-
Notifications
You must be signed in to change notification settings - Fork 256
/
chapter_11.html
1005 lines (721 loc) · 37.8 KB
/
chapter_11.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!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" />
<link href="libs/panelset-0.2.6/panelset.css" rel="stylesheet" />
<script src="libs/panelset-0.2.6/panelset.js"></script>
<script src="libs/htmlwidgets-1.6.4/htmlwidgets.js"></script>
<script src="libs/viz-1.8.2/viz.js"></script>
<link href="libs/DiagrammeR-styles-0.2/styles.css" rel="stylesheet" />
<script src="libs/grViz-binding-1.0.11/grViz.js"></script>
<link rel="stylesheet" href="css/zh-CN.css" type="text/css" />
<link rel="stylesheet" href="css/Custumed_Style.css" type="text/css" />
</head>
<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>
<script type="application/json" data-for="htmlwidget-15729d10e6c1d12556bb">{"x":{"diagram":"digraph {\n graph [layout = dot,rankdir = LR]\n \n # 定义节点\n node [shape = box, style = filled, fillcolor = \"lightblue\",height = 0.4,weight = 0.3,fontsize = 10]\n e1[style = NULL,fillcolor = NULL,penwidth = 0,height = 0.02,width = 0.02]\n \n # 定义边\n edge [color = black, arrowhead = vee]\n {rank = same; e1; Y}\n X -> Y [label = \"c\"]\n e1 -> Y\n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script>
]
------------------
<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[
<div class="grViz html-widget html-fill-item" id="htmlwidget-998346cb44a12602da36" style="width:540px;height:432px;"></div>
<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>
<style data-target="print-only">@media screen {.remark-slide-container{display:block;}.remark-slide-scaler{box-shadow:none;}}</style>
<script src="https://remarkjs.com/downloads/remark-latest.min.js"></script>
<script>var slideshow = remark.create({
"highlightLines": true,
"highlightStyle": "github",
"countIncrementalSlides": false,
"seal": true,
"ratio": "16:9"
});
if (window.HTMLWidgets) slideshow.on('afterShowSlide', function (slide) {
window.dispatchEvent(new Event('resize'));
});
(function(d) {
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?:/, '');