9 中介效果分析
本單元介紹如何以R語言做中介效果分析。
9.1 讀入資料並畫圖檢視
以JASP提供的mediation.csv為例，以R做分析。
此資料為一項假設的研究資料。在研究中以量表詢問了父母對孩子的養育採取自由放任態度的程度(laissez_faire)、孩子的獨立程度(independence)、以及孩子的探索行為量(exploration)。研究假設為：強烈的自由放任態度對孩子的獨立性有正向的效果。其可能的機制為，自由放任的態度會影響孩子的探索行為量，進而影響其獨立性。意即，探索是態度對獨立性影響的中介變項。
以read.table()獨入資料。
mData <- read.table("mediation.csv", header=TRUE, sep=",")| laissez_faire | exploration | independence | disobedience |
|---|---|---|---|
| 7 | 4 | 8 | 2 |
| 6 | 2 | 6 | 3 |
| 12 | 3 | 7 | 4 |
| 14 | 4 | 7 | 5 |
| 17 | 6 | 11 | 3 |
| 19 | 6 | 10 | 5 |
9.2 以R內建的lm函數來做分析
9.2.1 總效果檢驗
以laissez_faire預測independence，模型解釋力顯著。
##
## Call:
## lm(formula = independence ~ laissez_faire, data = mData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.6202 -1.5732 -0.0493 1.4424 6.5051
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.21426 0.61960 8.415 3.27e-13 ***
## laissez_faire 0.23433 0.05151 4.549 1.54e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.363 on 98 degrees of freedom
## Multiple R-squared: 0.1744, Adjusted R-squared: 0.1659
## F-statistic: 20.7 on 1 and 98 DF, p-value: 1.544e-059.2.2 以預測項來預測中介變項
以laissez_faire預測exploration，效果亦顯著。
##
## Call:
## lm(formula = exploration ~ laissez_faire, data = mData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.12610 -0.76207 -0.08926 0.60196 2.56513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.18840 0.27134 8.065 1.84e-12 ***
## laissez_faire 0.17281 0.02256 7.661 1.33e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.035 on 98 degrees of freedom
## Multiple R-squared: 0.3746, Adjusted R-squared: 0.3682
## F-statistic: 58.69 on 1 and 98 DF, p-value: 1.333e-119.2.3 中介變項與預測項共同預測依變項
##
## Call:
## lm(formula = independence ~ exploration + laissez_faire, data = mData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1713 -0.7227 -0.0016 0.8303 2.8300
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.84015 0.38843 2.163 0.033003 *
## exploration 1.99877 0.11211 17.829 < 2e-16 ***
## laissez_faire -0.11107 0.03165 -3.509 0.000684 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.148 on 97 degrees of freedom
## Multiple R-squared: 0.807, Adjusted R-squared: 0.803
## F-statistic: 202.7 on 2 and 97 DF, p-value: < 2.2e-169.2.4 中介效果檢驗
以stargazer套件的stargazer()函數來看三變項之間的關係。
##
## Baron and Kenny Method
## =========================================================================================
## Dependent variable:
## ---------------------------------------------------------------------
## independence exploration independence
## (1) (2) (3)
## -----------------------------------------------------------------------------------------
## exploration 1.999***
## (0.112)
##
## laissez_faire 0.234*** 0.173*** -0.111***
## (0.052) (0.023) (0.032)
##
## Constant 5.214*** 2.188*** 0.840**
## (0.620) (0.271) (0.388)
##
## -----------------------------------------------------------------------------------------
## Observations 100 100 100
## R2 0.174 0.375 0.807
## Adjusted R2 0.166 0.368 0.803
## Residual Std. Error 2.363 (df = 98) 1.035 (df = 98) 1.148 (df = 97)
## F Statistic 20.696*** (df = 1; 98) 58.688*** (df = 1; 98) 202.746*** (df = 2; 97)
## =========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01以multilevel套件的sobel()函數來做Sobel test檢驗中介效果，看indirect effect是否顯著。
library(multilevel)
sobel(mData$laissez_faire, mData$exploration, mData$independence)## $`Mod1: Y~X`
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.2142586 0.61960212 8.415495 3.267909e-13
## pred 0.2343293 0.05150847 4.549335 1.543558e-05
##
## $`Mod2: Y~X+M`
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8401457 0.38842542 2.162952 3.300257e-02
## pred -0.1110699 0.03165459 -3.508809 6.841546e-04
## med 1.9987717 0.11210741 17.829078 2.255937e-32
##
## $`Mod3: M~X`
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.1884004 0.2713435 8.065056 1.842647e-12
## pred 0.1728057 0.0225572 7.660779 1.333137e-11
##
## $Indirect.Effect
## [1] 0.3453992
##
## $SE
## [1] 0.04907255
##
## $z.value
## [1] 7.038542
##
## $N
## [1] 100以bda套件的mediation.test()函數來做Sobel mediation test，變項的順序依序為mv、iv、dv。
library(bda)
mediation.test(mData$exploration, mData$laissez_faire, mData$independence)## Sobel Aroian Goodman
## z.value 7.038542e+00 7.029215e+00 7.047906e+00
## p.value 1.942620e-12 2.076993e-12 1.816300e-129.3 以psych套件來分析
用psych套件的mediate()函數來做中介效果的分析。
library(psych)
m1 <- mediate(independence ~ laissez_faire + (exploration), data=mData, n.iter = 10000) 
summary(m1)## Call: mediate(y = independence ~ laissez_faire + (exploration), data = mData,
## n.iter = 10000)
##
## Direct effect estimates (traditional regression) (c') X + M on Y
## independence se t df Prob
## Intercept 0.84 0.39 2.16 97 3.30e-02
## laissez_faire -0.11 0.03 -3.51 97 6.84e-04
## exploration 2.00 0.11 17.83 97 2.26e-32
##
## R = 0.9 R2 = 0.81 F = 202.75 on 2 and 97 DF p-value: 2.26e-35
##
## Total effect estimates (c) (X on Y)
## independence se t df Prob
## Intercept 5.21 0.62 8.42 98 3.27e-13
## laissez_faire 0.23 0.05 4.55 98 1.54e-05
##
## 'a' effect estimates (X on M)
## exploration se t df Prob
## Intercept 2.19 0.27 8.07 98 1.84e-12
## laissez_faire 0.17 0.02 7.66 98 1.33e-11
##
## 'b' effect estimates (M on Y controlling for X)
## independence se t df Prob
## exploration 2 0.11 17.83 97 2.26e-32
##
## 'ab' effect estimates (through all mediators)
## independence boot sd lower upper
## laissez_faire 0.35 0.35 0.05 0.26 0.44畫圖呈現。
mediate.diagram(m1)
9.4 以mediation套件來做分析
以mediation套件來做中介效果的分析。
library(mediation)
fitM <- lm(exploration ~ laissez_faire, data=mData)
fitY <- lm(independence ~ laissez_faire + exploration, data=mData)
summary(fitM)##
## Call:
## lm(formula = exploration ~ laissez_faire, data = mData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.12610 -0.76207 -0.08926 0.60196 2.56513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.18840 0.27134 8.065 1.84e-12 ***
## laissez_faire 0.17281 0.02256 7.661 1.33e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.035 on 98 degrees of freedom
## Multiple R-squared: 0.3746, Adjusted R-squared: 0.3682
## F-statistic: 58.69 on 1 and 98 DF, p-value: 1.333e-11
summary(fitY)##
## Call:
## lm(formula = independence ~ laissez_faire + exploration, data = mData)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1713 -0.7227 -0.0016 0.8303 2.8300
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.84015 0.38843 2.163 0.033003 *
## laissez_faire -0.11107 0.03165 -3.509 0.000684 ***
## exploration 1.99877 0.11211 17.829 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.148 on 97 degrees of freedom
## Multiple R-squared: 0.807, Adjusted R-squared: 0.803
## F-statistic: 202.7 on 2 and 97 DF, p-value: < 2.2e-16中介分析的結果如下表。其中，ACME為Average Causal Mediation Effect (indirect effects)，ADE為Average Direct Effect，Prop. Mediated為ACME/Total Effect的比率。由結果可知，laissez_faire可預測independence (b = 0.233, p < .001)，而exploration在此關係中具有中介效果(b = 0.344, p < .001), laissez_faire有直接效果(b = -0.111, p < .001)。
##
## Causal Mediation Analysis
##
## Quasi-Bayesian Confidence Intervals
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME 0.346 0.256 0.44 <2e-16 ***
## ADE -0.111 -0.172 -0.05 <2e-16 ***
## Total Effect 0.235 0.130 0.33 <2e-16 ***
## Prop. Mediated 1.480 1.163 2.10 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 100
##
##
## Simulations: 1000效果圖示。
plot(fitMed)
9.4.1 Bootstrapping法
若為小樣本、資料違反常態，可用Bootstrapping法。
fitMedBoot <- mediate(fitM, fitY, boot=TRUE, sims=999, treat="laissez_faire", mediator="exploration")
summary(fitMedBoot)##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME 0.345 0.262 0.44 <2e-16 ***
## ADE -0.111 -0.172 -0.05 <2e-16 ***
## Total Effect 0.234 0.150 0.33 <2e-16 ***
## Prop. Mediated 1.474 1.202 1.95 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 100
##
##
## Simulations: 999
plot(fitMedBoot)