調節分析
資料與管理
#讀檔案，這是 CSV 檔（用逗號分隔的檔），可以用 notepad 或 EXCEL 開啟
dta <- read.csv("modmed2.csv", header = TRUE)調節徑路分析模型：總效果模型
方法一：調節效果，用 PROCESS 功能分析
#載入 PROCESS，特別記得要讓 process.r 可讀取（在同目錄，或特定目錄）
source('process.r')##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## PROCESS is now ready for use.
## Copyright 2020-2023 by Andrew F. Hayes ALL RIGHTS RESERVED
## Workshop schedule at http://haskayne.ucalgary.ca/CCRAM
## #用 PROCESS 處理
#套件的變項要用字串符號括入（統計能力好，程式能力待加強）
process (data = dta, y = 'Y', x = 'X', m='M',w ='Z', model = 59,
moments = 1,jn = 1,plot=1, modelbt= 1, boot = 999)##
## ********************* PROCESS for R Version 4.3.1 *********************
##
## Written by Andrew F. Hayes, Ph.D. www.afhayes.com
## Documentation available in Hayes (2022). www.guilford.com/p/hayes3
##
## ***********************************************************************
##
## Model : 59
## Y : Y
## X : X
## M : M
## W : Z
##
## Sample size: 2000
##
## Random seed: 112672
##
##
## ***********************************************************************
## Outcome Variable: M
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.4081 0.1665 0.9716 132.9261 3.0000 1996.0000 0.0000
##
## Model:
## coeff se t p LLCI ULCI
## constant -0.0142 0.0221 -0.6442 0.5195 -0.0575 0.0290
## X 0.3874 0.0220 17.5794 0.0000 0.3441 0.4306
## Z 0.0140 0.0222 0.6336 0.5264 -0.0294 0.0575
## Int_1 0.2068 0.0219 9.4498 0.0000 0.1639 0.2498
##
## Product terms key:
## Int_1 : X x Z
##
## Test(s) of highest order unconditional interaction(s):
## R2-chng F df1 df2 p
## X*W 0.0373 89.2985 1.0000 1996.0000 0.0000
## ----------
## Focal predictor: X (X)
## Moderator: Z (W)
##
## Conditional effects of the focal predictor at values of the moderator(s):
## Z effect se t p LLCI ULCI
## -0.9949 0.1816 0.0310 5.8631 0.0000 0.1208 0.2423
## 0.0012 0.3876 0.0220 17.5902 0.0000 0.3444 0.4308
## 0.9973 0.5936 0.0310 19.1307 0.0000 0.5328 0.6545
##
## Moderator value(s) defining Johnson-Neyman significance region(s):
## Value % below % above
## -2.4157 0.7000 99.3000
## -1.4983 6.6500 93.3500
##
## Conditional effect of focal predictor at values of the moderator:
## Z effect se t p LLCI ULCI
## -3.2621 -0.2874 0.0747 -3.8469 0.0001 -0.4339 -0.1409
## -2.8949 -0.2114 0.0671 -3.1524 0.0016 -0.3430 -0.0799
## -2.5276 -0.1355 0.0595 -2.2754 0.0230 -0.2522 -0.0187
## -2.4157 -0.1123 0.0573 -1.9612 0.0500 -0.2246 0.0000
## -2.1604 -0.0595 0.0522 -1.1409 0.2541 -0.1618 0.0428
## -1.7931 0.0165 0.0450 0.3660 0.7144 -0.0718 0.1047
## -1.4983 0.0775 0.0395 1.9612 0.0500 -0.0000 0.1549
## -1.4259 0.0924 0.0382 2.4204 0.0156 0.0175 0.1673
## -1.0586 0.1684 0.0320 5.2687 0.0000 0.1057 0.2311
## -0.6914 0.2444 0.0267 9.1453 0.0000 0.1920 0.2968
## -0.3241 0.3203 0.0231 13.8413 0.0000 0.2749 0.3657
## 0.0432 0.3963 0.0221 17.9673 0.0000 0.3530 0.4395
## 0.4104 0.4723 0.0238 19.8398 0.0000 0.4256 0.5189
## 0.7777 0.5482 0.0279 19.6802 0.0000 0.4936 0.6028
## 1.1449 0.6242 0.0334 18.6962 0.0000 0.5587 0.6897
## 1.5122 0.7001 0.0398 17.6005 0.0000 0.6221 0.7782
## 1.8794 0.7761 0.0467 16.6242 0.0000 0.6846 0.8677
## 2.2467 0.8521 0.0539 15.8066 0.0000 0.7464 0.9578
## 2.6140 0.9280 0.0613 15.1317 0.0000 0.8078 1.0483
## 2.9812 1.0040 0.0689 14.5733 0.0000 0.8689 1.1391
## 3.3485 1.0800 0.0766 14.1074 0.0000 0.9298 1.2301
## 3.7157 1.1559 0.0843 13.7148 0.0000 0.9906 1.3212
##
## Data for visualizing the conditional effect of the focal predictor:
## X Z M
## -0.9713 -0.9949 -0.2045
## 0.0293 -0.9949 -0.0229
## 1.0299 -0.9949 0.1588
## -0.9713 0.0012 -0.3907
## 0.0293 0.0012 -0.0028
## 1.0299 0.0012 0.3850
## -0.9713 0.9973 -0.5768
## 0.0293 0.9973 0.0172
## 1.0299 0.9973 0.6112
##
## ***********************************************************************
## Outcome Variable: Y
##
## Model Summary:
## R R-sq MSE F df1 df2 p
## 0.5565 0.3097 0.9955 178.9354 5.0000 1994.0000 0.0000
##
## Model:
## coeff se t p LLCI ULCI
## constant -0.0138 0.0223 -0.6198 0.5355 -0.0576 0.0299
## X 0.0008 0.0245 0.0325 0.9741 -0.0472 0.0488
## M 0.5001 0.0227 22.0683 0.0000 0.4557 0.5446
## Z 0.2894 0.0224 12.8998 0.0000 0.2454 0.3334
## Int_1 -0.0256 0.0245 -1.0443 0.2965 -0.0737 0.0225
## Int_2 0.1905 0.0226 8.4435 0.0000 0.1463 0.2348
##
## Product terms key:
## Int_1 : X x Z
## Int_2 : M x Z
##
## Test(s) of highest order unconditional interaction(s):
## R2-chng F df1 df2 p
## X*W 0.0004 1.0905 1.0000 1994.0000 0.2965
## M*W 0.0247 71.2925 1.0000 1994.0000 0.0000
## ----------
## Focal predictor: X (X)
## Moderator: Z (W)
##
## Data for visualizing the conditional effect of the focal predictor:
## X Z Y
## -0.9713 -0.9949 -0.3289
## 0.0293 -0.9949 -0.3026
## 1.0299 -0.9949 -0.2763
## -0.9713 0.0012 -0.0168
## 0.0293 0.0012 -0.0161
## 1.0299 0.0012 -0.0153
## -0.9713 0.9973 0.2952
## 0.0293 0.9973 0.2705
## 1.0299 0.9973 0.2457
## ----------
## Focal predictor: M (M)
## Moderator: Z (W)
##
## Conditional effects of the focal predictor at values of the moderator(s):
## Z effect se t p LLCI ULCI
## -0.9949 0.3105 0.0316 9.8339 0.0000 0.2486 0.3725
## 0.0012 0.5003 0.0227 22.0775 0.0000 0.4559 0.5448
## 0.9973 0.6901 0.0323 21.3935 0.0000 0.6269 0.7534
##
## Moderator value(s) defining Johnson-Neyman significance region(s):
## Value % below % above
## -2.0903 1.9500 98.0500
##
## Conditional effect of focal predictor at values of the moderator:
## Z effect se t p LLCI ULCI
## -3.2621 -0.1215 0.0766 -1.5860 0.1129 -0.2717 0.0287
## -2.9133 -0.0550 0.0691 -0.7958 0.4263 -0.1905 0.0805
## -2.5644 0.0115 0.0617 0.1861 0.8524 -0.1096 0.1325
## -2.2155 0.0780 0.0545 1.4313 0.1525 -0.0289 0.1848
## -2.0903 0.1018 0.0519 1.9612 0.0500 0.0000 0.2036
## -1.8666 0.1444 0.0474 3.0457 0.0024 0.0514 0.2375
## -1.5177 0.2109 0.0407 5.1844 0.0000 0.1311 0.2907
## -1.1688 0.2774 0.0344 8.0582 0.0000 0.2099 0.3449
## -0.8199 0.3439 0.0290 11.8725 0.0000 0.2871 0.4007
## -0.4710 0.4104 0.0248 16.5232 0.0000 0.3617 0.4591
## -0.1221 0.4768 0.0228 20.9385 0.0000 0.4322 0.5215
## 0.2268 0.5433 0.0233 23.2854 0.0000 0.4976 0.5891
## 0.5757 0.6098 0.0263 23.1439 0.0000 0.5581 0.6615
## 0.9246 0.6763 0.0311 21.7365 0.0000 0.6153 0.7373
## 1.2735 0.7428 0.0370 20.0984 0.0000 0.6703 0.8152
## 1.6224 0.8092 0.0434 18.6266 0.0000 0.7240 0.8944
## 1.9713 0.8757 0.0503 17.3992 0.0000 0.7770 0.9744
## 2.3201 0.9422 0.0575 16.3943 0.0000 0.8295 1.0549
## 2.6690 1.0087 0.0648 15.5705 0.0000 0.8816 1.1357
## 3.0179 1.0752 0.0722 14.8893 0.0000 0.9335 1.2168
## 3.3668 1.1416 0.0797 14.3199 0.0000 0.9853 1.2980
## 3.7157 1.2081 0.0873 13.8384 0.0000 1.0369 1.3793
##
## Data for visualizing the conditional effect of the focal predictor:
## M Z Y
## -1.0840 -0.9949 -0.6376
## -0.0051 -0.9949 -0.3026
## 1.0737 -0.9949 0.0325
## -1.0840 0.0012 -0.5558
## -0.0051 0.0012 -0.0161
## 1.0737 0.0012 0.5237
## -1.0840 0.9973 -0.4741
## -0.0051 0.9973 0.2705
## 1.0737 0.9973 1.0150
##
## ***********************************************************************
## Bootstrapping progress:
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##
## **************** DIRECT AND INDIRECT EFFECTS OF X ON Y ****************
##
## Conditional direct effect(s) of X on Y:
## Z effect se t p LLCI ULCI
## -0.9949 0.0263 0.0319 0.8233 0.4104 -0.0363 0.0889
## 0.0012 0.0008 0.0245 0.0313 0.9751 -0.0472 0.0488
## 0.9973 -0.0248 0.0371 -0.6681 0.5042 -0.0974 0.0479
##
## Conditional indirect effects of X on Y:
##
## INDIRECT EFFECT:
##
## X -> M -> Y
##
## Z Effect BootSE BootLLCI BootULCI
## -0.9949 0.0564 0.0107 0.0369 0.0787
## 0.0012 0.1939 0.0143 0.1668 0.2230
## 0.9973 0.4097 0.0285 0.3550 0.4676
##
## ********** BOOTSTRAP RESULTS FOR REGRESSION MODEL PARAMETERS **********
##
## Outcome variable: M
##
## Coeff BootMean BootSE BootLLCI BootULCI
## constant -0.0142 -0.0143 0.0222 -0.0574 0.0293
## X 0.3874 0.3870 0.0220 0.3430 0.4302
## Z 0.0140 0.0143 0.0213 -0.0274 0.0560
## Int_1 0.2068 0.2068 0.0203 0.1664 0.2456
## ----------
## Outcome variable: Y
##
## Coeff BootMean BootSE BootLLCI BootULCI
## constant -0.0138 -0.0143 0.0225 -0.0586 0.0299
## X 0.0008 0.0004 0.0242 -0.0480 0.0484
## M 0.5001 0.5004 0.0228 0.4546 0.5454
## Z 0.2894 0.2896 0.0221 0.2472 0.3332
## Int_1 -0.0256 -0.0257 0.0239 -0.0730 0.0208
## Int_2 0.1905 0.1905 0.0218 0.1475 0.2327
##
## ******************** ANALYSIS NOTES AND ERRORS ************************
##
## Level of confidence for all confidence intervals in output: 95
##
## Number of bootstraps for percentile bootstrap confidence intervals: 5000
##
## W values in conditional tables are the mean and +/- SD from the mean.#畫圖，這圖意義不大
m3 <- lm(Y ~ X+M+X:Z+M:Z, data = dta)
interactions::interact_plot(m3, pred = M, modx = Z, interval = TRUE,
int.type = "confidence", int.width = .8)
interactions::interact_plot(m3, pred = X, modx = Z, interval = TRUE,
int.type = "confidence", int.width = .8)
調節徑路分析模型：總效果模型
方法二：調節效果，用 lavaan 功能分析
dta$int1 <- dta$X*dta$Z
dta$int2 <- dta$M*dta$Z
k1 <- mean(dta$Z)-sd(dta$Z)
k2 <- mean(dta$Z)
k3 <- mean(dta$Z)+sd(dta$Z)
round(c(k1,k2,k3),3)## [1] -0.995 0.001 0.997model1 <-'
M ~ a1*X+a2*int1+a3*Z
Y ~ c1*X +c2*int1+c3*Z+b1*M + b2*int2
sslope1med1 := (b1+b2*(-.995))*(a1+a2*(-.995))
sslope1med2 := (b1+b2*(-0.001))*(a1+a2*(-0.001))
sslope1med3 := (b1+b2*(0.997))*(a1+a2*(0.997))
'#徑路分析報表
fit <- lavaan::sem(model1, data=dta)
summary(fit)## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 10
##
## Number of observations 2000
##
## Model Test User Model:
##
## Test statistic 0.816
## Degrees of freedom 1
## P-value (Chi-square) 0.366
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## M ~
## X (a1) 0.387 0.022 17.597 0.000
## int1 (a2) 0.207 0.022 9.459 0.000
## Z (a3) 0.014 0.022 0.634 0.526
## Y ~
## X (c1) 0.001 0.024 0.033 0.974
## int1 (c2) -0.026 0.024 -1.047 0.295
## Z (c3) 0.289 0.022 12.919 0.000
## M (b1) 0.500 0.023 22.106 0.000
## int2 (b2) 0.191 0.023 8.458 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .M 0.970 0.031 31.623 0.000
## .Y 0.993 0.031 31.623 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## sslope1med1 0.056 0.011 5.028 0.000
## sslope1med2 0.194 0.014 13.761 0.000
## sslope1med3 0.410 0.029 14.343 0.000#以拔靴法看徑路係數與簡單中介效果信賴區間
set.seed(1234)
fit <- lavaan::sem(model1, data=dta, test="bootstrap", bootstrap=501)
parameterEstimates(fit,ci=TRUE,boot.ci.type="bca.simple")| lhs | op | rhs | label | est | se | z | pvalue | ci.lower | ci.upper |
|---|---|---|---|---|---|---|---|---|---|
| M | ~ | X | a1 | 0.387 | 0.022 | 17.6 | 0 | 0.344 | 0.431 |
| M | ~ | int1 | a2 | 0.207 | 0.0219 | 9.46 | 0 | 0.164 | 0.25 |
| M | ~ | Z | a3 | 0.014 | 0.0221 | 0.634 | 0.526 | -0.0293 | 0.0574 |
| Y | ~ | X | c1 | 0.000795 | 0.0244 | 0.0326 | 0.974 | -0.047 | 0.0486 |
| Y | ~ | int1 | c2 | -0.0256 | 0.0245 | -1.05 | 0.295 | -0.0736 | 0.0223 |
| Y | ~ | Z | c3 | 0.289 | 0.0224 | 12.9 | 0 | 0.245 | 0.333 |
| Y | ~ | M | b1 | 0.5 | 0.0226 | 22.1 | 0 | 0.456 | 0.544 |
| Y | ~ | int2 | b2 | 0.191 | 0.0225 | 8.46 | 0 | 0.146 | 0.235 |
| M | ~~ | M | 0.97 | 0.0307 | 31.6 | 0 | 0.91 | 1.03 | |
| Y | ~~ | Y | 0.993 | 0.0314 | 31.6 | 0 | 0.931 | 1.05 | |
| X | ~~ | X | 1 | 0 | 1 | 1 | |||
| X | ~~ | int1 | -0.00142 | 0 | -0.00142 | -0.00142 | |||
| X | ~~ | Z | -0.0112 | 0 | -0.0112 | -0.0112 | |||
| X | ~~ | int2 | 0.21 | 0 | 0.21 | 0.21 | |||
| int1 | ~~ | int1 | 1.02 | 0 | 1.02 | 1.02 | |||
| int1 | ~~ | Z | 0.0452 | 0 | 0.0452 | 0.0452 | |||
| int1 | ~~ | int2 | 0.421 | 0 | 0.421 | 0.421 | |||
| Z | ~~ | Z | 0.992 | 0 | 0.992 | 0.992 | |||
| Z | ~~ | int2 | 0.0284 | 0 | 0.0284 | 0.0284 | |||
| int2 | ~~ | int2 | 1.2 | 0 | 1.2 | 1.2 | |||
| sslope1med1 | := | (b1+b2*(-.995))*(a1+a2*(-.995)) | sslope1med1 | 0.0564 | 0.0112 | 5.03 | 4.96e-07 | 0.0344 | 0.0784 |
| sslope1med2 | := | (b1+b2*(-0.001))*(a1+a2*(-0.001)) | sslope1med2 | 0.194 | 0.0141 | 13.8 | 0 | 0.166 | 0.221 |
| sslope1med3 | := | (b1+b2*(0.997))*(a1+a2*(0.997)) | sslope1med3 | 0.41 | 0.0286 | 14.3 | 0 | 0.354 | 0.466 |
#畫圖看模型與估計值
lavaanPlot::lavaanPlot(model = fit,
edge_options = list(color = "grey"),
coefs = TRUE,
stand = TRUE)#畫圖，這圖意義不大
m3 <- lm(Y ~ X+M+X:Z+M:Z, data = dta)
interactions::interact_plot(m3, pred = M, modx = Z, interval = TRUE,
int.type = "confidence", int.width = .8)
interactions::interact_plot(m3, pred = X, modx = Z, interval = TRUE,
int.type = "confidence", int.width = .8)