1
Supplemen a y Ma e ial o he pape : “Humans can lea n bimodal p io s
in complex senso imo o beha iou ”
S ephan Zahno, Damian Beck, E ns -Joachim Hossne , Kon ad Ko ding
Ex ended da a
Table 1. Mul ile el eg ession model o e o es ima ion on day 1 in he as condi ion.
Fixed e ec s
B
SE B
95%
CI
(2673) p wo-sided
In e cep
–18.32
4.01
[–26.19, –10.46]
–4.57
< .001
Ball posi ion
0.16
0.06
[0.03, 0.28]
2.45
.014
Segmen (0 = le , 1 = igh )
3.24
1.66
[–0.01, 6.49]
1.95
.153
Random e ec s
In e cep a iance (τ
00
)
280.98
–
–
–
–
Slope a iance (τ
11
)
0.06
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.99
–
–
–
–
Le el-1 esidual (σ2)
98.98
–
–
–
–
ICC
0.24
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .148. Model compa ison in Table 2.
Table 2. Model compa ison o mul ile el eg ession model o e o es ima ion on day 1 in he as condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
21171.00
21182.80
–10583.50
2 Base model
3
20755.30
20773.01
–10374.65
1 s 2
417.697
< .001
3 Base model + RI
4
20631.67
20655.28
–10311.84
2 s 3
125.632
< .001
4 Base model + RS
6
20211.17
20246.57
–10099.58
3 s 4
424.502
< .001
5 Base model + RS +
Bimodal segmen ac o
7
20209.35
20250.65
–10097.67
4 s 5
3.820
.051
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
2
Table 3. Mul ile el eg ession model o e o es ima ion on day 1 in he mode a e condi ion.
Fixed e ec s
B
SE B
95%
CI
(3096) p wo-sided
In e cep
–13.02
3.72
[–20.30, –5.73]
–3.50
< .001
Ball posi ion
0.17
0.06
[0.06, 0.28]
3.04
.002
Segmen (0 = le , 1 = igh )
0.27
1.46
[–2.60, 3.15]
0.19
.852
Random e ec s
In e cep a iance (τ
00
)
251.55
–
–
–
–
Slope a iance (τ
11
)
0.04
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.96
–
–
–
–
Le el-1 esidual (σ2)
90.90
–
–
–
–
ICC
0.29
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .090. Model compa ison in Table 4.
Table 4. Model compa ison o mul ile el eg ession model o e o es ima ion on day 1 in he mode a e condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
24246.25
24258.34
–12121.13
2 Base model
3
23938.17
23956.31
–11966.09
1 s 2
310.078
< .001
3 Base model + RI
4
23570.14
22594.32
–11781.07
2 s 3
370.034
< .001
4 Base model + RS
6
23107.90
23144.18
–11547.95
3 s 4
466.239
< .001
5 Base model + RS +
Bimodal segmen ac o
7
23109.87
23152.19
–11547.93
4 s 5
0.035
.852
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
3
Table 5. Mul ile el eg ession model o e o es ima ion on day 1 in he slow condi ion.
Fixed e ec s
B
SE B
95%
CI
(3049) p wo-sided
In e cep
1.53
3.25
[–4.84, 7.90]
0.47
.638
Ball posi ion
0.08
0.05
[–0.02, 0.18]
1.62
.105
Segmen (0 = le , 1 = igh )
–2.24
1.39
[–4.97, 0.49]
–1.61
.216
Random e ec s
In e cep a iance (τ
00
)
181.19
–
–
–
–
Slope a iance (τ
11
)
0.03
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.94
–
–
–
–
Le el-1 esidual (σ2)
79.84
–
–
–
–
ICC
0.29
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .003. Model compa ison in Table 6.
Table 6. Model compa ison o mul ile el eg ession model o e o es ima ion on day 1 in he slow condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
23242.37
23254.44
–11619.19
2 Base model
3
23229.23
23247.33
–11611.62
1 s 2
15.141
< .001
3 Base model + RI
4
22743.84
22767.97
–11367.92
2 s 3
487.399
< .001
4 Base model + RS
6
22366.15
22402.34
–11177.08
3 s 4
381.693
< .001
5 Base model + RS +
Bimodal segmen ac o
7
22365.56
22407.78
–11175.78
4 s 5
2.595
.108
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
4
Table 7. Mul ile el eg ession model o e o es ima ion on day 2+3 in he as condi ion.
Fixed e ec s
B
SE B
95%
CI
(5571) p one-sided
In e cep
–27.10
3.09
[–33.16, –21.04]
–8.76
< .001
Ball posi ion
0.36
0.05
[0.27, 0.45]
7.79
< .001
Segmen (0 = le , 1 = igh )
–2.36
1.04
[–4.39, –0.33]
–2.28
.023
Random e ec s
In e cep a iance (τ
00
)
190.39
–
–
–
–
Slope a iance (τ
11
)
0.04
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.98
–
–
–
–
Le el-1 esidual (σ2)
78.39
–
–
–
–
ICC
0.23
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .273. Model compa ison in Table 8.
Table 8. Model compa ison o mul ile el eg ession model o e o es ima ion on day 2+3 in he as condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
43268.33
43281.59
–21632.17
2 Base model
3
41641.60
41661.49
–20817.80
1 s 2
1628.732
< .001
3 Base model + RI
4
41273.01
41273.53
–20619.51
2 s 3
396.587
< .001
4 Base model + RS
6
40521.26
40521.04
–20234.63
3 s 4
769.756
< .001
5 Base model + RS +
Bimodal segmen ac o
7
40524.07
40524.48
–20232.04
4 s 5
5.184
.023
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
5
Table 9. Mul ile el eg ession model o e o es ima ion on day 2+3 in he mode a e condi ion.
Fixed e ec s
B
SE B
95%
CI
(6584) p one-sided
In e cep
–18.20
2.90
[–24.08, –12.70]
–6.28
< .001
Ball posi ion
0.29
0.04
[0.21, 0.37]
7.26
< .001
Segmen (0 = le , 1 = igh )
–2.64
0.91
[–4.36, –0.94]
–2.90
.006
Random e ec s
In e cep a iance (τ
00
)
171.07
–
–
–
–
Slope a iance (τ
11
)
0.03
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.97
–
–
–
–
Le el-1 esidual (σ2)
71.51
–
–
–
–
ICC
0.24
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .182. Model compa ison in Table 10.
Table 10. Model compa ison o mul ile el eg ession model o e o es ima ion on day 2+3 in he mode a e condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
50105.85
50119.45
–25050.93
2 Base model
3
48784.41
48804.80
–24389.21
1 s 2
1323.442
< .001
3 Base model + RI
4
48022.77
48049.96
–24007.39
2 s 3
763.638
< .001
4 Base model + RS
6
47179.99
47220.77
–23584.00
3 s 4
846.782
< .001
5 Base model + RS +
Bimodal segmen ac o
7
47173.56
47221.13
–23579.78
4 s 5
8.435
.004
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
6
Table 11. Mul ile el eg ession model o e o es ima ion on day 2+3 in he slow condi ion.
Fixed e ec s
B
SE B
95%
CI
(6462) p one-sided
In e cep
–0.95
2.34
[–5.53, 3.64]
–0.40
.686
Ball posi ion
0.10
0.03
[0.03, 0.16]
2.79
.005
Segmen (0 = le , 1 = igh )
–0.81
0.80
[–2.38, 0.76]
–1.02
.154
Random e ec s
In e cep a iance (τ
00
)
107.93
–
–
–
–
Slope a iance (τ
11
)
0.02
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.96
–
–
–
–
Le el-1 esidual (σ2)
54.89
–
–
–
–
ICC
0.24
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .033. Model compa ison in Table 12.
Table 12. Model compa ison o mul ile el eg ession model o e o es ima ion on day 2+3 in he slow condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
46272.21
46285.77
–23134.11
2 Base model
3
46045.41
46065.74
–23019.70
1 s 2
228.806
< .001
3 Base model + RI
4
45356.42
45383.53
–22674.21
2 s 3
690.987
< .001
4 Base model + RS
6
44591.78
44632.44
–22289.89
3 s 4
768.645
< .001
5 Base model + RS +
Bimodal segmen ac o
7
44592.74
44640.19
–22289.37
4 s 5
1.034
.309
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
7
Table 13. Mul ile el eg ession model o e o es ima ion o he con ol expe imen in he as condi ion.
Fixed e ec s
B
SE B
95%
CI
(2738) p wo-sided
In e cep
–31.69
2.72
[–37.02, –26.35]
–11.65
< .001
Ball posi ion
0.38
0.04
[0.31, 0.45]
10.80
< .001
Random e ec s
In e cep a iance (τ
00
)
156.34
–
–
–
–
Slope a iance (τ
11
)
0.03
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.91
–
–
–
–
Le el-1 esidual (σ2)
129.81
–
–
–
–
ICC
0.21
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .207. Model compa ison in Table 14.
Table 14. Model compa ison o mul ile el eg ession model o e o es ima ion o he con ol expe imen in he as
condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
22636.72
22648.57
–11316.36
2 Base model
4
21959.43
21977.20
–10976.71
1 s 2
679.295
< .001
3 Base model + RI
5
21539.11
21562.80
–10765.55
2 s 3
422.321
< .001
4 Base model + RS
7
21423.08
21458.62
–10705.54
3 s 4
120.028
< .001
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
8
Table 15. Mul ile el eg ession model o e o es ima ion o he con ol expe imen in he mode a e condi ion.
Fixed e ec s
B
SE B
95%
CI
(3018) p wo-sided
In e cep
–13.13
2.40
[–17.83, –8.42]
–5.46
< .001
Ball posi ion
0.15
0.03
[0.09, 0.21]
4.93
< .001
Random e ec s
In e cep a iance (τ
00
)
124.11
–
–
–
–
Slope a iance (τ
11
)
0.02
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.88
–
–
–
–
Le el-1 esidual (σ2)
100.02
–
–
–
–
ICC
0.25
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .050. Model compa ison in Table 16.
Table 16. Model compa ison o mul ile el eg ession model o e o es ima ion o he con ol expe imen in he mode a e
condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
23660.52
23672.56
–11828.26
2 Base model
4
23465.21
23483.28
–11729.61
1 s 2
197.304
< .001
3 Base model + RI
5
22921.17
22945.26
–11456.59
2 s 3
546.042
< .001
4 Base model + RS
7
22798.38
22834.51
–11393.19
3 s 4
126.790
< .001
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
9
Table 17. Mul ile el eg ession model o e o es ima ion o he con ol expe imen in he slow condi ion.
Fixed e ec s
B
SE B
95%
CI
(2894) p wo-sided
In e cep
7.22
2.18
[2.96, 11.49]
3.32
.001
Ball posi ion
–0.05
0.02
[–0.09, 0.00]
–1.96
.050
Random e ec s
In e cep a iance (τ
00
)
101.92
–
–
–
–
Slope a iance (τ
11
)
0.01
–
–
–
–
In e cep -slope co a iance (ρ
01
)
–0.88
–
–
–
–
Le el-1 esidual (σ2)
81.31
–
–
–
–
ICC
0.26
–
–
–
–
No e. B = uns anda dized eg ession coe icien s, SE = s anda d e o , CI = con idence in e als, (deg ees o eedom).
ICC = In e class co ela ion coe icien . Model s a is ics: Npa icipan s = 24, R2ma ginal = .006. Model compa ison in Table 18.
Table 18. Model compa ison o mul ile el eg ession model o e o es ima ion o he con ol expe imen in he slow
condi ion.
Model
d
AIC
BIC
logLik
Compa ison
χ2
p
1 In e cep
2
21976.13
21988.09
–10986.07
2 Base model
3
21963.32
21981.26
–10978.66
1 s 2
14.810
< .001
3 Base model + RI
4
21364.30
21370.22
–10669.15
2 s 3
619.024
< .001
4 Base model + RS
6
21263.17
21299.04
–10625.58
3 s 4
87.130
< .001
No e. d = deg ees o eedom, AIC = Akaike In o ma ion C i e ion, BIC = Bayesian In o ma ion C i e ion, logLik = log-
likelihood, RI = andom in e cep s, RS = andom in e cep and slopes. The base model includes he p edic o ball posi ion.
