Table 4 Open in new tab Population HMM:...

			Methods: Estimate (SE)
Discrete	Active	β₁₀	2.8973(0.8384)	10.8254(1.4074)	9.0154(1.2162)	8.5893(1.2036)
Time	to	β₁₁	−0.4182(0.0850)	−1.2431(0.1428)	−1.0828(0.1232)	−1.0395(0.1219)
	Rest	β₁₂	0.0288(0.0121)	0.0379(0.0184)	0.0257(0.0126)	0.0257(0.0126)
		β₁₃	0.0070(0.0124)	0.0052(0.0189)	0.0054(0.0130)	0.0050(0.0129)
			0.1099	0.2585	0.1171	0.1160
	Rest	β₂₀	−6.6357(0.3846)	−16.2898(1.3782)	−6.0404(0.4941)	−5.9631(0.5029)
	to	β₂₁	0.5359(0.0405)	1.5280(0.1401)	0.4671(0.0512)	0.4599(0.0521)
	Active	β₂₂	−0.0278(0.0190)	−0.0441(0.0203)	−0.0357(0.0183)	−0.0355(0.0183)
		β₂₃	−0.0431(0.0191)	−0.0541(0.0208)	−0.0503(0.0187)	−0.0505(0.0188)
			0.2802	0.3210	0.2631	0.2634
		μ₁	8.5321	8.0866	8.0251	8.0114
		μ₂	0.5238	0.4263	0.4195	0.4153
Heterogeneous	Active	β₁₀	0.3714(0.7637)	6.4420(1.2828)	2.8110(1.1055)	2.0846(1.0867)
Time	to	β₁₁	−0.2567(0.0786)	−0.7771(0.1305)	−0.5526(0.1130)	−0.5209(0.1120)
	Rest	β₁₂	0.0541(0.0214)	0.0496(0.0231)	0.0528(0.0233)	0.0685(0.0285)
		β₁₃	0.0867(0.0221)	0.0094(0.0241)	0.0840(0.0240)	0.1127(0.0296)
			0.3554	0.3941	0.4102	0.6132
	Rest	β₂₀	−6.4771(0.3775)	−20.1172(1.2551)	−6.9784(0.4544)	−6.8518(0.4673)
	to	β₂₁	0.4597(0.0411)	2.0046(0.1298)	0.5196(0.0481)	0.4889(0.0500)
	Active	β₂₂	−0.0211(0.0235)	−0.0620(0.0294)	−0.0383(0.0217)	−0.0327(0.0241)
		β₂₃	0.0033(0.0240)	−0.0874(0.0309)	−0.0199(0.0225)	−0.0077(0.0252)
			0.4051	0.6207	0.3422	0.4040
		μ₁	9.3939	9.0530	8.9522	8.9428
		μ₂	1.0534	0.9579	0.9528	0.9534

Methods: Estimate (SE)

Time

Transition

Parameters

PMM

DT-HMM

CT-HMM

PH-HMM

Discrete

Active

β₁₀

2.8973(0.8384)

10.8254(1.4074)

9.0154(1.2162)

8.5893(1.2036)

Time

β₁₁

−0.4182(0.0850)

−1.2431(0.1428)

−1.0828(0.1232)

−1.0395(0.1219)

Rest

β₁₂

0.0288(0.0121)

0.0379(0.0184)

0.0257(0.0126)

β₁₃

0.0070(0.0124)

0.0052(0.0189)

0.0054(0.0130)

0.0050(0.0129)

0.1099

0.2585

0.1171

0.1160

Rest

β₂₀

−6.6357(0.3846)

−16.2898(1.3782)

−6.0404(0.4941)

−5.9631(0.5029)

β₂₁

0.5359(0.0405)

1.5280(0.1401)

0.4671(0.0512)

0.4599(0.0521)

Active

β₂₂

−0.0278(0.0190)

−0.0441(0.0203)

−0.0357(0.0183)

−0.0355(0.0183)

β₂₃

−0.0431(0.0191)

−0.0541(0.0208)

−0.0503(0.0187)

−0.0505(0.0188)

0.2802

0.3210

0.2631

0.2634

μ₁

8.5321

8.0866

8.0251

8.0114

μ₂

0.5238

0.4263

0.4195

0.4153

Heterogeneous

Active

β₁₀

0.3714(0.7637)

6.4420(1.2828)

2.8110(1.1055)

2.0846(1.0867)

Time

β₁₁

−0.2567(0.0786)

−0.7771(0.1305)

−0.5526(0.1130)

−0.5209(0.1120)

Rest

β₁₂

0.0541(0.0214)

0.0496(0.0231)

0.0528(0.0233)

0.0685(0.0285)

β₁₃

0.0867(0.0221)

0.0094(0.0241)

0.0840(0.0240)

0.1127(0.0296)

0.3554

0.3941

0.4102

0.6132

Rest

β₂₀

−6.4771(0.3775)

−20.1172(1.2551)

−6.9784(0.4544)

−6.8518(0.4673)

β₂₁

0.4597(0.0411)

2.0046(0.1298)

0.5196(0.0481)

0.4889(0.0500)

Active

β₂₂

−0.0211(0.0235)

−0.0620(0.0294)

−0.0383(0.0217)

−0.0327(0.0241)

β₂₃

0.0033(0.0240)

−0.0874(0.0309)

−0.0199(0.0225)

−0.0077(0.0252)

0.4051

0.6207

0.3422

0.4040

μ₁

9.3939

9.0530

8.9522

8.9428

μ₂

1.0534

0.9579

0.9528

0.9534

			Methods: Estimate (SE)
Discrete	Active	β₁₀	2.8973(0.8384)	10.8254(1.4074)	9.0154(1.2162)	8.5893(1.2036)
Time	to	β₁₁	−0.4182(0.0850)	−1.2431(0.1428)	−1.0828(0.1232)	−1.0395(0.1219)
	Rest	β₁₂	0.0288(0.0121)	0.0379(0.0184)	0.0257(0.0126)	0.0257(0.0126)
		β₁₃	0.0070(0.0124)	0.0052(0.0189)	0.0054(0.0130)	0.0050(0.0129)
			0.1099	0.2585	0.1171	0.1160
	Rest	β₂₀	−6.6357(0.3846)	−16.2898(1.3782)	−6.0404(0.4941)	−5.9631(0.5029)
	to	β₂₁	0.5359(0.0405)	1.5280(0.1401)	0.4671(0.0512)	0.4599(0.0521)
	Active	β₂₂	−0.0278(0.0190)	−0.0441(0.0203)	−0.0357(0.0183)	−0.0355(0.0183)
		β₂₃	−0.0431(0.0191)	−0.0541(0.0208)	−0.0503(0.0187)	−0.0505(0.0188)
			0.2802	0.3210	0.2631	0.2634
		μ₁	8.5321	8.0866	8.0251	8.0114
		μ₂	0.5238	0.4263	0.4195	0.4153
Heterogeneous	Active	β₁₀	0.3714(0.7637)	6.4420(1.2828)	2.8110(1.1055)	2.0846(1.0867)
Time	to	β₁₁	−0.2567(0.0786)	−0.7771(0.1305)	−0.5526(0.1130)	−0.5209(0.1120)
	Rest	β₁₂	0.0541(0.0214)	0.0496(0.0231)	0.0528(0.0233)	0.0685(0.0285)
		β₁₃	0.0867(0.0221)	0.0094(0.0241)	0.0840(0.0240)	0.1127(0.0296)
			0.3554	0.3941	0.4102	0.6132
	Rest	β₂₀	−6.4771(0.3775)	−20.1172(1.2551)	−6.9784(0.4544)	−6.8518(0.4673)
	to	β₂₁	0.4597(0.0411)	2.0046(0.1298)	0.5196(0.0481)	0.4889(0.0500)
	Active	β₂₂	−0.0211(0.0235)	−0.0620(0.0294)	−0.0383(0.0217)	−0.0327(0.0241)
		β₂₃	0.0033(0.0240)	−0.0874(0.0309)	−0.0199(0.0225)	−0.0077(0.0252)
			0.4051	0.6207	0.3422	0.4040
		μ₁	9.3939	9.0530	8.9522	8.9428
		μ₂	1.0534	0.9579	0.9528	0.9534

Table 4

Open in new tab

Population HMM: parameter estimates for discrete-time and heterogeneous-time setting.

			Methods: Estimate (SE)
Time	Transition	Parameters	PMM	DT-HMM	CT-HMM	PH-HMM
Discrete	Active	β₁₀	2.8973(0.8384)	10.8254(1.4074)	9.0154(1.2162)	8.5893(1.2036)
Time	to	β₁₁	−0.4182(0.0850)	−1.2431(0.1428)	−1.0828(0.1232)	−1.0395(0.1219)
	Rest	β₁₂	0.0288(0.0121)	0.0379(0.0184)	0.0257(0.0126)	0.0257(0.0126)
		β₁₃	0.0070(0.0124)	0.0052(0.0189)	0.0054(0.0130)	0.0050(0.0129)
			0.1099	0.2585	0.1171	0.1160
	Rest	β₂₀	−6.6357(0.3846)	−16.2898(1.3782)	−6.0404(0.4941)	−5.9631(0.5029)
	to	β₂₁	0.5359(0.0405)	1.5280(0.1401)	0.4671(0.0512)	0.4599(0.0521)
	Active	β₂₂	−0.0278(0.0190)	−0.0441(0.0203)	−0.0357(0.0183)	−0.0355(0.0183)
		β₂₃	−0.0431(0.0191)	−0.0541(0.0208)	−0.0503(0.0187)	−0.0505(0.0188)
			0.2802	0.3210	0.2631	0.2634
		μ₁	8.5321	8.0866	8.0251	8.0114
		μ₂	0.5238	0.4263	0.4195	0.4153
Heterogeneous	Active	β₁₀	0.3714(0.7637)	6.4420(1.2828)	2.8110(1.1055)	2.0846(1.0867)
Time	to	β₁₁	−0.2567(0.0786)	−0.7771(0.1305)	−0.5526(0.1130)	−0.5209(0.1120)
	Rest	β₁₂	0.0541(0.0214)	0.0496(0.0231)	0.0528(0.0233)	0.0685(0.0285)
		β₁₃	0.0867(0.0221)	0.0094(0.0241)	0.0840(0.0240)	0.1127(0.0296)
			0.3554	0.3941	0.4102	0.6132
	Rest	β₂₀	−6.4771(0.3775)	−20.1172(1.2551)	−6.9784(0.4544)	−6.8518(0.4673)
	to	β₂₁	0.4597(0.0411)	2.0046(0.1298)	0.5196(0.0481)	0.4889(0.0500)
	Active	β₂₂	−0.0211(0.0235)	−0.0620(0.0294)	−0.0383(0.0217)	−0.0327(0.0241)
		β₂₃	0.0033(0.0240)	−0.0874(0.0309)	−0.0199(0.0225)	−0.0077(0.0252)
			0.4051	0.6207	0.3422	0.4040
		μ₁	9.3939	9.0530	8.9522	8.9428
		μ₂	1.0534	0.9579	0.9528	0.9534

			Methods: Estimate (SE)
Time	Transition	Parameters	PMM	DT-HMM	CT-HMM	PH-HMM
Discrete	Active	β₁₀	2.8973(0.8384)	10.8254(1.4074)	9.0154(1.2162)	8.5893(1.2036)
Time	to	β₁₁	−0.4182(0.0850)	−1.2431(0.1428)	−1.0828(0.1232)	−1.0395(0.1219)
	Rest	β₁₂	0.0288(0.0121)	0.0379(0.0184)	0.0257(0.0126)	0.0257(0.0126)
		β₁₃	0.0070(0.0124)	0.0052(0.0189)	0.0054(0.0130)	0.0050(0.0129)
			0.1099	0.2585	0.1171	0.1160
	Rest	β₂₀	−6.6357(0.3846)	−16.2898(1.3782)	−6.0404(0.4941)	−5.9631(0.5029)
	to	β₂₁	0.5359(0.0405)	1.5280(0.1401)	0.4671(0.0512)	0.4599(0.0521)
	Active	β₂₂	−0.0278(0.0190)	−0.0441(0.0203)	−0.0357(0.0183)	−0.0355(0.0183)
		β₂₃	−0.0431(0.0191)	−0.0541(0.0208)	−0.0503(0.0187)	−0.0505(0.0188)
			0.2802	0.3210	0.2631	0.2634
		μ₁	8.5321	8.0866	8.0251	8.0114
		μ₂	0.5238	0.4263	0.4195	0.4153
Heterogeneous	Active	β₁₀	0.3714(0.7637)	6.4420(1.2828)	2.8110(1.1055)	2.0846(1.0867)
Time	to	β₁₁	−0.2567(0.0786)	−0.7771(0.1305)	−0.5526(0.1130)	−0.5209(0.1120)
	Rest	β₁₂	0.0541(0.0214)	0.0496(0.0231)	0.0528(0.0233)	0.0685(0.0285)
		β₁₃	0.0867(0.0221)	0.0094(0.0241)	0.0840(0.0240)	0.1127(0.0296)
			0.3554	0.3941	0.4102	0.6132
	Rest	β₂₀	−6.4771(0.3775)	−20.1172(1.2551)	−6.9784(0.4544)	−6.8518(0.4673)
	to	β₂₁	0.4597(0.0411)	2.0046(0.1298)	0.5196(0.0481)	0.4889(0.0500)
	Active	β₂₂	−0.0211(0.0235)	−0.0620(0.0294)	−0.0383(0.0217)	−0.0327(0.0241)
		β₂₃	0.0033(0.0240)	−0.0874(0.0309)	−0.0199(0.0225)	−0.0077(0.0252)
			0.4051	0.6207	0.3422	0.4040
		μ₁	9.3939	9.0530	8.9522	8.9428
		μ₂	1.0534	0.9579	0.9528	0.9534

Note: Parameter estimates using EM algorithm and asymptotic standard errors. Regression for state transitions are given as formula ⁠, where formula are individual specific random intercepts, Android devices and males serve as baseline.

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