Measures

DTI

FA Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(FA ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

mixed.model_quadratic <- lmer(FA ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -3429.651 (-3409.105) -3417.589 (-3392.933) Change in AIC_Q is only marginally better (only 3 units less than AIC_L), suggesting only marginal support.
Anova p-value=0.02736* Anova model comparison => quadratic model significantly different from linear model at alpha=0.05

Confidence Intervals of Mixed Quadratic Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0313730 0.0613890
.sigma 0.0040341 0.0046288
(Intercept) 0.4363874 0.4793949
WeeksSinceTBI_z -0.0010997 -0.0002877
I(WeeksSinceTBI_z^2) -0.0009721 -0.0000667
HeadMotion_z -0.0008099 0.0000160

Plot

FA across Tracts

  • This plot illustrates the predicted FA across different values of time since TBI, accounting for both linear and quadratic effects and adjusting for random effects of Tract (i.e., holding random effects constant, focusing on the relationship between weeks since TBI with FA, in isolation).
FA across Specific Tracts
Forceps Major

AD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(AD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

mixed.model_quadratic <- lmer(AD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -9750.6 (-9730.1) - 9752.1 (-9727.4) Change in AIC_Q is only marginally better (less than 3 units), suggesting only marginal support. Keep linear.
Anova p-value=0.06229 No significant different between linear and quadratic models. Keep linear model.

Confidence Intervals of Mixed Linear Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000337 0.0000696
.sigma 0.0000037 0.0000043
(Intercept) 0.0007503 0.0007987
WeeksSinceTBI_z -0.0000019 -0.0000012
HeadMotion_z -0.0000016 -0.0000008

Plot

AD across Tracts

This plot illustrates the predicted AD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with AD, in isolation).

AD across Specific Tracts
Forceps Major

RD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(RD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

mixed.model_quadratic <- lmer(RD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -9898.6 (-9878.1) - 9910.7 (-9886.0) AIC_Q > AIC_L by 12 units. Quadratic model has stronger support.
Anova p-value=0.0001773 *** Quadratic fit is significantly different from linear fit.

Confidence Intervals of Mixed Quadratic Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000248 0.0000507
.sigma 0.0000031 0.0000036
(Intercept) 0.0003454 0.0003815
WeeksSinceTBI_z -0.0000006 0.0000001
I(WeeksSinceTBI_z^2) 0.0000003 0.0000010
HeadMotion_z -0.0000006 0.0000001

Plot

RD across Tracts

This plot illustrates the predicted RD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with RD, in isolation).

RD across Specific Tracts
Forceps Major

MD Trajectory

Model

WeeksSinceTBI_z | Tract: This tells the model to allow each tract to have its own slope for WeeksSinceTBI. Both the intercept and the slope can vary between tracts. We find that model with random slope leads to a boundary singular fit. Therefore, we go with the intercept model only (i.e., 1 | Tract)

 

mixed.model_linear <- lmer(MD ~ WeeksSinceTBI_z + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

mixed.model_quadratic <- lmer(MD ~ WeeksSinceTBI_z + I(WeeksSinceTBI_z^2) + HeadMotion_z + (1 | Tract), data = ctrl.df)

 

Which model is better?

Model Comparison Metric Linear Model Quadratic Model Interpretation
AIC (BIC) -10009 (-9988.0) - 10020 (-9995.3) AIC_Q > AIC_L by > 10 units. Quadratic model has stronger support.
Anova p-value=0.0002569 *** Quadratic fit is significantly different from linear fit.

Confidence Intervals of Mixed Quadratic Model Generated by Bootstrapping (n=1000)

2.5 % 97.5 %
.sig01 0.0000232 0.0000464
.sigma 0.0000028 0.0000032
(Intercept) 0.0004835 0.0005165
WeeksSinceTBI_z -0.0000010 -0.0000004
I(WeeksSinceTBI_z^2) 0.0000003 0.0000009
HeadMotion_z -0.0000008 -0.0000003

Plot

MD across Tracts

This plot illustrates the predicted MD across different values of time since TBI, adjusting for head motion as well as the variance attributed to different tract intercepts (i.e., holding effects due to head motion and random tract intercepts constant, and focusing on the relationship between weeks since TBI with MD, in isolation).

MD across Specific Tracts
Forceps Major

Cognitive

Trajectory

Antisaccade

days weekSinceInj_label weekSinceInj_num Trial Number Trial Type Accuracy Trimmed RT
1 Week1 1 1 Correct 1 786.3
1 Week1 1 2 Correct 1 774.0
1 Week1 1 3 Correct 1 658.5
180 Week27 27 54 Correct 1 562.1
180 Week27 27 55 Correct 1 606.2
180 Week27 27 56 Correct 1 459.6
weekSinceInj_num ANTISACC_MeanTrimmedCorrectRT ANTISACC_Accuracy
1 648.6389 0.9642857
2 630.1796 0.9821429
3 611.9500 0.9821429
4 596.2464 1.0000000
5 568.7796 0.9642857
7 556.5648 0.9821429
8 549.1691 1.0000000
10 568.2732 1.0000000
11 535.4571 1.0000000
12 529.3607 1.0000000
13 563.4571 1.0000000
14 564.9375 1.0000000
15 853.0870 1.0000000
16 481.2804 1.0000000
17 543.3709 1.0000000
18 486.4909 1.0000000
19 552.8607 1.0000000
20 552.9232 1.0000000
21 535.4927 1.0000000
22 542.6345 0.9821429
23 592.4268 1.0000000
24 510.1518 1.0000000
25 861.9340 1.0000000
26 547.4304 1.0000000
27 603.0906 1.0000000
Linear

Quadratic

Go-No-Go

days weekSinceInj_label weekSinceInj_num Trial Number Trial Type Accuracy Trimmed RT
1 Week1 1 1 Go 1 471.0
1 Week1 1 2 Go 1 309.4
1 Week1 1 3 Go 1 458.1
180 Week27 27 223 Go 1 392.9
180 Week27 27 224 NoGo 1 NA
180 Week27 27 225 Go 1 187.5
weekSinceInj_num GNG_MeanTrimmedCorrectGoRT GNG_GoTrialAccuracy GNG_MeanTrimmedNoGoRT GNG_NoGoTrialAccuracy dPrime
1 315.8799 1.000 278.2091 0.56 2.744707
2 243.7778 1.000 216.5786 0.44 2.459898
3 224.7039 0.995 216.3437 0.28 1.810168
4 217.9790 0.990 206.0765 0.24 1.542448
5 197.1581 0.990 202.6286 0.32 1.759555
7 220.4568 1.000 212.5529 0.28 2.059430
8 210.0659 1.000 223.1625 0.24 1.947812
10 195.0431 0.990 210.2200 0.24 1.542448
11 206.0088 1.000 203.4154 0.44 2.459898
12 221.8191 0.995 213.0200 0.28 1.810168
13 221.8242 1.000 222.6538 0.48 2.554762
14 217.7128 0.995 231.8000 0.52 2.400152
15 204.1026 1.000 220.4182 0.52 2.649414
16 205.2646 1.000 231.4000 0.60 2.841539
17 203.9762 1.000 227.6000 0.52 2.649414
18 206.5891 0.995 222.4857 0.40 2.114690
19 200.7759 1.000 225.3857 0.44 2.459898
20 217.4422 1.000 219.3286 0.44 2.459898
21 214.1905 0.995 245.5364 0.48 2.305500
22 204.2233 1.000 231.7200 0.60 2.841539
23 197.8517 0.995 234.8917 0.44 2.210636
24 182.4447 0.995 196.6100 0.44 2.210636
25 184.7151 0.985 198.4286 0.40 1.842374
26 183.6839 0.995 235.5364 0.36 2.016724
27 197.8026 0.995 235.0067 0.36 2.016724
Linear

Quadratic

Number-Symbol

days weekSinceInj_label weekSinceInj_num Task Name Practice_Test Trial Number Trial Type Accuracy Trimmed RT
1 Week1 1 Number Symbol Practice 1 Correct 1 NA
1 Week1 1 Number Symbol Practice 2 Correct 1 956.4
1 Week1 1 Number Symbol Practice 3 Correct 1 694.3
180 Week27 27 Number Symbol Trials 97 Incorrect 0 342.3
180 Week27 27 Number Symbol Trials 98 Correct 1 526.4
180 Week27 27 Number Symbol Trials 99 Correct 1 543.1
NUMSYM_MeanTrimmedCorrectRT NUMSYM_Accuracy
Week1 - 1 - Practice
952.6000 0.8888889
Week1 - 1 - Trials
661.2024 0.9797980
Week10 - 10 - Practice
487.0444 1.0000000
Week10 - 10 - Trials
481.0656 0.9494949
Week11 - 11 - Practice
494.9333 1.0000000
Week11 - 11 - Trials
458.7733 0.9292929
Week12 - 12 - Practice
470.3444 1.0000000
Week12 - 12 - Trials
468.2074 0.9494949
Week13 - 13 - Practice
528.6778 1.0000000
Week13 - 13 - Trials
476.6681 0.9595960
Week14 - 14 - Practice
552.3333 1.0000000
Week14 - 14 - Trials
455.8659 0.9191919
Week15 - 15 - Practice
457.0889 1.0000000
Week15 - 15 - Trials
448.6968 0.9494949
Week16 - 16 - Practice
550.4889 1.0000000
Week16 - 16 - Trials
453.6652 0.9292929
Week17 - 17 - Practice
477.3111 1.0000000
Week17 - 17 - Trials
446.6347 0.9595960
Week18 - 18 - Practice
466.1333 1.0000000
Week18 - 18 - Trials
436.0128 0.9494949
Week19 - 19 - Practice
493.7111 1.0000000
Week19 - 19 - Trials
448.4098 0.9292929
Week2 - 2 - Practice
742.9333 1.0000000
Week2 - 2 - Trials
602.7064 0.9797980
Week20 - 20 - Practice
477.5667 1.0000000
Week20 - 20 - Trials
431.0043 0.9494949
Week21 - 21 - Practice
561.0000 0.8888889
Week21 - 21 - Trials
433.9521 0.9595960
Week22 - 22 - Practice
443.2375 0.8888889
Week22 - 22 - Trials
420.5067 0.9090909
Week23 - 23 - Practice
467.9667 1.0000000
Week23 - 23 - Trials
425.1000 0.9494949
Week24 - 24 - Practice
472.0889 1.0000000
Week24 - 24 - Trials
427.3856 0.9191919
Week25 - 25 - Practice
432.9556 1.0000000
Week25 - 25 - Trials
419.9543 0.9393939
Week26 - 26 - Practice
460.8000 1.0000000
Week26 - 26 - Trials
417.0348 0.9292929
Week27 - 27 - Practice
412.7111 1.0000000
Week27 - 27 - Trials
420.7989 0.9292929
Week3 - 3 - Practice
635.6222 1.0000000
Week3 - 3 - Trials
575.5180 0.9595960
Week4 - 4 - Practice
627.0444 1.0000000
Week4 - 4 - Trials
531.2102 0.9494949
Week5 - 5 - Practice
655.5667 1.0000000
Week5 - 5 - Trials
522.6826 0.9595960
Week7 - 7 - Practice
652.7000 1.0000000
Week7 - 7 - Trials
524.6833 0.9797980
Week8 - 8 - Practice
538.5444 1.0000000
Week8 - 8 - Trials
504.5138 0.9696970
Linear

Quadratic

Mediation Models

Mediation model with quadratic effects of Weeks Since Injury on RT is NOT significant.