Pilot Analyses: Time Since Brain Injury-Mood-FA

Pilot Analyses

Trajectory

Depression

MODEL

model1 <- lm(Dep_BDI ~ Time.since.injury, data=tbi1) model2 <- lm(Dep_BDI ~ Time.since.injury + I(Time.since.injury^2), data=tbi1)

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SUMMARY

	Dep_LinearModel			Dep_QuadraticModel
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	25.99	24.57 – 27.41	<0.001	35.84	34.19 – 37.48	<0.001
Time since injury	-0.02	-0.03 – -0.01	0.004	-0.35	-0.40 – -0.31	<0.001
Time since injury^2				0.00	0.00 – 0.00	<0.001
Observations	486			486
R2 / R2 adjusted	0.017 / 0.015			0.368 / 0.365

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ANOVA COMPARISON

Analysis of Variance Table

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
484	32623
483	20992	1	11631	267.6	3.497e-48

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AIC

• AIC for model 1 (i.e., linear model) 3430

• AIC for model 2 (i.e.,quadratic model) 3217

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INTERPRETATION

• An ANOVA comparison suggests that there is a significant difference in the linear versus quadratic fit (p< 10^-29)
• The R-squared value of the linear model is 0.12. The adjusted R-squared value of the quadratic model is 0.32, suggesting more variance is explained by the second model.
• To ensure that that quadratic model is not better due to over-fitting, we also determined the AIC for each model. For the linear model, the AIC is 3152. For the quadratic model, the AIC is 3028. The ΔAIC is > 10, providing strong evidence that the model with lower AIC (i.e., the quadratic model) is a better fit.

Anxiety

MODEL

model1 <- lm(Anx_BAI ~ Time.since.injury, data=tbi1) model2 <- lm(Anx_BAI ~ Time.since.injury + I(Time.since.injury^2), data=tbi1)

---

SUMMARY

	Anx_LinearModel			Anx_QuadraticModel
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	17.06	16.11 – 18.00	<0.001	24.11	23.07 – 25.14	<0.001
Time since injury	-0.07	-0.08 – -0.06	<0.001	-0.31	-0.33 – -0.28	<0.001
Time since injury^2				0.00	0.00 – 0.00	<0.001
Observations	486			486
R2 / R2 adjusted	0.312 / 0.311			0.598 / 0.597

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ANOVA COMPARISON

Analysis of Variance Table

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
484	14325
483	8364	1	5961	344.2	2.063e-58

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AIC

• AIC for model 1 (i.e., linear model) 3030

• AIC for model 2 (i.e.,quadratic model) 2770

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INTERPRETATION

• An ANOVA comparison suggests that there is a significant difference in the linear versus quadratic fit (p< 10^-52)
• The R-squared value of the linear model is 0.35. The adjusted R-squared value of the quadratic model is 0.60, suggesting more variance is explained by the second model.
• To ensure that that quadratic model is not better due to over-fitting, we also determined the AIC for each model. For the linear model, the AIC is 2911. For the quadratic model, the AIC is 2678. The ΔAIC is >10, providing strong evidence that the model with lower AIC (i.e., the quadratic model) is a better fit.

FA

Across tracts

MODEL

model1 <- lm(FA ~ Time.since.injury, data=tbi1) model2 <- lm(FA ~ Time.since.injury + I(Time.since.injury^2), data=tbi1)

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SUMMARY

	FA_LinearModel			FA_QuadraticModel
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	0.54	0.53 – 0.55	<0.001	0.54	0.53 – 0.56	<0.001
Time since injury	-0.00	-0.00 – 0.00	0.396	-0.00	-0.00 – 0.00	0.397
Time since injury^2				0.00	-0.00 – 0.00	0.516
Observations	486			486
R2 / R2 adjusted	0.001 / -0.001			0.002 / -0.002

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ANOVA COMPARISON

Analysis of Variance Table

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
484	2.254
483	2.252	1	0.001968	0.4222	0.5161

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AIC

• AIC for model 1 (i.e., linear model) -1226

• AIC for model 2 (i.e.,quadratic model) -1225

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INTERPRETATION

• FA over Time since injury (without tract info) is not significantly different over time.

By tract

MODEL BY TRACT AND TIME

model1 <- lm(FA ~ Tract.ID + Time.since.injury + Tract.ID*Time.since.injury, data=tbi1) model2 <- lm(FA ~ Tract.ID + Time.since.injury + I(Time.since.injury^2) + Tract.ID:Time.since.injury + Tract.ID:I(Time.since.injury^2), data=tbi1)

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SUMMARY FOR MODEL BY TRACT AND TIME

	FA_LinearModel			FA_QuadraticModel
Predictors	Estimates	CI	p	Estimates	CI	p
(Intercept)	0.68	0.68 – 0.68	<0.001	0.69	0.68 – 0.69	<0.001
Tract ID forceps minor	-0.09	-0.10 – -0.08	<0.001	-0.09	-0.10 – -0.08	<0.001
Tract ID [left atr]	-0.18	-0.19 – -0.18	<0.001	-0.19	-0.19 – -0.18	<0.001
Tract ID [left cab]	-0.26	-0.26 – -0.25	<0.001	-0.26	-0.27 – -0.26	<0.001
Tract ID [left cing]	-0.03	-0.03 – -0.02	<0.001	-0.03	-0.04 – -0.02	<0.001
Tract ID [left cst]	-0.12	-0.13 – -0.11	<0.001	-0.12	-0.13 – -0.11	<0.001
Tract ID [left ilf]	-0.14	-0.14 – -0.13	<0.001	-0.14	-0.15 – -0.13	<0.001
Tract ID [left slfp]	-0.16	-0.17 – -0.16	<0.001	-0.16	-0.17 – -0.16	<0.001
Tract ID [left slft]	-0.13	-0.13 – -0.12	<0.001	-0.13	-0.14 – -0.12	<0.001
Tract ID [left unc]	-0.18	-0.18 – -0.17	<0.001	-0.18	-0.19 – -0.17	<0.001
Tract ID [right atr]	-0.19	-0.19 – -0.18	<0.001	-0.19	-0.20 – -0.18	<0.001
Tract ID [right cab]	-0.25	-0.26 – -0.24	<0.001	-0.26	-0.27 – -0.25	<0.001
Tract ID [right cing]	-0.01	-0.02 – -0.01	<0.001	-0.01	-0.02 – -0.01	0.001
Tract ID [right cst]	-0.12	-0.12 – -0.11	<0.001	-0.12	-0.13 – -0.11	<0.001
Tract ID [right ilf]	-0.14	-0.14 – -0.13	<0.001	-0.14	-0.15 – -0.13	<0.001
Tract ID [right slfp]	-0.18	-0.19 – -0.17	<0.001	-0.18	-0.19 – -0.17	<0.001
Tract ID [right slft]	-0.16	-0.16 – -0.15	<0.001	-0.16	-0.17 – -0.15	<0.001
Tract ID [right unc]	-0.18	-0.19 – -0.17	<0.001	-0.19	-0.19 – -0.18	<0.001
Time since injury	-0.00	-0.00 – -0.00	0.001	-0.00	-0.00 – -0.00	<0.001
Tract ID forceps minor × Time since injury	-0.00	-0.00 – 0.00	0.950	0.00	-0.00 – 0.00	0.500
Tract ID [left atr] × Time since injury	0.00	-0.00 – 0.00	0.081	0.00	-0.00 – 0.00	0.083
Tract ID [left cab] × Time since injury	0.00	0.00 – 0.00	0.011	0.00	0.00 – 0.00	0.001
Tract ID [left cing] × Time since injury	0.00	-0.00 – 0.00	0.518	0.00	-0.00 – 0.00	0.401
Tract ID [left cst] × Time since injury	0.00	-0.00 – 0.00	0.200	0.00	-0.00 – 0.00	0.236
Tract ID [left ilf] × Time since injury	0.00	-0.00 – 0.00	0.051	0.00	-0.00 – 0.00	0.356
Tract ID [left slfp] × Time since injury	0.00	-0.00 – 0.00	0.054	0.00	-0.00 – 0.00	0.135
Tract ID [left slft] × Time since injury	0.00	-0.00 – 0.00	0.122	0.00	-0.00 – 0.00	0.136
Tract ID [left unc] × Time since injury	0.00	0.00 – 0.00	0.032	0.00	-0.00 – 0.00	0.148
Tract ID [right atr] × Time since injury	-0.00	-0.00 – 0.00	0.472	0.00	-0.00 – 0.00	0.871
Tract ID [right cab] × Time since injury	0.00	-0.00 – 0.00	0.096	0.00	0.00 – 0.00	<0.001
Tract ID [right cing] × Time since injury	-0.00	-0.00 – -0.00	0.001	-0.00	-0.00 – 0.00	0.469
Tract ID [right cst] × Time since injury	0.00	-0.00 – 0.00	0.150	0.00	-0.00 – 0.00	0.121
Tract ID [right ilf] × Time since injury	-0.00	-0.00 – 0.00	0.708	0.00	-0.00 – 0.00	0.269
Tract ID [right slfp] × Time since injury	0.00	-0.00 – 0.00	0.302	0.00	-0.00 – 0.00	0.450
Tract ID [right slft] × Time since injury	-0.00	-0.00 – 0.00	0.493	0.00	-0.00 – 0.00	0.923
Tract ID [right unc] × Time since injury	-0.00	-0.00 – 0.00	0.307	0.00	0.00 – 0.00	0.043
Time since injury^2				0.00	0.00 – 0.00	0.001
Tract ID forceps minor × Time since injury^2				-0.00	-0.00 – 0.00	0.474
Tract ID [left atr] × Time since injury^2				-0.00	-0.00 – 0.00	0.197
Tract ID [left cab] × Time since injury^2				-0.00	-0.00 – -0.00	0.005
Tract ID [left cing] × Time since injury^2				-0.00	-0.00 – 0.00	0.496
Tract ID [left cst] × Time since injury^2				-0.00	-0.00 – 0.00	0.393
Tract ID [left ilf] × Time since injury^2				-0.00	-0.00 – 0.00	0.699
Tract ID [left slfp] × Time since injury^2				-0.00	-0.00 – 0.00	0.323
Tract ID [left slft] × Time since injury^2				-0.00	-0.00 – 0.00	0.274
Tract ID [left unc] × Time since injury^2				-0.00	-0.00 – 0.00	0.381
Tract ID [right atr] × Time since injury^2				-0.00	-0.00 – 0.00	0.706
Tract ID [right cab] × Time since injury^2				-0.00	-0.00 – -0.00	0.001
Tract ID [right cing] × Time since injury^2				-0.00	-0.00 – 0.00	0.848
Tract ID [right cst] × Time since injury^2				-0.00	-0.00 – 0.00	0.234
Tract ID [right ilf] × Time since injury^2				-0.00	-0.00 – 0.00	0.211
Tract ID [right slfp] × Time since injury^2				-0.00	-0.00 – 0.00	0.630
Tract ID [right slft] × Time since injury^2				-0.00	-0.00 – 0.00	0.765
Tract ID [right unc] × Time since injury^2				-0.00	-0.00 – -0.00	0.017
Observations	486			486
R2 / R2 adjusted	0.993 / 0.993			0.995 / 0.994

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ANOVA COMPARISON FOR MODELS BY TRACT AND TIME

Analysis of Variance Table

Res.Df	RSS	Df	Sum of Sq	F	Pr(>F)
450	0.01487
432	0.01212	18	0.002743	5.431	1.614e-11

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AIC FOR MODELS BY TRACT AND TIME

• AIC for model 1 (i.e., linear model) -3599

• AIC for model 2 (i.e.,quadratic model) -3662

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INTERPRETATION

• For models by tract and time, quadratic models are preferred (see ANOVA results, AIC scores)

Moderation Models

Statistical Framework

Should Tract.ID be considered a control variable or a moderating variable?

• Control variables are measured but their effect is not hypothesized. Moderator variables are measured, and their effect is hypothesized.
• In the statistical models below, Tract.ID is hypothesized to directly affect FA, not the relationship between time since injury and FA. So, it can be considered a control variable.
• Reference: https://business.fiu.edu/academics/graduate/insights/posts/control-and-moderation-its-easy-when-you-understand.html#:~:text=You%20decide%20which%20is%20which,latter%2C%20it%20is%20a%20moderator.

All Tracts

Time-Dep-FA

Research Q: How does depression moderate the relationship between time since injury and FA trajectory/recovery?

Hypotheses:

• Time since injury has a positive effect on FA.
• The positive effect of FA on time since injury is stronger for individuals with lower depressive symptoms.

Model Specification

time.Dep.FA.lme.model <- nlme::lme(zFA ~ zTime.since.injury*zDep_BDI,random=list(ParticipantID=~1, Tract.ID=~1), data=tbi)

Checking Model Assumptions

ASSUMPTION 1: Linearity

ASSUMPTION 2: Normal Distribution of Residuals

ASSUMPTION 3: Homoscedasticity of model and random effects

## OK: Error variance appears to be homoscedastic (p = 0.879).

ASSUMPTION 4: No Auto-Correlation of Residuals

ASSUMPTION 5: NO MULTI-COLLINEARITY

## # Check for Multicollinearity
## 
## Low Correlation
## 
##                         Term  VIF    VIF 95% CI Increased SE Tolerance
##           zTime.since.injury 1.03 [1.00,  1.40]         1.01      0.97
##                     zDep_BDI 1.03 [1.00,  1.37]         1.02      0.97
##  zTime.since.injury:zDep_BDI 1.01 [1.00, 13.12]         1.01      0.99
##  Tolerance 95% CI
##      [0.71, 1.00]
##      [0.73, 1.00]
##      [0.08, 1.00]

Results

## Linear mixed-effects model fit by REML
##   Data: tbi 
##         AIC       BIC   logLik
##   -968.3397 -936.1501 491.1698
## 
## Random effects:
##  Formula: ~1 | ParticipantID
##          (Intercept)
## StdDev: 0.0001090306
## 
##  Formula: ~1 | Tract.ID %in% ParticipantID
##         (Intercept)  Residual
## StdDev:   0.9638819 0.1019467
## 
## Fixed effects:  zFA ~ zTime.since.injury * zDep_BDI 
##                                   Value  Std.Error  DF   t-value p-value
## (Intercept)                 -0.01741002 0.16070895 699 -0.108333  0.9138
## zTime.since.injury          -0.03147903 0.00381327 699 -8.255130  0.0000
## zDep_BDI                     0.03496452 0.00724110 699  4.828620  0.0000
## zTime.since.injury:zDep_BDI -0.00721407 0.00313233 699 -2.303096  0.0216
##  Correlation: 
##                             (Intr) zTm.s. zD_BDI
## zTime.since.injury           0.002              
## zDep_BDI                     0.013  0.156       
## zTime.since.injury:zDep_BDI -0.001 -0.071 -0.083
## 
## Standardized Within-Group Residuals:
##         Min          Q1         Med          Q3         Max 
## -4.20172246 -0.55503697 -0.01485419  0.55910632  4.49691635 
## 
## Number of Observations: 738
## Number of Groups: 
##               ParticipantID Tract.ID %in% ParticipantID 
##                           2                          36

##                             numDF denDF  F-value p-value
## (Intercept)                     1   699  0.02743  0.8685
## zTime.since.injury              1   699 85.56834  <.0001
## zDep_BDI                        1   699 21.66266  <.0001
## zTime.since.injury:zDep_BDI     1   699  5.30425  0.0216

Plots

Time-Anx-FA

Research Q: How does anxiety moderate the relationship between time since injury and FA trajectory/recovery?

Hypotheses:

• Time since injury has a positive effect on FA.
• The positive effect of FA on time since injury is stronger for individuals with lower anxiety symptoms.

Model Specification

time.Anx.FA.lme.model <- nlme::lme(zFA ~ zTime.since.injury*zAnx_BAI,random=list(ParticipantID=~1, Tract.ID=~1), data=tbi)

Checking Model Assumptions

ASSUMPTION 1: Linearity

ASSUMPTION 2: Normal Distribution of Residuals

ASSUMPTION 3: Homoscedasticity of model and random effects

## OK: Error variance appears to be homoscedastic (p = 0.883).

ASSUMPTION 4: No Auto-Correlation of Residuals

ASSUMPTION 5: NO MULTI-COLLINEARITY

## # Check for Multicollinearity
## 
## Low Correlation
## 
##                         Term  VIF   VIF 95% CI Increased SE Tolerance
##           zTime.since.injury 1.36 [1.25, 1.50]         1.16      0.74
##                     zAnx_BAI 1.95 [1.76, 2.18]         1.39      0.51
##  zTime.since.injury:zAnx_BAI 1.51 [1.39, 1.68]         1.23      0.66
##  Tolerance 95% CI
##      [0.67, 0.80]
##      [0.46, 0.57]
##      [0.60, 0.72]

Results

## Linear mixed-effects model fit by REML
##   Data: tbi 
##         AIC       BIC   logLik
##   -957.5886 -925.3991 485.7943
## 
## Random effects:
##  Formula: ~1 | ParticipantID
##          (Intercept)
## StdDev: 0.0001030225
## 
##  Formula: ~1 | Tract.ID %in% ParticipantID
##         (Intercept)  Residual
## StdDev:   0.9652455 0.1027296
## 
## Fixed effects:  zFA ~ zTime.since.injury * zAnx_BAI 
##                                    Value  Std.Error  DF   t-value p-value
## (Intercept)                 -0.025654550 0.16094147 699 -0.159403  0.8734
## zTime.since.injury          -0.027729077 0.00441384 699 -6.282304  0.0000
## zAnx_BAI                     0.015299363 0.00678076 699  2.256292  0.0244
## zTime.since.injury:zAnx_BAI -0.006003478 0.00419150 699 -1.432297  0.1525
##  Correlation: 
##                             (Intr) zTm.s. zA_BAI
## zTime.since.injury          0.006               
## zAnx_BAI                    0.013  0.491        
## zTime.since.injury:zAnx_BAI 0.013  0.154  0.565 
## 
## Standardized Within-Group Residuals:
##          Min           Q1          Med           Q3          Max 
## -4.194119185 -0.561723620 -0.001038555  0.564403242  4.297677826 
## 
## Number of Observations: 738
## Number of Groups: 
##               ParticipantID Tract.ID %in% ParticipantID 
##                           2                          36

##                             numDF denDF  F-value p-value
## (Intercept)                     1   699  0.02735  0.8687
## zTime.since.injury              1   699 84.26891  <.0001
## zAnx_BAI                        1   699 13.79525  0.0002
## zTime.since.injury:zAnx_BAI     1   699  2.05147  0.1525

Mediation Models

Across all tracts

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00294     -0.01283         0.00    0.40
## ADE            -0.02780     -0.09614         0.05    0.43
## Total Effect   -0.03074     -0.10015         0.04    0.40
## Prop. Mediated  0.09577     -0.98504         0.83    0.60
## 
## Sample Size Used: 738 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.02510     -0.05358         0.00   0.072 .
## ADE            -0.00564     -0.08112         0.07   0.916  
## Total Effect   -0.03074     -0.10249         0.04   0.450  
## Prop. Mediated  0.81651     -7.45417         5.36   0.470  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 738 
## 
## 
## Simulations: 1000

FA as Mediator

Model does not hold since step 2 condition of mediator model requirement is not met.

Forceps Major

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.02004     -0.21199         0.17    0.86
## ADE            -0.00209     -0.10813         0.11    0.99
## Total Effect   -0.02214     -0.21907         0.17    0.86
## Prop. Mediated  0.90543     -6.14765         8.10    0.33
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.16796     -0.31387        -0.01   0.034 *
## ADE              0.14582     -0.00176         0.29   0.054 .
## Total Effect    -0.02214     -0.23229         0.19   0.852  
## Prop. Mediated   7.58691    -17.96670        18.92   0.822  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.03123     -0.29124         0.23    0.82
## ADE            -0.00624     -0.21004         0.21    0.94
## Total Effect   -0.03747     -0.38195         0.31    0.82
## Prop. Mediated  0.83350     -4.67290         5.86    0.39
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME            -0.0243      -0.2322         0.21   0.832   
## ADE             -0.3297      -0.5779        -0.10   0.002 **
## Total Effect    -0.3539      -0.7070        -0.04   0.030 * 
## Prop. Mediated   0.0686      -2.4398         0.53   0.802   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Forceps Minor

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.00374     -0.04121         0.03   0.808  
## ADE            -0.04696     -0.08153        -0.01   0.018 *
## Total Effect   -0.05069     -0.10221        -0.01   0.030 *
## Prop. Mediated  0.07373     -1.98667         0.76   0.782  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0317      -0.0692         0.00   0.040 *
## ADE             -0.0190      -0.0604         0.02   0.336  
## Total Effect    -0.0507      -0.1059         0.00   0.038 *
## Prop. Mediated   0.6248      -0.1127         2.24   0.062 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.2633      -0.5545         0.01   0.072 .
## ADE              0.2258      -0.0719         0.48   0.118  
## Total Effect    -0.0375      -0.4281         0.34   0.818  
## Prop. Mediated   7.0266     -16.5026        20.37   0.750  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.20696     -0.50781         0.00   0.052 .
## ADE            -0.14699     -0.40936         0.14   0.322  
## Total Effect   -0.35394     -0.70106        -0.05   0.026 *
## Prop. Mediated  0.58471     -0.00837         1.95   0.062 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L anterior thalamic radiation

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00375     -0.04934         0.03    0.82
## ADE             0.00598     -0.02919         0.04    0.70
## Total Effect    0.00223     -0.04704         0.05    0.92
## Prop. Mediated -1.67717     -9.75377         9.24    0.53
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.03288     -0.06490         0.00    0.03 *
## ADE              0.03512     -0.00860         0.07    0.10  
## Total Effect     0.00223     -0.04620         0.05    0.94  
## Prop. Mediated -14.71969    -20.99155        23.69    0.97  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            0.00926     -0.19487         0.19    0.90
## ADE            -0.04673     -0.32046         0.22    0.70
## Total Effect   -0.03747     -0.41416         0.32    0.83
## Prop. Mediated -0.24705     -3.80303         4.95    0.55
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME            0.00754     -0.15245         0.16   0.986   
## ADE            -0.36148     -0.63845        -0.09   0.008 **
## Total Effect   -0.35394     -0.69979        -0.05   0.026 * 
## Prop. Mediated -0.02129     -1.40240         0.38   0.988   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L cingulum-angular bundle

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0507      -0.4506         0.65    0.87
## ADE             -0.1213      -0.4427         0.16    0.38
## Total Effect    -0.0706      -0.5988         0.47    0.77
## Prop. Mediated  -0.7172      -5.0503         8.42    0.46
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             0.4200       0.0192         0.81   0.042 *
## ADE             -0.4906      -0.8615        -0.11   0.012 *
## Total Effect    -0.0706      -0.5754         0.46   0.838  
## Prop. Mediated  -5.9462     -22.8915        42.62   0.880  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0372      -0.2437         0.30    0.84
## ADE             -0.0746      -0.2934         0.14    0.46
## Total Effect    -0.0375      -0.4141         0.32    0.79
## Prop. Mediated  -0.9915      -5.5359         7.50    0.49
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME             0.0286      -0.1778         0.24   0.808   
## ADE             -0.3825      -0.6663        -0.12   0.004 **
## Total Effect    -0.3539      -0.7135        -0.02   0.038 * 
## Prop. Mediated  -0.0807      -2.9586         0.43   0.842   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L cingulum-cingulate gyrus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.01073     -0.12529         0.10    0.86
## ADE             0.00579     -0.05803         0.08    0.81
## Total Effect   -0.00495     -0.12271         0.12    0.95
## Prop. Mediated  2.17040     -4.69361         5.94    0.35
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.08668     -0.17003         0.00   0.048 *
## ADE              0.08174     -0.01410         0.17   0.080 .
## Total Effect    -0.00495     -0.11345         0.11   0.996  
## Prop. Mediated  17.52667    -23.68006        18.50   0.956  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0122      -0.3137         0.26    0.98
## ADE             -0.0253      -0.2269         0.19    0.83
## Total Effect    -0.0375      -0.4202         0.33    0.86
## Prop. Mediated   0.3246      -6.2489         6.44    0.37
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME           -0.00911     -0.22901         0.21   0.928   
## ADE            -0.34483     -0.62210        -0.10   0.006 **
## Total Effect   -0.35394     -0.72054        -0.02   0.036 * 
## Prop. Mediated  0.02574     -1.96134         0.62   0.896   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L cortico-spinal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00506     -0.05623         0.05    0.80
## ADE            -0.00791     -0.04670         0.03    0.69
## Total Effect   -0.01297     -0.07337         0.05    0.69
## Prop. Mediated  0.39046     -4.70047         6.78    0.46
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0401      -0.0797         0.00   0.048 *
## ADE              0.0271      -0.0207         0.07   0.258  
## Total Effect    -0.0130      -0.0780         0.05   0.664  
## Prop. Mediated   3.0896     -12.7076        12.21   0.616  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0559      -0.3363         0.22    0.74
## ADE              0.0185      -0.2125         0.24    0.90
## Total Effect    -0.0375      -0.3966         0.32    0.88
## Prop. Mediated   1.4929      -6.6462         9.32    0.43
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0411      -0.2334         0.18   0.726  
## ADE             -0.3129      -0.5881        -0.06   0.016 *
## Total Effect    -0.3539      -0.6814        -0.01   0.048 *
## Prop. Mediated   0.1160      -1.9707         0.71   0.682  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L inferior-longitudinal fasciculus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            0.00561     -0.04652         0.07    0.82
## ADE            -0.02859     -0.07444         0.02    0.22
## Total Effect   -0.02298     -0.08198         0.04    0.44
## Prop. Mediated -0.24402     -7.99338         7.07    0.81
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             0.04575      0.00434         0.09   0.038 *
## ADE             -0.06873     -0.12002        -0.01   0.026 *
## Total Effect    -0.02298     -0.07956         0.04   0.484  
## Prop. Mediated  -1.99055    -23.85632        21.83   0.518  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0821      -0.1336         0.30    0.45
## ADE             -0.1196      -0.3735         0.19    0.45
## Total Effect    -0.0375      -0.3780         0.34    0.84
## Prop. Mediated  -2.1920     -10.6890         9.27    0.79
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME             0.0621      -0.0999         0.25   0.422   
## ADE             -0.4161      -0.7030        -0.14   0.008 **
## Total Effect    -0.3539      -0.6827        -0.03   0.034 * 
## Prop. Mediated  -0.1756      -2.0264         0.29   0.456   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L superior-longitudinal fasciculus-parietal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0113      -0.1390         0.10    0.85
## ADE              0.0318      -0.0271         0.10    0.32
## Total Effect     0.0205      -0.1049         0.13    0.75
## Prop. Mediated  -0.5546      -8.7850         7.43    0.48
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0951      -0.1726         0.00   0.048 *
## ADE              0.1156       0.0370         0.19   0.016 *
## Total Effect     0.0205      -0.0856         0.14   0.724  
## Prop. Mediated  -4.6476     -35.5563        24.11   0.772  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0502      -0.2242         0.34    0.72
## ADE             -0.0877      -0.2747         0.13    0.40
## Total Effect    -0.0375      -0.3696         0.34    0.85
## Prop. Mediated  -1.3400     -11.5895         8.97    0.52
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME              0.039       -0.173         0.29   0.724    
## ADE              -0.393       -0.649        -0.16  <2e-16 ***
## Total Effect     -0.354       -0.693        -0.01   0.046 *  
## Prop. Mediated   -0.110       -3.703         0.52   0.770    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L superior-longitudinal fasciculus-temporal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0133      -0.1572         0.12    0.83
## ADE              0.0309      -0.0475         0.11    0.41
## Total Effect     0.0176      -0.1195         0.16    0.87
## Prop. Mediated  -0.7587      -7.3925         7.58    0.43
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.1116      -0.2062        -0.01   0.046 *
## ADE              0.1292       0.0297         0.22   0.014 *
## Total Effect     0.0176      -0.1228         0.16   0.786  
## Prop. Mediated  -6.3512     -21.3880        21.76   0.832  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0365      -0.2411         0.31    0.79
## ADE             -0.0740      -0.2613         0.12    0.46
## Total Effect    -0.0375      -0.4074         0.31    0.82
## Prop. Mediated  -0.9741      -4.9361         8.84    0.48
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME             0.0283      -0.1881         0.28   0.754   
## ADE             -0.3823      -0.6487        -0.13   0.004 **
## Total Effect    -0.3539      -0.7078        -0.02   0.036 * 
## Prop. Mediated  -0.0801      -2.6833         0.43   0.786   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

L unicinate fasciculus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00493     -0.05561         0.04    0.81
## ADE            -0.00113     -0.03498         0.04    0.98
## Total Effect   -0.00606     -0.06402         0.05    0.88
## Prop. Mediated  0.81426     -7.77070         8.21    0.48
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.03978     -0.07895         0.00   0.046 *
## ADE              0.03372     -0.01063         0.08   0.146  
## Total Effect    -0.00606     -0.06531         0.06   0.858  
## Prop. Mediated   6.56677    -24.14379        14.69   0.812  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0272      -0.3116         0.23    0.81
## ADE             -0.0102      -0.2601         0.23    0.86
## Total Effect    -0.0375      -0.4358         0.31    0.81
## Prop. Mediated   0.7269      -6.8426         6.80    0.43
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0204      -0.2065         0.17   0.882  
## ADE             -0.3336      -0.6115        -0.08   0.012 *
## Total Effect    -0.3539      -0.7042        -0.02   0.034 *
## Prop. Mediated   0.0576      -2.0947         0.56   0.852  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R anterior thalamic radiation

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME            0.00425     -0.03630         0.05   0.834    
## ADE            -0.08121     -0.12506        -0.03  <2e-16 ***
## Total Effect   -0.07696     -0.12973        -0.02   0.014 *  
## Prop. Mediated -0.05521     -1.81982         0.40   0.848    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME            0.03241      0.00491         0.07   0.026 *  
## ADE            -0.10937     -0.15686        -0.06  <2e-16 ***
## Total Effect   -0.07696     -0.13077        -0.02   0.006 ** 
## Prop. Mediated -0.42119     -2.28744        -0.04   0.032 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             0.2909       0.0873         0.51   0.012 *
## ADE             -0.3284      -0.6187         0.01   0.056 .
## Total Effect    -0.0375      -0.4149         0.34   0.862  
## Prop. Mediated  -7.7623     -27.4073        26.71   0.874  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME              0.206        0.049         0.41   0.004 ** 
## ADE              -0.560       -0.884        -0.28  <2e-16 ***
## Total Effect     -0.354       -0.698        -0.01   0.040 *  
## Prop. Mediated   -0.582       -6.871        -0.02   0.044 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R cingulum-angular bundle

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0193      -0.1688         0.26    0.77
## ADE             -0.0811      -0.2025         0.04    0.20
## Total Effect    -0.0618      -0.2751         0.15    0.62
## Prop. Mediated  -0.3121      -8.5439        10.66    0.65
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             0.1653       0.0132         0.32   0.034 *
## ADE             -0.2271      -0.3818        -0.07   0.014 *
## Total Effect    -0.0618      -0.2403         0.15   0.552  
## Prop. Mediated  -2.6734     -22.4208        28.62   0.582  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME             0.0833      -0.2014         0.35    0.53
## ADE             -0.1207      -0.3338         0.11    0.26
## Total Effect    -0.0375      -0.4391         0.33    0.81
## Prop. Mediated  -2.2222      -9.3862        12.06    0.68
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME             0.0662      -0.1380         0.29   0.562    
## ADE             -0.4201      -0.6686        -0.16  <2e-16 ***
## Total Effect    -0.3539      -0.6995        -0.04   0.028 *  
## Prop. Mediated  -0.1869      -2.9733         0.29   0.590    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R cingulum-cingulate gyrus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.0342      -0.4340         0.26    0.82
## ADE             -0.0137      -0.2094         0.19    0.92
## Total Effect    -0.0480      -0.3874         0.28    0.74
## Prop. Mediated   0.7138      -6.2708         5.96    0.34
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.2863      -0.5615        -0.01   0.044 *
## ADE              0.2384      -0.0124         0.48   0.060 .
## Total Effect    -0.0480      -0.3904         0.28   0.724  
## Prop. Mediated   5.9703     -27.4057        25.28   0.684  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.03904     -0.32743         0.22    0.81
## ADE             0.00157     -0.18768         0.20    1.00
## Total Effect   -0.03747     -0.40598         0.34    0.85
## Prop. Mediated  1.04191     -4.37686         4.91    0.30
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME            -0.0303      -0.2237         0.20   0.762   
## ADE             -0.3237      -0.5817        -0.08   0.006 **
## Total Effect    -0.3539      -0.7209        -0.01   0.034 * 
## Prop. Mediated   0.0856      -2.6799         0.70   0.728   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R cortico-spinal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00541     -0.06239         0.05    0.84
## ADE            -0.00546     -0.04120         0.03    0.79
## Total Effect   -0.01088     -0.07524         0.05    0.78
## Prop. Mediated  0.49783     -5.93734         7.99    0.36
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0434      -0.0855         0.00   0.034 *
## ADE              0.0325      -0.0121         0.07   0.154  
## Total Effect    -0.0109      -0.0764         0.05   0.730  
## Prop. Mediated   3.9871     -15.9116        27.75   0.696  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.04736     -0.32765         0.23    0.75
## ADE             0.00989     -0.23889         0.24    0.86
## Total Effect   -0.03747     -0.40357         0.34    0.87
## Prop. Mediated  1.26389     -4.79437         8.11    0.38
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME            -0.0352      -0.2400         0.16   0.724   
## ADE             -0.3188      -0.5978        -0.08   0.006 **
## Total Effect    -0.3539      -0.7241        -0.02   0.042 * 
## Prop. Mediated   0.0994      -1.2769         0.76   0.682   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R inferior-longitudinal fasciculus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME            0.00194     -0.01617         0.02    0.84    
## ADE            -0.06899     -0.09838        -0.04  <2e-16 ***
## Total Effect   -0.06705     -0.09676        -0.04  <2e-16 ***
## Prop. Mediated -0.02888     -0.53712         0.24    0.84    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                 Estimate 95% CI Lower 95% CI Upper p-value    
## ACME            0.012406    -0.000807         0.03   0.064 .  
## ADE            -0.079458    -0.108154        -0.05  <2e-16 ***
## Total Effect   -0.067052    -0.097574        -0.03  <2e-16 ***
## Prop. Mediated -0.185019    -0.661798         0.01   0.064 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME             0.3877       0.1865         0.60  <2e-16 ***
## ADE             -0.4251      -0.7549        -0.02   0.042 *  
## Total Effect    -0.0375      -0.4154         0.33   0.804    
## Prop. Mediated -10.3446     -49.4268        32.15   0.804    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME             0.2303       0.0744         0.42   0.006 ** 
## ADE             -0.5843      -0.9109        -0.23  <2e-16 ***
## Total Effect    -0.3539      -0.7062        -0.01   0.048 *  
## Prop. Mediated  -0.6507      -4.2917         0.20   0.054 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R superior-longitudinal fasciculus-parietal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.01005     -0.11853         0.09    0.85
## ADE             0.00865     -0.04198         0.06    0.67
## Total Effect   -0.00140     -0.10642         0.11    0.99
## Prop. Mediated  7.17272     -4.72707         6.74    0.36
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0877      -0.1592        -0.01   0.036 *
## ADE              0.0863       0.0175         0.16   0.016 *
## Total Effect    -0.0014      -0.1084         0.11   0.992  
## Prop. Mediated  62.6503     -23.1667        23.97   0.956  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME           -0.00387     -0.29885         0.26    0.93
## ADE            -0.03360     -0.22507         0.16    0.70
## Total Effect   -0.03747     -0.39029         0.30    0.74
## Prop. Mediated  0.10331     -4.81631         5.63    0.35
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value    
## ACME           -0.00314     -0.22651         0.24    1.00    
## ADE            -0.35081     -0.57875        -0.13  <2e-16 ***
## Total Effect   -0.35394     -0.68080        -0.01    0.05 *  
## Prop. Mediated  0.00886     -2.67763         0.88    0.95    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R superior-longitudinal fasciculus-temporal

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0043      -0.0502         0.04   0.824  
## ADE             -0.0324      -0.0654         0.00   0.058 .
## Total Effect    -0.0367      -0.0887         0.01   0.160  
## Prop. Mediated   0.1171      -4.9339         4.90   0.676  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.04276     -0.08170         0.00   0.044 *
## ADE             0.00605     -0.03101         0.04   0.736  
## Total Effect   -0.03671     -0.09194         0.02   0.210  
## Prop. Mediated  1.16490     -3.75051         5.96   0.178  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value
## ACME            -0.1978      -0.4908         0.08    0.17
## ADE              0.1604      -0.0527         0.41    0.18
## Total Effect    -0.0375      -0.3984         0.33    0.88
## Prop. Mediated   5.2797     -13.3867        15.92    0.71
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME             -0.183       -0.463         0.08   0.170  
## ADE              -0.171       -0.379         0.03   0.100 .
## Total Effect     -0.354       -0.741        -0.02   0.036 *
## Prop. Mediated    0.516       -0.803         1.28   0.146  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

R unicinate fasciculus

Depression as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value   
## ACME           -0.00781     -0.09222         0.07   0.798   
## ADE            -0.09261     -0.15712        -0.03   0.004 **
## Total Effect   -0.10042     -0.19422        -0.02   0.018 * 
## Prop. Mediated  0.07779     -2.11526         0.76   0.780   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety as Mediator

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.0617      -0.1086         0.00   0.046 *
## ADE             -0.0387      -0.1151         0.04   0.320  
## Total Effect    -0.1004      -0.1923         0.00   0.044 *
## Prop. Mediated   0.6143      -0.1184         2.47   0.074 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

FA as Mediator

Depression (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME            -0.2718      -0.5286         0.00    0.05 *
## ADE              0.2344      -0.0504         0.51    0.11  
## Total Effect    -0.0375      -0.4051         0.33    0.83  
## Prop. Mediated   7.2542     -22.8614        18.97    0.78  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Anxiety (Y)

## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the Percentile Method
## 
##                Estimate 95% CI Lower 95% CI Upper p-value  
## ACME           -0.19908     -0.38930        -0.03   0.032 *
## ADE            -0.15487     -0.46028         0.11   0.248  
## Total Effect   -0.35394     -0.70831        -0.05   0.026 *
## Prop. Mediated  0.56246      0.00662         1.87   0.050 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 41 
## 
## 
## Simulations: 1000

Report

References

Trajectory-Related

Equations

• https://stats.stackexchange.com/questions/409537/how-to-include-an-interaction-with-a-quadratic-term

Plots

• https://stackoverflow.com/questions/42764028/fitting-a-quadratic-curve-in-ggplot
  
• https://stackoverflow.com/questions/24342162/regression-tables-in-markdown-format-for-flexible-use-in-r-markdown-v2

AIC

• https://stats.stackexchange.com/questions/282686/what-percentage-decrease-in-aic-is-significant
• https://stats.stackexchange.com/questions/84076/negative-values-for-aic-in-general-mixed-model

Moderation-Related

Equations

• https://uedufy.com/how-to-run-multiple-moderation-analysis-in-r-like-a-pro/
• https://stats.stackexchange.com/questions/22988/how-to-obtain-the-p-value-check-significance-of-an-effect-in-a-lme4-mixed-mode

Plots

• https://rdrr.io/cran/interactions/man/interact_plot.html
• https://interactions.jacob-long.com/reference/interact_plot.html

Assumptions of LMES

• https://stats.stackexchange.com/questions/14914/how-to-test-the-autocorrelation-of-the-residuals
• https://stats.stackexchange.com/questions/576562/heavy-tailed-residuals-in-linear-mixed-model
• https://bbolker.github.io/mixedmodels-misc/notes/corr_braindump.html
• https://stats.stackexchange.com/questions/52856/vif-values-and-interactions-in-multiple-regression
• https://easystats.github.io/performance/

Mediation Related

• https://stats.stackexchange.com/questions/59769/alternatives-to-the-baron-kenny-approach-to-modeling-mediation
• https://uedufy.com/how-to-run-mediation-analysis-in-r/
• https://stats.stackexchange.com/questions/369939/interpreting-mediation-output-when-acme-is-stat-sig-but-ade-and-total-are-not
• https://stats.stackexchange.com/questions/376204/interpreting-mediation-output-when-acme-is-negative

Citations

• Burnham & Anderson, Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach, and Burnham & Anderson, “Multimodel Inference: Understanding AIC and BIC in Model Selection” (2004, Sociological Methods & Research)

Notes

AIC-related

• Typically, you’d say that an AIC difference: ΔAIC<2 is little evidence, 2 ≤ΔAIC< 5 is weak evidence,
  5 ≤ΔAIC< 10 is medium evidence, and, 10 ≤ΔAIC is strong evidence …in favor of the model with the lower AIC value.

• The AIC is defined as: AIC=2𝑘−2ln(𝐿), where k denotes the number of parameters and 𝐿denotes the maximized value of the likelihood function.

• For model comparison, the model with the lowest AIC score is preferred. The absolute values of the AIC scores do not matter. These scores can be negative or positive.

• Absolute values do not matter: In a model with AIC=−237.847 is preferred over the model with AIC=−201.928

VIC-related (assumptions of lmes)

• Ignore VIF > 5 (i.e. high correlation among variables) for interaction terms