. .. .. ..$ : NULL
.. ..$ fitted.values: num [1:4, 1] 0 0 0 0
.. .. ..- attr(*, "dimnames")=List of 2
.. .. .. ..$ : chr [1:4] "9" "10" "11" "12"
.. .. .. ..$ : NULL
[...]
..- attr(*, "error.qr")=List of 5
.. ..$ qr : num [1:12, 1:8] -3.464 0.289 0.289 0.289 0.289 ...
.. .. ..- attr(*, "dimnames")=List of 2
.. .. .. ..$ : chr [1:12] "1" "2" "3" "4" ...
.. .. .. ..$ : chr [1:8] "(Intercept)" "Sub1" "Sub2" "Sub3" ...
.. .. ..- attr(*, "assign")= int [1:8] 0 1 1 1 2 2 2 2
.. .. ..- attr(*, "contrasts")=List of 1
.. .. .. ..$ Sub: chr "contr.helmert"
[...]
...看起来对我没有什么帮助。因此答案可能是“不存在”或“不明显存在”，其他人也同意：ggplot2 residuals with ezANOVA
改用afex :: aov_ez
因此，您可以改用：
library(afex)
model2 <- aov_ez(
id = "Sub", # subject
dv = "Depvariable",
data = data,
between = c("Group"),
within = c("WithinFactor"),
type = "III" # or 3; type III sums of squares
)
anova(model2)
summary(model2)
residuals(model2$lm)
...这确实会给您残差。
但是，它也会给出不同的
F / p值。注意为什么aov_ez和ezANOVA在这里给出不同的答案
我们有：
> mod.ez
$ANOVA
Effect DFn DFd SSn SSd F p p<.05 ges
1 Group 1 2 0.024449088 0.05070517 0.96436277 0.4296328 0.134418588
2 WithinFactor 1 2 0.001296481 0.10673345 0.02429382 0.8904503 0.008167579
3 Group:WithinFactor 1 2 0.015557350 0.10673345 0.29151781 0.6433264 0.089928978
> anova(model2)
Anova Table (Type III tests)
Response: Depvariable
num Df den Df MSE F ges Pr(>F)
Group 1.0000 2.0000 0.025353 0.9644 0.07197 0.4296
WithinFactor 1.4681 2.9363 0.090093 0.2322 0.08876 0.7471
Group:WithinFactor 1.4681 2.9363 0.090093 1.5001 0.38628 0.3370
结果不同。请注意来自mod.ez的警告消息：
Warning: "WithinFactor" will be treated as numeric
...即作为连续预测变量（协变量），而不是离散预测变量（因子）。因此，我们应该查看
covariate和factorize参数；参见?aov_ez。我必须说，我在这里努力研究如何做一个受试者内部ANCOVA。如果我正确阅读了文档，factorize部分仅适用于对象间预测变量，同样，covariate仅适用于对象间协变量。快速检查一下，如果您使用ezANOVA并强制其将InsideFactor用作离散（非连续）预测变量，如下所示：
data$WithinCovariate <- data$WithinFactor # so the name is clearer!
data$WithinFactorDiscrete <- as.factor(data$WithinFactor)
mod.ez.discrete <- ezANOVA(
data,
dv = .(Depvariable),
wid = .(Sub), # subject
within = .(WithinFactorDiscrete),
between = .(Group),
type = 3,
detailed = TRUE,
return_aov = TRUE)
...您得到与
F匹配的p / aov_ez值：> mod.ez.discrete
$ANOVA
Effect DFn DFd SSn SSd F p p<.05 ges
1 (Intercept) 1 2 0.65723113 0.05070517 25.9236350 0.03647725 * 0.67583504
2 Group 1 2 0.02444909 0.05070517 0.9643628 0.42963280 0.07197457
3 WithinFactorDiscrete 2 4 0.03070651 0.26453641 0.2321534 0.80280844 0.08876045
4 Group:WithinFactorDiscrete 2 4 0.19841198 0.26453641 1.5000731 0.32651697 0.38627588
这样一来，除了对象内协变量之外的所有内容，您都可以获得匹配的结果以及Greenhouse-Geisser / Huynh-Feldt校正和残差。
最后...
用连续的对象内部预测变量检查球形度是什么意思？我完全不清楚；球形度涉及在对象内因子的不同水平上的值对之间的差异的方差的均匀性。如果预测变量是连续的，则没有对。
所以冒犯错误的风险，我要么
（a）信任ezANOVA并放弃残差；
（b）使用可以完成除球形度测试之外的所有操作的东西，例如：
library(lme4)
library(lmerTest) # upgrades reports from lme4 to include p values! ;)
mod.lmer.wscov_interact <- lmer(
Depvariable ~
Group * WithinCovariate
+ (1 | Sub),
data = data
)
anova(mod.lmer.wscov_interact)
residuals(mod.lmer.wscov_interact)
mod.lmer.wscov_no_interact <- lmer(
Depvariable ~
Group + WithinCovariate
+ (1 | Sub),
data = data
)
anova(mod.lmer.wscov_no_interact)
mod.lmer.wsfac <- lmer(
Depvariable ~
Group * WithinFactorDiscrete
+ (1 | Sub),
data = data
)
anova(mod.lmer.wsfac)
给予
> anova(mod.lmer.wscov_interact)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
Group 0.033586 0.033586 1 8 0.50936 0.4957
WithinCovariate 0.001296 0.001296 1 8 0.01966 0.8920
Group:WithinCovariate 0.015557 0.015557 1 8 0.23594 0.6402
> residuals(mod.lmer.wscov_interact)
1 2 3 4 5 6 7 8 9 10 11 12
0.130059250 -0.219344250 -0.156546500 0.030059250 -0.261011250 0.476783500 -0.009225679 -0.118156464 0.002383643 -0.059225679 0.323510536 -0.139286357
> anova(mod.lmer.wscov_no_interact)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
Group 0.0244491 0.0244491 1 9 0.40519 0.5403
WithinCovariate 0.0012965 0.0012965 1 9 0.02149 0.8867
> anova(mod.lmer.wsfac)
Analysis of Variance Table of type III with Satterthwaite
approximation for degrees of freedom
Sum Sq Mean Sq NumDF DenDF F.value Pr(>F)
Group 0.024449 0.024449 1 6 0.46534 0.5206
WithinFactorDiscrete 0.030707 0.015353 2 6 0.29222 0.7567
Group:WithinFactorDiscrete 0.198412 0.099206 2 6 1.88819 0.2312