Anxiety, ADHD, Stress, and Depression
Let’s skim through the data to see if it looks correct. Let me know if you think there’s anything off
## Participant.code Executive.Networks Anxiety Depression Stress ADHD
## 1 SADP01 149.55 14 18 18 35
## 2 SADP05 187.46 25 23 26 56
## 3 SADP09 125.05 28 31 41 60
## 4 SADP11 124.16 16 22 27 62
## 5 SADP13 182.02 38 40 47 63
## 6 SADP14 218.83 28 20 26 49
## 7 SADP15 152.98 15 14 14 48
## 8 SADP18 179.28 14 14 20 54
## 9 SADP25 116.82 18 42 27 36
## 10 SADP27 216.76 44 48 42 53
## 11 SADP29 287.74 28 25 31 57
## 12 SADP30 170.71 16 19 15 36
## 13 SADP36 78.94 19 15 21 40
## 14 SADP37 216.64 18 18 22 31
## 15 SADP40 78.42 14 14 14 36
## 16 SADP42 160.49 25 34 29 38
## 17 SADP43 136.10 16 14 16 36
## 18 SADP44 363.52 46 23 51 73
## 19 SADP45 242.28 34 33 45 68
## 20 SADP46 88.30 15 11 18 53
## 21 SADP47 146.93 7 9 11 67
## 22 SADP49 266.71 28 18 17 58
## 23 SADP50 102.96 24 17 22 70
## 24 SADP51 150.27 22 17 26 65
## 25 SADP52 156.36 35 37 37 67
## 26 SADP53 235.12 21 16 24 75
## 27 SADP54 -38.92 6 8 5 53
## 28 SADP55 298.51 29 34 28 51
## 29 SADP56 -10.14 15 10 12 45
## 30 SADP57 174.66 9 17 14 64
## 31 SADP58 224.30 9 8 6 33
## 32 SADP59 183.41 20 17 19 54
## 33 SADP60 143.33 13 8 10 58
## 34 SADP61 204.91 8 17 11 45
## 35 SADP62 227.43 11 0 8 33
## 36 SADP63 281.91 8 16 23 57
## 37 SADP65 189.78 7 2 5 39
## 38 SADP67 108.24 12 7 14 56
## 39 SADP69 201.20 9 1 5 31
## 40 SADP70 206.99 17 13 23 60
## 41 SADP71 240.47 4 1 10 62
## 42 SADP72 218.00 25 28 26 78
## 43 SADP73 114.94 4 8 21 42
## 44 SADP74 266.21 1 2 9 37
## 45 SADP75 101.80 12 16 8 59
## 46 SADP76 193.02 18 13 28 57
## 47 SADP77 64.52 29 10 29 66
## 48 SADP78 193.88 10 3 17 43
## 49 SADP80 35.83 6 5 10 53
## 50 SADP82 130.55 20 18 23 63
## 51 SADP83 293.04 17 16 20 62
## 52 SADP81 205.33 1 3 4 44
## 53 SADP85 160.77 25 22 18 53
## 54 SADP66 158.42 5 4 3 39
## 55 SADP68 16.19 10 4 8 27Correlation
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 only
NOTE: The significance pairs are being colored.
They are:
- Anxiety - ADHD: r = 0.46
- Anxiety - Depression: r = 0.79
- Stress - Anxiety: r = 0.88
- Stress - ADHD: r = 0.5
- Stress - Depression: r = 0.8
In this plot, the darker shade of blue indicated a stronger relationship.
Therefore, I think we should focus on: Anxiety, ADHD, Stress, and Depression
Multilinear regression against Anxiety
##
## Call:
## lm(formula = Anxiety ~ Depression + ADHD + Stress, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.7677 -2.9800 0.2037 2.5421 11.6059
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.31265 2.74910 -0.114 0.910
## Depression 0.23621 0.09922 2.381 0.021 *
## ADHD 0.04030 0.05942 0.678 0.501
## Stress 0.59514 0.10684 5.570 9.58e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.775 on 51 degrees of freedom
## Multiple R-squared: 0.7988, Adjusted R-squared: 0.7869
## F-statistic: 67.48 on 3 and 51 DF, p-value: < 2.2e-16Based on the result, there are significant relationship between:
Stress and Anxiety (positive correlation, slope beta = 0.59514, p < 0.0001).
This means that for an increase of 1 unit of stress, anxiety will increase by 0.59514 unit.Anxiety and Depression (positive correlation, slope beta = 0.23621, p < 0.05)
Since only Stress - Anxiety pair is significance in the multi-linear
regression, I think we should visualize the relationship for each pairs
without the other variables.
The equation shown in the visualization is the simple linear regression
equation between Anxiety and Stress.
Visualization for Anxiety and Stress
Visualization for Anxiety and Depression
Multilinear Regression against Stress
##
## Call:
## lm(formula = Stress ~ Depression + ADHD + Anxiety, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.9510 -2.9353 -0.5047 1.9573 13.3733
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.70024 2.81605 -0.959 0.34214
## Depression 0.30274 0.09942 3.045 0.00368 **
## ADHD 0.12768 0.05904 2.163 0.03527 *
## Anxiety 0.63558 0.11410 5.570 9.58e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.935 on 51 degrees of freedom
## Multiple R-squared: 0.8212, Adjusted R-squared: 0.8107
## F-statistic: 78.08 on 3 and 51 DF, p-value: < 2.2e-16Based on the result, there are a significant relationship between:
Stress and Anxiety - this matches with our result above, so see previous section.
Stress and Depression - positive correlation, slope beta = 0.30274, p < 0.01.
This means that for an increase of 1 unit of depression, stress will increase by 0.302744 unit.Stress and ADHD - positive correlation, slope beta = 0.12768, p < 0.05.
This means that for an increase of 1 unit of ADHD, stress will increase by 0.12768 unit.
Since we already visualize the relationship between stress and
anxiety, we just need to do it for Stress and Depression now.
Again the equation shown in the visualization is the simple linear
regression equation between the pairs without other variables.
Visualization for Stress - Depression
Visualization for Stress - ADHD
Multilinear regression model agaisn Depression.
##
## Call:
## lm(formula = Depression ~ Stress + ADHD + Anxiety, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.8143 -3.4080 -0.5757 3.0481 20.1398
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.5054 3.6268 1.242 0.21983
## Stress 0.5082 0.1669 3.045 0.00368 **
## ADHD -0.1108 0.0784 -1.413 0.16372
## Anxiety 0.4234 0.1779 2.381 0.02105 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.394 on 51 degrees of freedom
## Multiple R-squared: 0.6876, Adjusted R-squared: 0.6692
## F-statistic: 37.42 on 3 and 51 DF, p-value: 6.3e-13This model confirmed the relationship we discussed in previous model:
- Stress - Depression
- Anxiety Depression
Multilinear regression against ADHD
##
## Call:
## lm(formula = ADHD ~ Stress + Depression + Anxiety, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.637 -9.214 0.879 6.842 24.579
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 40.2910 3.1258 12.890 <2e-16 ***
## Stress 0.6580 0.3042 2.163 0.0353 *
## Depression -0.3401 0.2407 -1.413 0.1637
## Anxiety 0.2218 0.3270 0.678 0.5007
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.2 on 51 degrees of freedom
## Multiple R-squared: 0.2816, Adjusted R-squared: 0.2393
## F-statistic: 6.663 on 3 and 51 DF, p-value: 0.0006981Only Stress has a positive relationship with ADHD (positive slope,
beta = 0.6580, p < 0.05)
This means that for an increase of 1 unit of stress, ADHD will increase
by 0.6580 unit.
This model confirmed the relationship we discussed in previous model.
Conclusion Note:
Of course, we can see the redundant when running correlation test and
regression because they only confirm the relationship.
What make them different is that regression can help us with making
prediction.
What we have so far for these model:
- Anxiety and Stress (R-squared = 0.78)
- Anxiety and Depression (R-squared = 0.63)
- Stress and Depression (R-squared = 0.64)
- Stress and ADHD (R-squared = 0.25)
Although all four models show a linear trend, Anxiety and Stress
model is the most reliable model to make prediction regarding the
relationship between the two variables.
Stress and ADHD model is somewhat the least reliable. We can see that
they did not really form a linear trend. This confirms their
relationship is weaker, and more difficult to predict.
Executive - Depression - Anxiety - Stress (11/13)
Multilinear Regression against Excutive.Networks is NOT SIGNIFICANT*
##
## Call:
## lm(formula = Executive.Networks ~ Depression + Anxiety + Stress,
## data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -172.029 -45.247 5.318 50.822 123.678
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 125.5093 21.2453 5.908 2.86e-07 ***
## Depression -1.1736 1.6358 -0.717 0.476
## Anxiety 0.7605 2.2227 0.342 0.734
## Stress 2.4851 2.0678 1.202 0.235
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 76.14 on 51 degrees of freedom
## Multiple R-squared: 0.1083, Adjusted R-squared: 0.05589
## F-statistic: 2.066 on 3 and 51 DF, p-value: 0.1163Simple Linear Regression Exc.Networks - Depression is NOT SIGNIFICANT
##
## Call:
## lm(formula = Executive.Networks ~ Depression, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -196.487 -45.267 2.449 47.068 184.674
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 146.2176 18.7511 7.798 2.36e-10 ***
## Depression 1.4186 0.9484 1.496 0.141
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 77.48 on 53 degrees of freedom
## Multiple R-squared: 0.0405, Adjusted R-squared: 0.0224
## F-statistic: 2.237 on 1 and 53 DF, p-value: 0.1406Simple Linear Regression Exc.Networks - Anxiety is 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: 0.0347Simple Linear Regression Exc.Networks - Stress is SIGNIFICANT (p<0.05)
##
## Call:
## lm(formula = Executive.Networks ~ Stress, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -175.653 -49.010 5.063 54.088 126.760
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 125.8609 20.7230 6.073 1.38e-07 ***
## Stress 2.1745 0.9008 2.414 0.0193 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 75.08 on 53 degrees of freedom
## Multiple R-squared: 0.09905, Adjusted R-squared: 0.08205
## F-statistic: 5.827 on 1 and 53 DF, p-value: 0.01927MEDIATION MODEL: Excutive.Networks (IV) - Stress (Mediator) - Anxiety (DV)
Here is a step by step procedure I perform
Prerequisite of significance must exist in these simple linear regressions:
Effect of Executive.Networks (IV) on Stress (Mediator) — SIGNIFICANT p<0.05
##
## Call:
## lm(formula = Stress ~ Executive.Networks, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -17.704 -6.003 -1.164 5.081 26.357
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.35148 3.51830 3.511 0.000922 ***
## Executive.Networks 0.04555 0.01887 2.414 0.019272 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.87 on 53 degrees of freedom
## Multiple R-squared: 0.09905, Adjusted R-squared: 0.08205
## F-statistic: 5.827 on 1 and 53 DF, p-value: 0.01927Effect of Executive.Networks (IV) on Anxiety (DV) —- SIGNIFICANT p<0.05
##
## Call:
## lm(formula = Anxiety ~ Executive.Networks, data = df[, -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -20.2431 -7.5410 -0.4858 6.2429 24.6199
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.21392 3.24051 3.461 0.00107 **
## Executive.Networks 0.03767 0.01738 2.168 0.03470 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.01 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 Stress (Mediator) on Anxiety (DV) - SIGNIFICANT p<0.001
##
## Call:
## lm(formula = Anxiety ~ Executive.Networks + Stress, data = df[,
## -1])
##
## Residuals:
## Min 1Q Median 3Q Max
## -14.278 -3.339 0.721 3.122 12.746
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.320100 1.792770 0.736 0.465
## Executive.Networks 0.001187 0.009125 0.130 0.897
## Stress 0.801023 0.063045 12.706 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.987 on 52 degrees of freedom
## Multiple R-squared: 0.7762, Adjusted R-squared: 0.7676
## F-statistic: 90.18 on 2 and 52 DF, p-value: < 2.2e-16The result suggest a possibility of a COMPLETE MEDIATION, however it does not guarantee if the mediation is significant
A Causal Mediation Model with Bootstraping technique.
This step is to assess whether the mediation is significant
##
## Causal Mediation Analysis
##
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
##
## Estimate 95% CI Lower 95% CI Upper p-value
## ACME 0.03649 0.00288 0.06 0.034 *
## ADE 0.00119 -0.01697 0.02 0.914
## Total Effect 0.03767 -0.00206 0.07 0.060 .
## Prop. Mediated 0.96850 0.03785 2.73 0.049 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Sample Size Used: 55
##
##
## Simulations: 10000Based on the result:
- The indirect effect of Executive.Networks (IV) on
Anxiety (DV) is significant at alpha = 0.05 (ACME =
0.036487, p < 0.05)
- The direct effect of Executive.Networks (IV) on
Anxiety (DV) is NOT significant (ADE = 0.001187, p = 0.92)
- The total effect of Executive.Networks (IV) on Anxiety (DV) is significant at alpha = 0.1 but NOT SIGNIFICANT at alpha = 0.05 (Total Effect = 0.968497, p = 0.06)