我正在使用ezANOVA来实现具有内部主题变量和主题变量之间的实验设计的分析。我成功实施了ezANOVA如下：
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)
我坚持检查残差正态分布的程序。 我尝试了以下内容：
shapiro.test(as.numeric(residuals(mod.ez$aov)))
但是我收到以下错误
shapiro.test中的错误（as.numeric（residuals（mod.ez $ aov）））： 样本量必须介于3到5000之间
如果我调用residuals(mod.ez$aov)，结果为NULL。
我选择使用lmer来检查残差似乎很直接
plot(fitted(model_lmer), residuals(model_lmer))
然而，由于ezANOVA也已经实施了球形测试和修正，我想坚持下去，并找到一种检查假设的方法来恢复残差的正常性。
任何帮助非常感谢
答案 0 :(得分：3)
分步骤：
完整示例
首先，您的代码的完整版本是：
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，如果你找不到残差（等等），那么问题是：ezANOVA的结果是否真的包含它们，或者它是否已经清除了信息？对于这类问题，我喜欢使用这个函数：
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))
}
因此：
wtf_is(mod.ez)
搜索ezANOVA输出中的残差
输出很长。我们正在查找长度为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内容。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"
[...]
......这一切对我来说都没什么用。所以答案可能是＆＃34;它不在那里＆＃34;，或者＃34;显然不存在＆＃34;，而其他人同意：ggplot2 residuals with ezANOVA
改用afex :: aov_ez
所以你可以改用：
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)
......这确实会给你留下残余物。
但是，它还会提供不同的F / p值。
注意为什么aov_ez和ezANOVA在这里给出了不同的答案
我们有：
> mod.ez
$ANOVA
Effect DFn DFd SSn SSd F p p<.05 ges
1 Group 1 2 0.024449088 0.05070517 0.96436277 0.4296328 0.134418588
2 WithinFactor 1 2 0.001296481 0.10673345 0.02429382 0.8904503 0.008167579
3 Group:WithinFactor 1 2 0.015557350 0.10673345 0.29151781 0.6433264 0.089928978
> anova(model2)
Anova Table (Type III tests)
Response: Depvariable
num Df den Df MSE F ges Pr(>F)
Group 1.0000 2.0000 0.025353 0.9644 0.07197 0.4296
WithinFactor 1.4681 2.9363 0.090093 0.2322 0.08876 0.7471
Group:WithinFactor 1.4681 2.9363 0.090093 1.5001 0.38628 0.3370
不同的结果。请注意mod.ez的警告消息：
Warning: "WithinFactor" will be treated as numeric
...即作为连续预测因子（协变量），而不是离散预测因子（因子）。所以我们应该看看covariate和factorize个参数;见?aov_ez。我必须说我在这里努力学习如何做一个内部ANCOVA。 factorize部分仅适用于主题间预测变量，如果我正确阅读文档，covariate仅适用于主题间协变量。
作为一个快速检查，如果您使用ezANOVA并强制它使用WithinFactor作为离散（非连续）预测器，如下所示：
data$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)
...您获得与F匹配的p / aov_ez个值：
> 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
这样可以获得匹配的结果，以及Greenhouse-Geisser / Huynh-Feldt校正和残差，除了受试者内的协变量之外的所有内容。
<强>最后...
用连续的受试者内预测因子检查球形度是什么意思？我完全不清楚;球形度涉及在受试者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。
因此，冒着错误的风险，我也会 （a）信任ezANOVA和放弃残余; （b）使用能够做除球形测试之外的所有事情的东西，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
> 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