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<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>chapter_11.knit</title>
<meta charset="utf-8" />
<meta name="author" content="" />
<<<<<<< HEAD
<script src="libs/header-attrs-2.25/header-attrs.js"></script>
=======
<script src="libs/header-attrs-2.26/header-attrs.js"></script>
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
<link href="libs/remark-css-0.0.1/default.css" rel="stylesheet" />
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<link href="libs/DiagrammeR-styles-0.2/styles.css" rel="stylesheet" />
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<body>
<textarea id="source">
class: center, middle
<span style="font-size: 50px;">**第十一章**</span> <br>
<span style="font-size: 50px;">回归模型(四)：中介分析</span> <br>
<span style="font-size: 30px;">胡传鹏</span> <br>
<span style="font-size: 20px;"> </span> <br>
<span style="font-size: 30px;">2024-05-15</span> <br>
<span style="font-size: 20px;"> Made with Rmarkdown</span> <br>
---
<style type="text/css">
.bigfont {
font-size: 30px;
}
.size5{
font-size: 24px;
}
.titfont{
font-size: 60px;
}
.foot{
font-size: 10px;
}
</style>
## 准备工作
```r
# Packages
if (!requireNamespace('pacman', quietly = TRUE)) {
install.packages('pacman')
}
pacman::p_load(tidyverse,easystats,magrittr,
# 中介分析
lavaan, bruceR,tidySEM,
# 数据集
quartets,
# 绘图
patchwork,DiagrammeR,magick)
<<<<<<< HEAD
```
```
## 程序包'magick'打开成功，MD5和检查也通过
##
## 下载的二进制程序包在
## C:\Users\dazai osamu\AppData\Local\Temp\RtmpoxA4eJ\downloaded_packages里
```
```r
=======
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
options(scipen=99999,digits = 3)
set.seed(1002)
```
---
class: inverse, middle ,center
.titfont[线性模型回顾]
---
# 0.1 线性模型及模型检验
- 回归方程用于分析一个因变量与多个自变量之间的关系。在回归中，将一个或多个自变量视为整体，对因变量进行预测，通过OLS或ML进行拟合，解释不了的成分则被视为残差；而我们的目的在于，舍弃残差（随机部分），而获得可解释的成分。
.panelset[
.panel[.panel-name[anscombe_quartet]
<img src="chapter_11_files/figure-html/unnamed-chunk-2-1.png" width="540" style="display: block; margin: auto;" />
.panel[.panel-name[performance]
```r
lm(y ~ x,data = anscombe_quartet %>%
dplyr::filter(dataset == '(3) Outlier')) %>%
* performance::check_model(check = c('linearity','outliers'))
```
<img src="chapter_11_files/figure-html/Outlier-1.png" width="540" style="display: block; margin: auto;" />
]]]
---
# 0.2 多元线性模型的局限
.size5[
- 模型可分为三类 `\(^*\)`：描述模型、推断模型、预测模型
- 回归兼具这三种功能：
- 使用LOESS(即geom_smooth()中method默认的参数)可以对数据进行描述；
- 关注各个变量的(偏)回归系数的显著性可以进行统计推断(如果是离散变量的时候即等价与ANOVA)
- 进行预测时，则不关注各个变量之间的复杂关系，因而将自变量当做整体，关注其是否能够预测因变量(拟合指标)
]
--
### 局限
.size5[
如果所有自变量都相互独立，使用多元回归是合理的；
但在现实中，变量之间存在相互作用更为普遍，而多元回归值仅关注到自变量对因变量的独立作用(偏回归系数)，很难描述变量间复杂的关系。变量越多，这个问题越明显。
]
.footnote[
-----------
.footfont[
Ref: [https://www.tmwr.org/software-modeling](https://www.tmwr.org/software-modeling)
]
]
---
class: inverse, middle ,center
.titfont[中介分析]
---
# 2.1 对于“机制”的表示——“图”
- 变量间关系中，我们期望验证因果关系。
- 对于因果关系，可以用“图”来表示：
- 图包括两部分：节点和边。节点表示具体变量，而箭头表示变量之间的关系；
- 对节点来说，在SEM中，观测变量用椭圆表示，潜变量用椭圆表示。
- 边表示变量间关系，**单箭头直线表示直接因果关系，从原因指向结果；双曲线箭头则表示相关
- 使用的图多为有向无环图(Directed Acyclic Graph, DAGs)，而图本身是对理论因果关系的表征
.pull-left[
<div class="grViz html-widget html-fill-item" id="htmlwidget-eb68ae1ca613bc458c42" style="width:540px;height:100px;"></div>
<script type="application/json" data-for="htmlwidget-eb68ae1ca613bc458c42">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X1 ->X2\n X2 -> X3\n X1 -> X3\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
.pull-right[
<div class="grViz html-widget html-fill-item" id="htmlwidget-c74d20ac9049b4ab04e2" style="width:540px;height:100px;"></div>
<script type="application/json" data-for="htmlwidget-c74d20ac9049b4ab04e2">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X1 ->X2\n X2 -> X3\n X3 -> X1\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
---
# 2.2 中介分析
- 中介分析：
关注变量间因果关系，自变量如何影响因变量（即机制），如X通过M作用于Y，M为中介变量。中介的存在意味着时间上发生的先后顺序： `\(X \rightarrow M \rightarrow Y\)` 。
对于中介过程的量化包括路径分析和SEM（同时包含测量模型和结构模型），后面的介绍基于路径分析。
<div class="grViz html-widget html-fill-item" id="htmlwidget-35b3c2d84228862c5168" style="width:540px;height:100px;"></div>
<script type="application/json" data-for="htmlwidget-35b3c2d84228862c5168">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X -> M\n X -> Y\n M -> Y\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
---
# 2.2 中介分析
.pull-left[
.bigfont[
总方程:
`$$Y = i_1 + cX + e_1$$`
]
]
.pull-right[
<div class="grViz html-widget html-fill-item" id="htmlwidget-15729d10e6c1d12556bb" style="width:540px;height:200px;"></div>
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]
------------------
<br>
.pull-left[
.bigfont[
分解:
`$$M = i_2 + aX + e_2$$`
`$$Y = i_3 + c'X + bM + e_3$$`
]
]
.pull-right[
<div class="grViz html-widget html-fill-item" id="htmlwidget-fadd34694e292ff98532" style="width:540px;height:200px;"></div>
<script type="application/json" data-for="htmlwidget-fadd34694e292ff98532">{"x":{"diagram":"digraph {\n graph [layout = dot]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n e2[style = NULL,fillcolor = NULL,penwidth = 0,\n height = 0.02,width = 0.02]\n e3[style = NULL,fillcolor = NULL,penwidth = 0,\n height = 0.02,width = 0.02]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n # {rank = min; X; Med}\n {rank = same; e2 Med}\n {rank = same; X Y}\n\n X -> Med [label = \"a\", len = 1] \n Med -> Y [label = \"b\", len = 1] \n X -> Y [label = \"c′\", len = 15] \n e3 -> Y [len = 1] \n e2 -> Med [len = 1] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
---
# 2.3 中介效应
.pull-left[
$$ Y = i_1 + cX + e_1$$
$$ M = i_2 + aX + e_2$$
`$$Y = i_3 + c'X + bM + e_3$$`
如果将第二个方程代入第三个方程：
$$ Y = i_3 + c'X + b(i_2 + aX + e_2) + e_3$$
`$$= (b*i_2 + i_3) + c'X + abX + (b*e_2 + e_3)$$`
`$$= i_4 + c'X + abX + e_5$$`
可以发现，将X对Y的效应分解成了中介效应ab和直接效应c'
- 在中介模型路径图中， `\(X \rightarrow Y\)`路径上的回归系数 `\(c'\)`为直接效应
- 中介效应：ab，或 `\(c - c'\)`。在M和Y均为连续变量的时候，有： `\(ab = c - c'\)`
- 中介效应分为两类：完全中介（即c' = 0）和部分中介(c' ≠ 0)
- 但问题是，回归系数意味着变量间存在因果关系么？
]
.pull-right[
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<script type="application/json" data-for="htmlwidget-998346cb44a12602da36">{"x":{"diagram":"digraph {\n graph [layout = dot]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n e2[style = NULL,fillcolor = NULL,penwidth = 0,\n height = 0.02,width = 0.02]\n e3[style = NULL,fillcolor = NULL,penwidth = 0,\n height = 0.02,width = 0.02]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n # {rank = min; X; Med}\n {rank = same; e2 Med}\n {rank = same; X Y}\n\n X -> Med [label = \"a\", len = 1] \n Med -> Y [label = \"b\", len = 1] \n X -> Y [label = \"c′\", len = 15] \n e3 -> Y [len = 1] \n e2 -> Med [len = 1] \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
---
# 2.3 中介效应
.size5[
- 回归系数本质上只是(偏)相关( `\(\beta = \frac{S_y}{S_x}·r\)`)，比如对于总效应c来说：]
```r
tot = lm(CBT ~ DEQ,data = pg_raw %>%
dplyr::filter(romantic == 1))
# 计算相关
r = pg_raw %>%
dplyr::filter(romantic == 1) %>%
correlation::correlation(select = cc("DEQ,CBT")) %>%
.$r
# 比较回归系数与相关
data.frame('相关系数' =
(sd(pg_raw$CBT,na.rm = T)/sd(pg_raw$DEQ,na.rm = T))*r,
'回归系数' = tot$coefficients[2]) %>% print()
```
```
## 相关系数 回归系数
## DEQ -0.00214 -0.00222
```
.size5[
- 而中介效应ab也只是两个回归方程的回归系数的乘积，或者说是 `\(r_{XM}\)` 与 `\(r_{MY}\)`的乘积；而相关不等于因果，所以使用测量中介实际上是无法确认因果关系！
]
---
# 2.4 中介效应的检验
.size5[
中介效应的检验方法很多，如四步法、Sobel检验等，但最常用的是通过Bootstrap 来计算中介效应的置信区间(且两个随机变量的乘积很多情境中并非服从正态分布)，如果其置信区间不包含0则认为该参数估计值显著：
- Bootstrap对原始样本进行有放回的重复抽样（允许重复抽取相同数据），抽样次数通常等于数据本身大小N相同，假设重复抽取1000次；
- 然后对每次抽取的样本计算中介效应ab，就得到了1000个ab的值，据此估计中介效应ab的分布情况，进而取2.5%和97.5%个百分位点计算95%置信区间。
]
---
# 2.5 问题提出
在第六章中，我们使用Penguins数据研究了社交复杂度(CSI)是否影响核心体温(CBT)，特别是在离赤道比较远的（低温）地区(DEQ)。
这里，我们复现论文中第一个中介模型：社会复杂度(CSI)可以保护处于恋爱中的个体的体温(CBT)免受寒冷气候(DEQ)的影响。具体来说：
- DEQ为自变量，CBT为因变量，CSI为中介变量。
- 赤道距离(DEQ)应当正向预测社会复杂度(CSI)，而社会复杂度应当正向预测体温(CBT)，但赤道距离(DEQ)应当负向预测体温(CBT)(即遮掩效应，如下图)
.panelset[
.panel[.panel-name[假设]
<div class="grViz html-widget html-fill-item" id="htmlwidget-8b5ea12c3ecaffd5a5a8" style="width:540px;height:300px;"></div>
<script type="application/json" data-for="htmlwidget-8b5ea12c3ecaffd5a5a8">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n DEQ -> CSI[label = \"+\"]\n DEQ -> CBT[label = \"-\"]\n CSI -> CBT[label = \"+\"]\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
.panel[.panel-name[数据导入]
```r
# 数据导入
pg_raw = bruceR::import(here::here('data','penguin','penguin_rawdata_full.csv'))
```
.panel[.panel-name[计算CSI]
```r
# 计算CSI
### get the column names:
snDivNames <- c("SNI3", "SNI5", "SNI7", "SNI9", "SNI11", "SNI13", "SNI15", "SNI17","SNI18","SNI19","SNI21")
extrDivName <- c("SNI28","SNI29","SNI30","SNI31","SNI32") # colnames of the extra groups
### create a empty dataframe for social network diversity
snDivData <- setNames(data.frame(matrix(ncol = length(snDivNames), nrow = nrow(pg_raw))), snDivNames)
### recode Q10 (spouse): 1-> 1; else ->0
snDivData$SNI1_r <- car::recode(pg_raw$SNI1,"1= 1; else = 0")
####re-code Q12 ~ Q30: NA -> 0; 0 -> 0; 1~10 -> 1
snDivData[,snDivNames] <- apply(pg_raw[,snDivNames],2,function(x) {x <- car::recode(x,"0 = 0; NA = 0; 1:10 = 1;"); x})
### add suffix to the colnames
colnames(snDivData[,snDivNames]) <- paste(snDivNames,"div", sep = "_")
### recode the social network at work by combining SNI17, SNI18
snDivData$SNIwork <- snDivData$SNI17 + snDivData$SNI18
snDivData$SNIwork_r <- car::recode(snDivData$SNIwork,"0 = 0;1:10 = 1")
### re-code extra groups, 0/NA --> 0; more than 0 --> 1
extrDivData <- pg_raw[,extrDivName] # Get extra data
extrDivData$sum <- rowSums(extrDivData) # sum the other groups
snDivData$extrDiv_r <- car::recode(extrDivData$sum,"0 = 0; NA = 0; else = 1") # recode
### Get the column names for social diversity
snDivNames_r <- c("SNI1_r","SNI3","SNI5","SNI7","SNI9","SNI11","SNI13","SNI15","SNIwork_r",
"SNI19","SNI21","extrDiv_r")
### Get the social diveristy score
snDivData$SNdiversity <- rowSums(snDivData[,snDivNames_r])
pg_raw$socialdiversity <- snDivData$SNdiversity
```
.panel[.panel-name[计算CBT]
```r
## 更改列名
pg_raw %<>% dplyr::rename(CSI = socialdiversity)
### 计算CBT（mean）
# 筛选大于34.99 的被试
# pg_raw %<>%
# filter(Temperature_t1 > 34.99 &
# Temperature_t2 > 34.99)
# 前测后测求均值
pg_raw %<>%
dplyr::mutate(CBT = (Temperature_t1 + Temperature_t2)/2)
```
]]]]]
---
layout: true
# 2.6 代码实现
---
## 2.6.1 lavaan 介绍
- lavaan包专门用于结构方程模型（SEM）的估计，如CFA、EFA、Multiple groups、Growth curves等。
- 基本语法 `\(^*\)`：
| formula type | operator | mnemonic |
|----------------------------|----------|--------------------|
| latent variable definition | `=~` | is measured by |
| regression | `~` | is regressed on |
| (residual) (co)variance | `~~` | is correlated with |
| intercept | `~ 1` | intercept |
| ‘defines’ new parameters | `:= ` | defines |
.footnote[
-----------
.footfont[
Ref: [https://lavaan.ugent.be/tutorial/syntax1.html](https://lavaan.ugent.be/tutorial/syntax1.html)
]
]
---
## 2.6.2 lavaan语句
.panelset[
.panel[.panel-name[lavaan语句]
```r
med_model <- "
# 直接效应(Y = cX)
CBT ~ c*DEQ # 语法同回归，但需要声明回归系数
# 中介路径(M)
CSI ~ a*DEQ
CBT ~ b*CSI
# 定义间接效应c'
#注： `:=`意思是根据已有的参数定义新的参数
ab := a*b
# 总效应
total := c + (a*b)"
# 注：这里数据仅以处于浪漫关系中的个体为例
fit <- lavaan::sem(med_model,
data = pg_raw %>% dplyr::filter(romantic == 1),
bootstrap = 100 # 建议1000
)
```
.panel[.panel-name[lavaan-output]
```r
fit %>% summary() %>% capture.output() %>% .[21:38]
```
```
## [1] "Regressions:"
## [2] " Estimate Std.Err z-value P(>|z|)"
## [3] " CBT ~ "
## [4] " DEQ (c) -0.004 0.001 -3.520 0.000"
## [5] " CSI ~ "
## [6] " DEQ (a) 0.026 0.004 7.400 0.000"
## [7] " CBT ~ "
## [8] " CSI (b) 0.071 0.011 6.316 0.000"
## [9] ""
## [10] "Variances:"
## [11] " Estimate Std.Err z-value P(>|z|)"
## [12] " .CBT 0.197 0.010 19.900 0.000"
## [13] " .CSI 1.949 0.098 19.900 0.000"
## [14] ""
## [15] "Defined Parameters:"
## [16] " Estimate Std.Err z-value P(>|z|)"
## [17] " ab 0.002 0.000 4.804 0.000"
## [18] " total -0.002 0.001 -1.930 0.054"
```
.panel[.panel-name[中介图-Paper]
<<<<<<< HEAD
<img src="picture/chp11/lav.png" style="display: block; margin: auto;" />
=======
<img src="picture/chp11/lav.png" width="1158" style="display: block; margin: auto;" />
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
.panel[.panel-name[中介图-tidySEM]
这里绘图使用的是tidySEM包，当然也有semPlot等包可以选择；tidySEM使用了tidyverse风格，并支持lavaan和Mplus等语法对SEM进行建模，可使用help(package = tidySEM)进行查看。
.pull-left[
```r
## 与DiagrammeR::get_edges相冲突
detach("package:DiagrammeR", unload = TRUE)
## 细节修改可在Vignettes中查看tidySEM::Plotting_graphs
lay = get_layout("", "CSI", "",
"DEQ", "", "CBT",
rows = 2)
tidySEM::graph_sem(fit,digits = 3,
layout = lay)
```
]
.pull-right[
<img src="chapter_11_files/figure-html/unnamed-chunk-18-1.png" width="540" style="display: block; margin: auto;" />
]
]]]]]
---
## 2.6.3 PROCESS in bruceR()
.panelset[
.panel[.panel-name[bruceR::PROCESS]
```r
## RUN IN CONSOLE !!!
pg_raw %>% dplyr::filter(romantic == 1) %>%
bruceR::PROCESS( ## 注意这里默认nsim = 100，建议1000
x = 'DEQ', y = 'CBT',meds = 'CSI',nsim = 100)
```
```
##
## ****************** PART 1. Regression Model Summary ******************
##
## PROCESS Model Code : 4 (Hayes, 2018; www.guilford.com/p/hayes3)
## PROCESS Model Type : Simple Mediation
## - Outcome (Y) : CBT
## - Predictor (X) : DEQ
## - Mediators (M) : CSI
## - Moderators (W) : -
## - Covariates (C) : -
## - HLM Clusters : -
##
## All numeric predictors have been grand-mean centered.
## (For details, please see the help page of PROCESS.)
##
## Formula of Mediator:
## - CSI ~ DEQ
## Formula of Outcome:
## - CBT ~ DEQ + CSI
##
## CAUTION:
## Fixed effect (coef.) of a predictor involved in an interaction
## denotes its "simple effect/slope" at the other predictor = 0.
## Only when all predictors in an interaction are mean-centered
## can the fixed effect denote the "main effect"!
##
## Model Summary
##
## ──────────────────────────────────────────────────
## (1) CBT (2) CSI (3) CBT
## ──────────────────────────────────────────────────
## (Intercept) 36.386 *** 7.111 *** 36.386 ***
## (0.016) (0.050) (0.016)
## DEQ -0.002 0.026 *** -0.004 ***
## (0.001) (0.004) (0.001)
## CSI 0.071 ***
## (0.011)
## ──────────────────────────────────────────────────
## R^2 0.005 0.065 0.052
## Adj. R^2 0.003 0.063 0.050
## Num. obs. 792 792 792
## ──────────────────────────────────────────────────
## Note. * p < .05, ** p < .01, *** p < .001.
##
## ************ PART 2. Mediation/Moderation Effect Estimate ************
##
## Package Use : ‘mediation’ (v4.5.0)
## Effect Type : Simple Mediation (Model 4)
## Sample Size : 792 (38 missing observations deleted)
## Random Seed : set.seed()
## Simulations : 100 (Bootstrap)
##
## Running 100 simulations...
## Indirect Path: "DEQ" (X) ==> "CSI" (M) ==> "CBT" (Y)
## ───────────────────────────────────────────────────────────────
## Effect S.E. z p [Boot 95% CI]
## ───────────────────────────────────────────────────────────────
<<<<<<< HEAD
## Indirect (ab) 0.002 (0.000) 5.233 <.001 *** [ 0.001, 0.003]
## Direct (c') -0.004 (0.001) -3.718 <.001 *** [-0.006, -0.002]
## Total (c) -0.002 (0.001) -2.074 .038 * [-0.004, -0.000]
=======
## Indirect (ab) 0.002 (0.000) 5.055 <.001 *** [ 0.001, 0.003]
## Direct (c') -0.004 (0.001) -3.555 <.001 *** [-0.006, -0.002]
## Total (c) -0.002 (0.001) -2.035 .042 * [-0.004, -0.000]
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
## ───────────────────────────────────────────────────────────────
## Percentile Bootstrap Confidence Interval
## (SE and CI are estimated based on 100 Bootstrap samples.)
##
## Note. The results based on bootstrapping or other random processes
## are unlikely identical to other statistical software (e.g., SPSS).
## To make results reproducible, you need to set a seed (any number).
## Please see the help page for details: help(PROCESS)
## Ignore this note if you have already set a seed. :)
```
.panel[.panel-name[bruceR::PROCESS-Regression]
```
## [1] "Model Summary"
## [2] ""
## [3] "──────────────────────────────────────────────────"
## [4] " (1) CBT (2) CSI (3) CBT "
## [5] "──────────────────────────────────────────────────"
## [6] "(Intercept) 36.386 *** 7.111 *** 36.386 ***"
## [7] " (0.016) (0.050) (0.016) "
## [8] "DEQ -0.002 0.026 *** -0.004 ***"
## [9] " (0.001) (0.004) (0.001) "
## [10] "CSI 0.071 ***"
## [11] " (0.011) "
## [12] "──────────────────────────────────────────────────"
## [13] "R^2 0.005 0.065 0.052 "
## [14] "Adj. R^2 0.003 0.063 0.050 "
## [15] "Num. obs. 792 792 792 "
## [16] "──────────────────────────────────────────────────"
## [17] "Note. * p < .05, ** p < .01, *** p < .001."
```
.panel[.panel-name[bruceR::PROCESS-Mediation]
```
## [1] "Package Use : ‘mediation’ (v4.5.0)"
## [2] "Effect Type : Simple Mediation (Model 4)"
## [3] "Sample Size : 792 (38 missing observations deleted)"
## [4] "Random Seed : set.seed()"
## [5] "Simulations : 100 (Bootstrap)"
## [6] ""
## [7] "Running 100 simulations..."
## [8] "Indirect Path: \"DEQ\" (X) ==> \"CSI\" (M) ==> \"CBT\" (Y)"
## [9] "───────────────────────────────────────────────────────────────"
## [10] " Effect S.E. z p [Boot 95% CI]"
## [11] "───────────────────────────────────────────────────────────────"
<<<<<<< HEAD
## [12] "Indirect (ab) 0.002 (0.000) 4.812 <.001 *** [ 0.001, 0.003]"
## [13] "Direct (c') -0.004 (0.001) -3.355 <.001 *** [-0.006, -0.002]"
## [14] "Total (c) -0.002 (0.001) -2.037 .042 * [-0.004, -0.000]"
=======
## [12] "Indirect (ab) 0.002 (0.000) 5.804 <.001 *** [ 0.001, 0.002]"
## [13] "Direct (c') -0.004 (0.001) -3.750 <.001 *** [-0.006, -0.002]"
## [14] "Total (c) -0.002 (0.001) -2.135 .033 * [-0.005, -0.001]"
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
## [15] "───────────────────────────────────────────────────────────────"
```
]]]]
---
layout: false
# 2.7 反思
<br>
.size5[
在刚才的分析中，我们希望证明：社会复杂度(CSI)可以保护处于恋爱中的个体的体温(CBT)免受寒冷气候(DEQ)的影响，因而通过中介分析来验证假设，但实际上我们得到的只是变量间的相关，而不能得到期望的因果关系。
那么我们应该如何去验证变量间的因果关系？
]
---
# 3.1 因果推断(Casual Inference)
.size5[
确认变量间存在因果关系至少满足三个条件 `\(^*\)`：
1.时间顺序：因在果之前发生；
2.共变：因果之间存在相关，原因的变化伴随结果的变化；
3.排除其他可能的解释
]
--
.size5[
目前社科中常用的一个因果推断框架是反事实(conterfactual)推断，即观察到与事实情况相反的情况：
- 如，一个人得了感冒， 而服用感冒药以后症状得到了缓解，而对药效的归因则因为“如果当时不吃药，感冒就好不了”（即反事实）
- 但反事实理论框架要求需要针对特定的个体——相同个体，当时在感冒发生时不吃药，且最后“感冒好不了”
- 由于反事实的“不可观测性”，实际研究中使用随机对照的方式来解决（找到发生在相似个体身上的“反事实情况”）。
]
.footnote[
.footsize[
刘国芳,程亚华,辛自强.作为因果关系的中介效应及其检验[J].心理技术与应用,2018,6(11):665-676
]
]
---
# 3.2 因果推断与概率
假设100万儿童中已有99%接种了疫苗，1%没有接种。
- 接种疫苗：有1%的可能性出现不良反应，这种不良反应有1%的可能性导致儿童死亡，但不可能得天花。
- 未接种疫苗：有2%的概率得天花。最后，假设天花的致死率是20%。
要不要接种？
--
- 99万接种：则有990000\*1% = 9900的人出现不良反应，9900\*1% = 99人因不良反应死亡
- 1万未接种：有10000\*2% = 200人得了天花，共200\*20% = 40人因天花死亡
不接种疫苗更好？
--
如果基于一个反事实问题：疫苗接种率为0时会如何？
共100万\*2% = 20000人得天花，20000\*20% = 4000人会因天花死亡。
.size5[
“‘因果关系不能被简化为概率’这个认识来之 不易……这个概念也存在于我们的直觉中，并且根深蒂固。例如，当我们说“鲁莽驾驶会导致交通事故”或“你会因为懒惰而挂科”时，我们很清楚地知道，前者只是增加了后者发生的可能性，而非必然会让后者发生。”]
.footnote[
-----------
Ref: 《The Book of Why: The New Science of Cause and Effect》
]
---
# 3.3 基于实验的中介
.pull-left[
.size5[
如何验证中介中的因果？
]]
.pull-right[
<div class="grViz html-widget html-fill-item" id="htmlwidget-e2617df3851641c94082" style="width:540px;height:200px;"></div>
<script type="application/json" data-for="htmlwidget-e2617df3851641c94082">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X -> M\n X -> Y\n M -> Y\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
--
假设：教材难度(X)通过焦虑(M)来影响努力程度(Y)，可以穷举出在哪些情况下我们不能验证中介中的因果：
- 教材难度(X)不能影响焦虑(M)
- 焦虑(M)不能影响努力程度(Y)
- 教材难度(X)可以影响焦虑(M)，焦虑(M)也可以影响努力程度(Y)，由 X 的变化引起的 M 的变化并不会导致 Y 的变化（即 M 对 Y 的影响与 X 对 Y 的影响无关）。
---
.size5[
• 操纵X
• 测量 M
• 测量 Y
对X进行操纵（如使用不同难度的教材），可以验证X对M的因果关系，但M与Y之间的因果关系并没有得到验证
]
<div class="grViz html-widget html-fill-item" id="htmlwidget-d175c2bf8b0efa5b56e9" style="width:540px;height:200px;"></div>
<script type="application/json" data-for="htmlwidget-d175c2bf8b0efa5b56e9">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X -> M\n X -> Y\n M -> Y\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
---
.size5[
但如果我们理论假设错误，测量的是焦虑（A），但实际上实验操纵引发的中介应为恐惧(M,即实际路径应为X - M - Y,而我们测量路径为X - A - Y)，那么刚才的实验设计可能无法证伪，因此需要对A进行操纵：
• 操纵 X
• 操纵 A
• 测量 Y
对X(如使用不同难度的教材)和A(控制组 vs 提供相关辅导以减轻焦虑)进行操纵，如果对A的操纵不能影响Y，则可以证明中介路径不合理
]
<div class="grViz html-widget html-fill-item" id="htmlwidget-aca18bd523be5ef902ca" style="width:540px;height:200px;"></div>
<script type="application/json" data-for="htmlwidget-aca18bd523be5ef902ca">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.3,weight = 0.3,fontsize = 10]\n \n # 定义边\n edge [color = black, arrowhead = vee,fontsize = 10]\n\n X -> M\n X -> Y\n M -> Y\n X -> A\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
---
.size5[
Ref
- lavaan(提供了完整的SEM代码教程): [https://lavaan.ugent.be/tutorial/](https://lavaan.ugent.be/tutorial/)
<<<<<<< HEAD
- 调节验证中介：[https://doi.org/10.1016/j.jesp.2023.104507](https://doi.org/10.1016/j.jesp.2023.104507)
- 内隐中介分析：[https://journals.sagepub.com/doi/10.1177/25152459211047227](https://journals.sagepub.com/doi/10.1177/25152459211047227)
=======
- 通过实验来验证中介效应([葛枭语, 2023](https://doi.org/10.1016/j.jesp.2023.104507))
- 内隐中介分析([Bullock et al , 2023, AMPPS](https://journals.sagepub.com/doi/10.1177/25152459211047227))
- 相关不等于因果([Rohrer, 2018](https://doi.org/10.1177/2515245917745629))
- A lot of processes ([Rohrer, 2022](https://doi.org/10.1177/25152459221095827))
>>>>>>> cc43e2413a99a12b8a8a6d535263c085c1fec44f
]
</textarea>
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var s = d.createElement("style"), r = d.querySelector(".remark-slide-scaler");
if (!r) return;
s.type = "text/css"; s.innerHTML = "@page {size: " + r.style.width + " " + r.style.height +"; }";
d.head.appendChild(s);
})(document);
(function(d) {
var el = d.getElementsByClassName("remark-slides-area");
if (!el) return;
var slide, slides = slideshow.getSlides(), els = el[0].children;
for (var i = 1; i < slides.length; i++) {
slide = slides[i];
if (slide.properties.continued === "true" || slide.properties.count === "false") {
els[i - 1].className += ' has-continuation';
}
}
var s = d.createElement("style");
s.type = "text/css"; s.innerHTML = "@media print { .has-continuation { display: none; } }";
d.head.appendChild(s);
})(document);
// delete the temporary CSS (for displaying all slides initially) when the user
// starts to view slides
(function() {
var deleted = false;
slideshow.on('beforeShowSlide', function(slide) {
if (deleted) return;
var sheets = document.styleSheets, node;
for (var i = 0; i < sheets.length; i++) {
node = sheets[i].ownerNode;
if (node.dataset["target"] !== "print-only") continue;
node.parentNode.removeChild(node);
}
deleted = true;
});
})();
// add `data-at-shortcutkeys` attribute to <body> to resolve conflicts with JAWS
// screen reader (see PR #262)
(function(d) {
let res = {};
d.querySelectorAll('.remark-help-content table tr').forEach(tr => {
const t = tr.querySelector('td:nth-child(2)').innerText;
tr.querySelectorAll('td:first-child .key').forEach(key => {
const k = key.innerText;
if (/^[a-z]$/.test(k)) res[k] = t; // must be a single letter (key)
});
});
d.body.setAttribute('data-at-shortcutkeys', JSON.stringify(res));
})(document);
(function() {
"use strict"
// Replace <script> tags in slides area to make them executable
var scripts = document.querySelectorAll(
'.remark-slides-area .remark-slide-container script'
);
if (!scripts.length) return;
for (var i = 0; i < scripts.length; i++) {
var s = document.createElement('script');
var code = document.createTextNode(scripts[i].textContent);
s.appendChild(code);
var scriptAttrs = scripts[i].attributes;
for (var j = 0; j < scriptAttrs.length; j++) {
s.setAttribute(scriptAttrs[j].name, scriptAttrs[j].value);
}
scripts[i].parentElement.replaceChild(s, scripts[i]);
}
})();
(function() {
var links = document.getElementsByTagName('a');
for (var i = 0; i < links.length; i++) {
if (/^(https?:)?\/\//.test(links[i].getAttribute('href'))) {
links[i].target = '_blank';
}
}
})();
// adds .remark-code-has-line-highlighted class to <pre> parent elements
// of code chunks containing highlighted lines with class .remark-code-line-highlighted
(function(d) {
const hlines = d.querySelectorAll('.remark-code-line-highlighted');
const preParents = [];
const findPreParent = function(line, p = 0) {
if (p > 1) return null; // traverse up no further than grandparent
const el = line.parentElement;
return el.tagName === "PRE" ? el : findPreParent(el, ++p);
};
for (let line of hlines) {
let pre = findPreParent(line);
if (pre && !preParents.includes(pre)) preParents.push(pre);
}
preParents.forEach(p => p.classList.add("remark-code-has-line-highlighted"));
})(document);</script>
<script>
slideshow._releaseMath = function(el) {
var i, text, code, codes = el.getElementsByTagName('code');
for (i = 0; i < codes.length;) {
code = codes[i];
if (code.parentNode.tagName !== 'PRE' && code.childElementCount === 0) {
text = code.textContent;
if (/^\\\((.|\s)+\\\)$/.test(text) || /^\\\[(.|\s)+\\\]$/.test(text) ||
/^\$\$(.|\s)+\$\$$/.test(text) ||
/^\\begin\{([^}]+)\}(.|\s)+\\end\{[^}]+\}$/.test(text)) {
code.outerHTML = code.innerHTML; // remove <code></code>
continue;
}
}
i++;
}
};
slideshow._releaseMath(document);
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement('script');
script.type = 'text/javascript';
script.src = 'https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-MML-AM_CHTML';
if (location.protocol !== 'file:' && /^https?:/.test(script.src))
script.src = script.src.replace(/^https?:/, '');