Hutchinson MJ, Goosey-Tolfrey VL, Rethinking aerobic exercise intensity prescription in 
adults with spinal cord injury: time to end the use of “moderate to vigorous” intensity? 
Supplementary Material 1: Dynamic model with lagged independent variable for RPE 
and %V̇ O2peak 
𝑥𝑥 = % V̇ O2peak  
𝑦𝑦 = RPE 
Z1 = 1, when i = 1 (i = measurement occasion) 
Z2 = 1, when i > 1 
TETRA = 1, if Group = TETRA 
 
𝑦𝑦𝑖𝑖𝑖𝑖 = 𝛽𝛽1𝑖𝑖𝑍𝑍1𝑖𝑖𝑖𝑖 + 𝛽𝛽2𝑖𝑖𝑍𝑍1. 𝑥𝑥𝑖𝑖𝑖𝑖 + 𝛽𝛽3𝑖𝑖𝑍𝑍2𝑖𝑖𝑖𝑖 + 𝛽𝛽4𝑖𝑖𝑍𝑍2. 𝑥𝑥𝑖𝑖𝑖𝑖 + 𝛽𝛽5𝑖𝑖𝑍𝑍2. 𝑥𝑥𝑖𝑖−1𝑖𝑖 + 𝛽𝛽6𝑖𝑖𝑍𝑍2. 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝑢𝑢0𝑖𝑖 
𝛽𝛽1𝑖𝑖 = 𝛽𝛽1 + 𝑒𝑒1𝑖𝑖𝑖𝑖 
𝛽𝛽2𝑖𝑖 = 𝛽𝛽2 + 𝑢𝑢2𝑖𝑖 
𝛽𝛽3𝑖𝑖 = 𝛽𝛽3 + 𝑒𝑒3𝑖𝑖𝑖𝑖 
𝛽𝛽4𝑖𝑖 = 𝛽𝛽4 + 𝑢𝑢4𝑖𝑖 
𝛽𝛽5𝑖𝑖 = 𝛽𝛽5 + 𝑢𝑢5𝑖𝑖 
𝛽𝛽6𝑖𝑖 = 𝛽𝛽6 + 𝑒𝑒6𝑖𝑖𝑖𝑖 
 
⎝
⎜
⎛
𝑢𝑢0𝑖𝑖
𝑢𝑢2𝑖𝑖
𝑢𝑢4𝑖𝑖
𝑢𝑢5𝑖𝑖
⎠
⎟
⎞ ~𝑁𝑁(0, Ω𝑢𝑢): Ω𝑢𝑢 =
⎣
⎢
⎢
⎢
⎡ 𝜎𝜎𝑢𝑢0
2
𝜎𝜎𝑢𝑢02
𝜎𝜎𝑢𝑢2
2
𝜎𝜎𝑢𝑢04
0
𝜎𝜎𝑢𝑢4
2
𝜎𝜎𝑢𝑢05
0
𝜎𝜎𝑢𝑢45
𝜎𝜎𝑢𝑢5
2 ⎦
⎥
⎥
⎥
⎤
 
ቌ
𝑒𝑒1𝑖𝑖𝑖𝑖
𝑒𝑒3𝑖𝑖𝑖𝑖
𝑒𝑒6𝑖𝑖𝑖𝑖
ቍ ~𝑁𝑁(0, Ω𝑒𝑒): Ω𝑒𝑒 = ቎
𝜎𝜎𝑒𝑒1
2
0
𝜎𝜎𝑒𝑒3
2
0
𝜎𝜎𝑒𝑒36
𝜎𝜎𝑒𝑒6
2
቏ 
 
 
 
Hutchinson MJ, Goosey-Tolfrey VL, Rethinking aerobic exercise intensity prescription in 
adults with spinal cord injury: time to end the use of “moderate to vigorous” intensity? 
𝑦𝑦𝑖𝑖𝑖𝑖 =  5.133𝑍𝑍1𝑖𝑖𝑖𝑖 + 0.074𝑍𝑍1. 𝑥𝑥𝑖𝑖𝑖𝑖 + 3.411𝑍𝑍2𝑖𝑖𝑖𝑖 + 0.093𝑍𝑍2. 𝑥𝑥𝑖𝑖𝑖𝑖 + 0.074𝑍𝑍2. 𝑥𝑥𝑖𝑖−1𝑖𝑖
− 1.081𝑍𝑍2. 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑖𝑖 + 𝑢𝑢0𝑖𝑖 
−2𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒𝑙𝑙𝑙𝑙ℎ𝑙𝑙𝑙𝑙𝑜𝑜 = 2744.893 
⎝
⎜
⎛
𝑢𝑢0𝑖𝑖
𝑢𝑢2𝑖𝑖
𝑢𝑢4𝑖𝑖
𝑢𝑢5𝑖𝑖
⎠
⎟
⎞ ~𝑁𝑁(0, Ω𝑢𝑢): Ω𝑢𝑢 = ൦
3.524 (0.459)
−0.047 (0.009)
0.001 (0.000)
0.000
0
0.000
0.000
0
0.000
0.000
൪ 
ቌ
𝑒𝑒1𝑖𝑖𝑖𝑖
𝑒𝑒3𝑖𝑖𝑖𝑖
𝑒𝑒6𝑖𝑖𝑖𝑖
ቍ ~𝑁𝑁(0, Ω𝑒𝑒): Ω𝑒𝑒 = ቎
0.768 (0.381)
0
1.044 (0.069)
0
0.212  (0.126)
0.000
቏ 
 
Level 1 variance: 
𝑍𝑍1 = 𝜎𝜎𝑒𝑒1
2 = 0.768  
𝑍𝑍2 (𝑃𝑃𝑇𝑇𝑇𝑇𝑇𝑇) = 𝜎𝜎𝑒𝑒3
2 = 1.044 
𝑍𝑍3 = 𝜎𝜎𝑒𝑒3
2 + 2𝜎𝜎36 + 𝜎𝜎𝑒𝑒6
2 = 1.469 
 
Level 2 variance 
𝑍𝑍1 = 𝜎𝜎𝑢𝑢0
2 + 2𝜎𝜎𝑢𝑢02 + 𝜎𝜎𝑢𝑢2
2 = 3.431 
𝑍𝑍2 = 𝜎𝜎𝑢𝑢0
2 + 2𝜎𝜎𝑢𝑢04 + 𝜎𝜎𝑢𝑢4
2 + 2𝜎𝜎𝑢𝑢05 + 2𝜎𝜎𝑢𝑢45 + 𝜎𝜎𝑢𝑢5
2 = 3.524 
 
Coefficient 
Value 
Standard error 
P 
𝛽𝛽1 
5.113 
0.473 
< 0.0005 
𝛽𝛽2 
0.074 
0.013 
< 0.0005 
𝛽𝛽3 
3.411 
0.242 
< 0.0005 
𝛽𝛽4 
0.093 
0.009 
< 0.0005 
𝛽𝛽5 
0.074 
0.010 
< 0.0005 
𝛽𝛽6 
-1.081 
0.419 
0.009 
 
 
 
Hutchinson MJ, Goosey-Tolfrey VL, Rethinking aerobic exercise intensity prescription in 
adults with spinal cord injury: time to end the use of “moderate to vigorous” intensity? 
Supplementary Material 2: Dynamic model with lagged independent variable for RPE 
and %HRpeak 
𝑥𝑥 = % HRpeak  
𝑦𝑦 = RPE 
Z1 = 1, when i = 1 (i = measurement occasion) 
Z2 = 1, when i > 1 
PARA = 1, if Group = PARA 
 
𝑦𝑦𝑖𝑖𝑖𝑖 = 𝛽𝛽1𝑖𝑖𝑍𝑍1𝑖𝑖𝑖𝑖 + 𝛽𝛽2𝑍𝑍1. 𝑥𝑥𝑖𝑖𝑖𝑖 + 𝛽𝛽3𝑖𝑖𝑍𝑍2𝑖𝑖𝑖𝑖 + 𝛽𝛽4𝑍𝑍2. 𝑥𝑥𝑖𝑖𝑖𝑖 + 𝛽𝛽5𝑍𝑍2. 𝑥𝑥𝑖𝑖−1𝑖𝑖 + 𝛽𝛽6𝑖𝑖𝑃𝑃𝑇𝑇𝑇𝑇𝑇𝑇 + 𝑢𝑢0𝑖𝑖 
𝛽𝛽1𝑖𝑖 = 𝛽𝛽1 + 𝑒𝑒1𝑖𝑖𝑖𝑖 
𝛽𝛽3𝑖𝑖 = 𝛽𝛽3 + 𝑒𝑒3𝑖𝑖𝑖𝑖 
൫𝑢𝑢0𝑖𝑖൯~𝑁𝑁(0, Ω𝑢𝑢): Ω𝑢𝑢 = [𝜎𝜎𝑢𝑢0
2 ] 
൬𝑒𝑒1𝑖𝑖𝑖𝑖
𝑒𝑒3𝑖𝑖𝑖𝑖൰ ~𝑁𝑁(0, Ω𝑒𝑒): Ω𝑒𝑒 = ቈ𝜎𝜎𝑒𝑒1
2
0
𝜎𝜎𝑒𝑒3
2 ቉ 
 
𝑦𝑦𝑖𝑖𝑖𝑖 = −1.375𝑍𝑍1𝑖𝑖𝑖𝑖 + 0.160𝑍𝑍1. 𝑥𝑥𝑖𝑖𝑖𝑖 − 3.044𝑍𝑍2𝑖𝑖𝑖𝑖 + 0.168𝑍𝑍2. 𝑥𝑥𝑖𝑖𝑖𝑖 + 0.044𝑍𝑍2. 𝑥𝑥𝑖𝑖−1𝑖𝑖
+ 0.707𝑃𝑃𝑇𝑇𝑇𝑇𝑇𝑇 + 𝑢𝑢0𝑖𝑖 
−2𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑒𝑒𝑙𝑙𝑙𝑙ℎ𝑙𝑙𝑙𝑙𝑜𝑜 = 2727.763 
൫𝑢𝑢0𝑖𝑖൯~𝑁𝑁(0, Ω𝑢𝑢): Ω𝑢𝑢 = [2.929 (0.387)] 
൬𝑒𝑒1𝑖𝑖𝑖𝑖
𝑒𝑒3𝑖𝑖𝑖𝑖൰ ~𝑁𝑁(0, Ω𝑒𝑒): Ω𝑒𝑒 = ൤1.471 (0.209)
0
1.182 (0.073)൨ 
 
Coefficient 
Value 
Standard error 
P 
𝛽𝛽1 
-1.375 
0.814 
0.091 
𝛽𝛽2 
0.160 
0.014 
< 0.0005 
𝛽𝛽3 
-3.044 
0.355 
< 0.0005 
𝛽𝛽4 
0.168 
0.010 
< 0.0005 
𝛽𝛽5 
0.044 
0.011 
< 0.0005 
𝛽𝛽6 
0.707 
0.324 
0.029 
 

Rethinking aerobic exercise intensity prescription in adults with spinal cord injury: time to end the use of "moderate to vigorous" intensity?
Hutchinson, Michael J,Goosey-Tolfrey, Victoria L