Mediation (NEW)
2022-11-15
Correlation
Correlation Matrix
## Executive.Networks Anxiety Depression Stress ADHD
## Executive.Networks 1.00 0.29 0.20 0.31 0.19
## Anxiety 0.29 1.00 0.79 0.88 0.46
## Depression 0.20 0.79 1.00 0.80 0.31
## Stress 0.31 0.88 0.80 1.00 0.50
## ADHD 0.19 0.46 0.31 0.50 1.00The Significance (p-value) of the correlation matrix
## Executive.Networks Anxiety Depression Stress
## Executive.Networks 0.00000000 3.470147e-02 1.406429e-01 1.927158e-02
## Anxiety 0.03470147 0.000000e+00 5.794143e-13 7.337602e-19
## Depression 0.14064292 5.794143e-13 0.000000e+00 2.020561e-13
## Stress 0.01927158 7.337602e-19 2.020561e-13 0.000000e+00
## ADHD 0.17231945 4.484795e-04 2.009350e-02 9.250119e-05
## ADHD
## Executive.Networks 1.723195e-01
## Anxiety 4.484795e-04
## Depression 2.009350e-02
## Stress 9.250119e-05
## ADHD 0.000000e+00Correlation Plot (Heat Map) showing the significance pair at alpha = 0.05
Those in Blue color is significant at alpha = 0.05.
Those in Blank/White color is NOT significant at alpha = 0.05.
In this plot, the darker shade of blue indicated a stronger relationship.
MEDIATION MODEL: Excutive.Networks (DV) - Stress (Mediator) - Anxiety (IV)
Here is a step by step procedure I perform
Prerequisite of significance must exist in these simple linear regressions:
Effect of Anxiety (IV) on Executive.Networks (DV) —- SIGNIFICANT p<0.05
##
## Call:
## lm(formula = Executive.Networks ~ Anxiety, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -183.356 -46.655 1.956 48.273 133.152
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 131.4666 20.3101 6.473 3.17e-08 ***
## Anxiety 2.1615 0.9972 2.168 0.0347 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 75.81 on 53 degrees of freedom
## Multiple R-squared: 0.08143, Adjusted R-squared: 0.0641
## F-statistic: 4.698 on 1 and 53 DF, p-value: 0.0347Effect of Anxiety (IV) on Stress (Mediator) — SIGNIFICANT p<0.001
##
## Call:
## lm(formula = Stress ~ Anxiety, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.1171 -3.7197 0.1222 2.6477 14.0623
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.07450 1.45119 2.119 0.0388 *
## Anxiety 0.96581 0.07125 13.555 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.417 on 53 degrees of freedom
## Multiple R-squared: 0.7761, Adjusted R-squared: 0.7719
## F-statistic: 183.7 on 1 and 53 DF, p-value: < 2.2e-16Effect of Stress (Mediator) on Executive.Networks (DV) —- NOT SIGNIFICANT!!!!
##
## Call:
## lm(formula = Executive.Networks ~ Anxiety + Stress, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -175.79 -49.43 4.34 54.20 125.79
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 125.458 21.146 5.933 2.46e-07 ***
## Anxiety 0.274 2.107 0.130 0.897
## Stress 1.954 1.922 1.017 0.314
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 75.78 on 52 degrees of freedom
## Multiple R-squared: 0.09934, Adjusted R-squared: 0.0647
## F-statistic: 2.868 on 2 and 52 DF, p-value: 0.06585The result suggest NO mediation exist.
##
## Mediation/Moderation Analysis
## Call: mediate(y = "Executive.Networks", x = "Anxiety", m = "Stress",
## data = df[, -1], n.iter = 10000)
##
## The DV (Y) was Executive.Networks . The IV (X) was Anxiety . The mediating variable(s) = Stress .
##
## Total effect(c) of Anxiety on Executive.Networks = 2.16 S.E. = 1 t = 2.17 df= 53 with p = 0.035
## Direct effect (c') of Anxiety on Executive.Networks removing Stress = 0.27 S.E. = 2.11 t = 0.13 df= 52 with p = 0.9
## Indirect effect (ab) of Anxiety on Executive.Networks through Stress = 1.89
## Mean bootstrapped indirect effect = 1.99 with standard error = 1.95 Lower CI = -1.52 Upper CI = 6.08
## R = 0.32 R2 = 0.1 F = 2.87 on 2 and 52 DF p-value: 0.0453
##
##
## Full output
## Call: mediate(y = "Executive.Networks", x = "Anxiety", m = "Stress",
## data = df[, -1], n.iter = 10000)
##
## Direct effect estimates (traditional regression) (c') X + M on Y
## Executive.Networks se t df Prob
## Intercept 125.46 21.15 5.93 52 2.46e-07
## Anxiety 0.27 2.11 0.13 52 8.97e-01
## Stress 1.95 1.92 1.02 52 3.14e-01
##
## R = 0.32 R2 = 0.1 F = 2.87 on 2 and 52 DF p-value: 0.0658
##
## Total effect estimates (c) (X on Y)
## Executive.Networks se t df Prob
## Intercept 131.47 20.31 6.47 53 3.17e-08
## Anxiety 2.16 1.00 2.17 53 3.47e-02
##
## 'a' effect estimates (X on M)
## Stress se t df Prob
## Intercept 3.07 1.45 2.12 53 3.88e-02
## Anxiety 0.97 0.07 13.56 53 7.34e-19
##
## 'b' effect estimates (M on Y controlling for X)
## Executive.Networks se t df Prob
## Stress 1.95 1.92 1.02 52 0.314
##
## 'ab' effect estimates (through all mediators)
## Executive.Networks boot sd lower upper
## Anxiety 1.89 1.99 1.95 -1.52 6.08Retest for indirect effect (aka mediation effect) – ACME NOT SIGNIFICANT
##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME 1.887 -1.501 6.17 0.315
## ADE 0.274 -4.535 4.24 0.901
## Total Effect 2.162 -0.094 4.31 0.062 .
## Prop. Mediated 0.873 -2.412 7.80 0.354
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 55
##
##
## Simulations: 10000