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♣r❡❢♠♦❞✿ ♥❡✇s ❛♥❞ ❡①t❡♥s✐♦♥s

❘❡✐♥❤♦❧❞ ❍❛t③✐♥❣❡r ✫ ❘❡❣✐♥❛ ❉✐ttr✐❝❤ ■♥st✐t✉t❡ ❢♦r ❙t❛t✐st✐❝s ❛♥❞ ▼❛t❤❡♠❛t✐❝s ❲❯ ❱✐❡♥♥❛

Ps②❝❤♦❝♦ ✷✵✶✶ ✶ ■♥tr♦❞✉❝t✐♦♥

P❛rt ■✿ ■♥tr♦❞✉❝t✐♦♥

▸ ❘✲P❛❝❦❛❣❡ ♣r❡❢♠♦❞

❝♦❧❧❡❝t✐♦♥ ♦❢ ✉t✐❧✐t✐❡s t♦ ✜t ❛ ✈❛r✐❡t② ♦❢ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥ ♠♦❞❡❧s

▸ ♣r❡❢❡r❡♥❝❡ ♠♦❞❡❧s ❜❛s❡❞ ♦♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s

♦❜❥❡❝t✐✈❡ ✐s t♦ ❡st❛❜❧✐s❤ ❛ ♣r❡❢❡r❡♥❝❡ s❝❛❧❡ ❢♦r ❝❡rt❛✐♥ ♦❜❥❡❝ts ✕ ❢♦♦❞✱ ❝r✐♠❡s✱ ♣❛✐♥✱ t❡❛❝❤✐♥❣ st②❧❡s✱ ♣♦rt❢♦❧✐♦s✱ ✳ ✳ ✳

▸ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s

J ♦❜❥❡❝ts ❛r❡ ❝♦♠♣❛r❡❞ ✐♥ ♣❛✐rs ❛❝❝♦r❞✐♥❣ t♦ ❛ s♣❡❝✐✜❝ ❛ttr✐❜✉t❡ ✕ t❛st❡s ❜❡tt❡r✱ ♠❛❦❡s ♠❡ ♣✉t ♦♥ ♠♦r❡ ✇❡✐❣❤t✱ ✳ ✳ ✳ ✇❡ ♦❜s❡r✈❡ (J

2) ❝♦♠♣❛r✐s♦♥s ✭r❡s♣♦♥s❡s✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✷ ■♥tr♦❞✉❝t✐♦♥

▼♦❞❡❧ ❝♦r❡ ♠♦❞❡❧ ✐♥ ♣r❡❢♠♦❞ ✐s t❤❡ ❇r❛❞❧❡②✲❚❡rr② s♣❡❝✐✜❝❛t✐♦♥ P{Yjk = 1∣πj,πk} = πj πj + πk ♦r P{Yjk = −1∣πj,πk} = πk πj + πk

Yjk = 1 ✳ ✳ ✳ ♦❜❥❡❝t j ♣r❡❢❡rr❡❞ t♦ k✱ Yjk = −1 ✳ ✳ ✳ ♦❜❥❡❝t k ♣r❡❢❡rr❡❞ t♦ j πj ✳ ✳ ✳ ❧♦❝❛t✐♦♥ ♦❢ ♦❜❥❡❝t j ♦♥ ♣r❡❢❡r❡♥❝❡ s❝❛❧❡

✐♥❞❡♣❡♥❞❡♥❝❡ ♠♦❞❡❧ ✭❇r❛❞❧❡②✲❚❡rr②✮✿ r❡s♣♦♥s❡ ✐s yjk p(yjk) = c( √πj √πk )

yjk

♣❛tt❡r♥ ♠♦❞❡❧✿ r❡s♣♦♥s❡ ✐s y = {y12,y13,...,yjk,...,yJ−1,J} p(y12,...,yJ−1,J) = c∏

j<k

( √πj √πk )

yjk Ps②❝❤♦❝♦ ✷✵✶✶ ✸ ■♥tr♦❞✉❝t✐♦♥

■♥❞❡♣❡♥❞❡♥❝❡✿ ▲▲❇❚ ✭❧♦❣❧✐♥❡❛r ❇r❛❞❧❡②✲❚❡rr② ♠♦❞❡❧✮ ✇❡ ✉s❡ t❤❡ ❧♦❣❧✐♥❡❛r r❡♣r❡s❡♥t❛t✐♦♥ ✭❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ✶✾✾✽✮ lnm(yjk) = µ(jk) + yjk(λj − λk) ❞❡s✐❣♥ str✉❝t✉r❡ ❢♦r ✸ ♦❜❥❡❝ts✿

µ λ1 λ2 λ3 ❝♦♠♣❛r✐s♦♥ ❞❡❝✐s✐♦♥ ❝♦✉♥ts ❝♦♥st y12 y13 y23 ✭✶✷✮ O1 n(1≻2) ✶ ✶ ✲✶ ✵ ✭✶✷✮ O2 n(2≻1) ✶ ✲✶ ✶ ✵ ✭✶✸✮ O1 n(1≻3) ✷ ✶ ✵ ✲✶ ✭✶✸✮ O3 n(3≻1) ✷ ✲✶ ✵ ✶ ✭✷✸✮ O2 n(2≻3) ✸ ✵ ✶ ✲✶ ✭✷✸✮ O3 n(3≻2) ✸ ✵ ✲✶ ✶ ❢❛❝t♦r ❢♦r ♥♦r♠❛❧✐③✐♥❣ ❝♦♥st❛♥ts µ Ps②❝❤♦❝♦ ✷✵✶✶ ✹

■♥tr♦❞✉❝t✐♦♥

P❛tt❡r♥ ♠♦❞❡❧ ❧♦❣❧✐♥❡❛r ♠♦❞❡❧ ✭❈❙❉❆✱ ✷✵✵✷✮ ln m(y12,...,yJ−1,J) = ηy = µ+

J

∑

j=1

λjxj = µ+

J

∑

j=1

λj ⎛ ⎝

J

∑

ν=j+1

yjν −

j−1

∑

ν=1

yνj ⎞ ⎠ ❞❡s✐❣♥ str✉❝t✉r❡ ❢♦r ✸ ♦❜❥❡❝ts✿

µ λ1 λ2 λ3 ♣❛tt❡r♥ y12 y13 y23 ❝♦✉♥ts ❝♦♥st x1 x2 x3 ℓ1 1 1 1 n1 1 ✷ ✵ ✲✷ ℓ2 1 1 −1 n2 1 ✷ ✲✷ ✵ ℓ3 1 −1 1 n3 1 ✵ ✵ ✵ ℓ4 1 −1 −1 n4 1 ✵ ✲✷ ✷ ℓ5 −1 1 1 n5 1 ✵ ✷ ✲✷ ℓ6 −1 1 −1 n6 1 ✵ ✵ ✵ ℓ7 −1 −1 1 n7 1 ✲✷ ✷ ✵ ℓ8 −1 −1 −1 n8 1 ✲✷ ✵ ✷ xj ❂ ★✭Oj ✐s ♣r❡❢❡rr❡❞ ✐♥ ℓ✮ ✲ ★✭Oj ♥♦t ♣r❡❢❡rr❡❞ ✐♥ ℓ✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✺ ■♥tr♦❞✉❝t✐♦♥

❊①t❡♥s✐♦♥s ❢♦r s✉❜❥❡❝t ❛♥❞ ♦❜❥❡❝t ❡✛❡❝ts

O1 O2 O3 O4 C2 C1 O3 O4 O1 O2 C1 C2

• bje t

• bje t

s✉❜❥❡❝t ❡✛❡❝ts✿ ❞✉♣❧✐❝❛t❡ t❛❜❧❡ ❢♦r ❡❛❝❤ ❝♦✈❛r✐❛t❡ ❣r♦✉♣ s ♦❜❥❡❝t ❡✛❡❝ts✿ λj = ∑q βC

q xjq bjq ✳ ✳ ✳ ❝♦✈❛r✐❛t❡ ❢♦r ❝❤❛r❛❝t❡r✐st✐❝ Cq βC

q ✳ ✳ ✳ ❡✛❡❝t ♦❢ ❝❤❛r❛❝t❡r✐st✐❝ Cq

Ps②❝❤♦❝♦ ✷✵✶✶ ✻ ■♥tr♦❞✉❝t✐♦♥

❊①t❡♥s✐♦♥s✿ ❖✈❡r✈✐❡✇ ❡①t❡♥s✐♦♥s ❢♦r ▲▲❇❚ ❛♥❞ ♣❛tt❡r♥ ♠♦❞❡❧

• ✉♥❞❡❝✐❞❡❞ ✭3(J

2) ❞✐✛❡r❡♥t ♣❛tt❡r♥s✮✱ ♣♦s✐t✐♦♥ ❡✛❡❝ts

• s✉❜❥❡❝t ❝♦✈❛r✐❛t❡s✱ ♦❜❥❡❝t s♣❡❝✐✜❝ ❝♦✈❛r✐❛t❡s

❛❞❞✐t✐♦♥❛❧ ❡①t❡♥s✐♦♥s ❢♦r ♣❛tt❡r♥ ♠♦❞❡❧s ✇❡ ❝❛♥ ❣✐✈❡ ✉♣ t❤❡ ❛ss✉♠♣t✐♦♥ ♦❢ ✐♥❞❡♣❡♥❞❡♥t ❞❡❝✐s✐♦♥s

• ❞❡♣❡♥❞❡♥❝❡ ♣❛r❛♠❡t❡rs θ(jk)(jl) ✭✐♥t❡r❛❝t✐♦♥s✮

❢♦r ♣❛✐rs ♦❢ ❝♦♠♣❛r✐s♦♥s ✇✐t❤ ♦♥❡ ♦❜❥❡❝t ✐♥ ❝♦♠♠♦♥ ❛♥❞ ✇❡ ❝❛♥ ❛❧s♦ ❞❡❛❧ ✇✐t❤ ✈❛r✐♦✉s ♦t❤❡r r❡s♣♦♥s❡ ❢♦r♠❛ts

• r❛♥❦✐♥❣ ❞❛t❛
• r❛t✐♥❣ ✭▲✐❦❡rt✮ ❞❛t❛ ✭✏r❛♥❦✐♥❣s ✇✐t❤ t✐❡s✑✮
• ♣✐❧✐♥❣✱ ♠✉❧t✐♣❧❡ r❡s♣♦♥s❡s✱ ✳ ✳ ✳

Ps②❝❤♦❝♦ ✷✵✶✶ ✼ ■♥tr♦❞✉❝t✐♦♥

❉❡r✐✈❡❞ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s✿ ❊①❛♠♣❧❡✿ r❛♥❦✐♥❣ ✇✐t❤ ✸ ♦❜❥❡❝ts ✇❡ tr❛♥s❢♦r♠ r❛♥❦✐♥❣s t♦ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s

• ♥✉♠❜❡r ♦❢ ♣♦ss✐❜❧❡ ♣❛tt❡r♥s ✐s 3! = 6 ❝♦♠♣❛r❡❞ t♦ 2(3

2) = 8

• ♣❛tt❡r♥ ♠♦❞❡❧ ❜❛s❡❞ ♦♥ r❡❞✉❝❡❞ ♥✉♠❜❡r ♦❢ ❞✐✛❡r❡♥t ♣❛tt❡r♥s
• ✉s✐♥❣ t❤❡ ▲▲❇❚ ❧❡❛❞s t♦ ❜✐❛s❡❞ ❡st✐♠❛t❡s ❢♦r t❤❡ λ✬s

→

Ps②❝❤♦❝♦ ✷✵✶✶ ✽

■♥tr♦❞✉❝t✐♦♥

❚❤❡ ▲▲❇❚ ✐♥ ♣r❡❢♠♦❞

▸ ✉s❡r✲❢r✐❡♥❞❧② ❢✉♥❝t✐♦♥ ✭r❡str✐❝t❡❞ ❢✉♥❝t✐♦♥❛❧✐t②✮✿

❧❧❜tP❈✳❢✐t✭♦❜❥✱ ♥✐t❡♠s✱ ❢♦r♠❡❧ ❂ ⑦✶✱ ❡❧✐♠ ❂ ⑦✶✱ r❡s♣t②♣❡ ❂ ✧♣❛✐r❝♦♠♣✧✱ ♦❜❥✳♥❛♠❡s ❂ ◆❯▲▲✱ ✉♥❞❡❝ ❂ ❋❆▲❙❊✮

▸ ❢♦r ♠♦r❡ s♣❡❝✐❛❧✐s❡❞ ♠♦❞❡❧s✿ ❣❡♥❡r❛t❡ ❛ ❞❡s✐❣♥ ♠❛tr✐①

✉s❡ ❣♥♠✭✮ ♦r ❣❧♠✭✮ t♦ ✜t t❤❡ ♠♦❞❡❧

❧❧❜t✳❞❡s✐❣♥✭❞❛t❛✱ ♥✐t❡♠s ❂ ◆❯▲▲✱ ♦❜❥♥❛♠❡s ❂ ✧✧✱ ♦❜❥❝♦✈s ❂ ◆❯▲▲✱ ❝❛t✳s❝♦✈s ❂ ◆❯▲▲✱ ♥✉♠✳s❝♦✈s ❂ ◆❯▲▲✱ ❝❛s❡✇✐s❡ ❂ ❋❆▲❙❊✱ ✳✳✳✮

▸ ❝❛❧❝✉❧❛t❡ t❤❡ π✬s ✭λ✬s✮ ❢r♦♠ t❤❡ ❡st✐♠❛t❡❞ ♠♦❞❡❧

❧❧❜t✳✇♦rt❤✭❢✐t♦❜❥✱ ♦✉t♠❛t ❂ ✧✇♦rt❤✧✮

▸ ♣❧♦t t❤❡ π✬s ✭λ✬s✮ ❢r♦♠ t❤❡ ❧❧❜t✳✇♦rt❤✭✮ ♦✉t♣✉t

♣❧♦t✇♦rt❤✭✇♦rt❤♠❛t✱ ♠❛✐♥ ❂ ✧Pr❡❢❡r❡♥❝❡s✧✱ ②❧❛❜ ❂ ✧❊st✐♠❛t❡✧✱ ♣s②♠❜ ❂ ◆❯▲▲✱ ♣❝♦❧ ❂ ◆❯▲▲✱ ②❧✐♠ ❂ r❛♥❣❡✭✇♦rt❤♠❛t✮✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✾ ■♥tr♦❞✉❝t✐♦♥

▲▲❇❚ ❡①❛♠♣❧❡✿ ❈❊▼❙ ❡①❝❤❛♥❣❡ ♣r♦❣r❛♠ st✉❞❡♥ts ♦❢ t❤❡ ❲❯ ❝❛♥ st✉❞② ❛❜r♦❛❞ ✈✐s✐t✐♥❣ ♦♥❡ ♦❢ ❝✉rr❡♥t❧② ✶✼ ❈❊▼❙ ✉♥✐✈❡rs✐t✐❡s ❛✐♠ ♦❢ t❤❡ st✉❞②✿

• ♣r❡❢❡r❡♥❝❡ ♦r❞❡r✐♥❣s ♦❢ st✉❞❡♥ts ❢♦r ❞✐✛❡r❡♥t ❧♦❝❛t✐♦♥s
• ✐❞❡♥t✐❢② r❡❛s♦♥s ❢♦r t❤❡s❡ ♣r❡❢❡r❡♥❝❡s

❞❛t❛✿

• ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥ r❡s♣♦♥s❡s ❢♦r ✻ s❡❧❡❝t❡❞ ❈❊▼❙ ✭▲♦♥❞♦♥✱

P❛r✐s✱ ▼✐❧❛♥✱ ❇❛r❝❡❧♦♥❛✱ ❙t✳●❛❧❧✱ ❙t♦❝❦❤♦❧♠✮

• s❡✈❡r❛❧ s✉❜❥❡❝t ❝♦✈❛r✐❛t❡s ✭❡✳❣✳✱ ❣❡♥❞❡r✱ ✇♦r❦✐♥❣ st❛t✉s✱ ❧❛♥✲

❣✉❛❣❡ ❛❜✐❧✐t✐❡s✱ ❡t❝✳✮

• s❡✈❡r❛❧ ♦❜❥❡❝t ❝♦✈❛r✐❛t❡s ✭❡✳❣✳✱ s♣❡❝✐❛❧✐s❛t✐♦♥✱ r❡❣✐♦♥✱ ❡t❝✳✮

Ps②❝❤♦❝♦ ✷✵✶✶ ✶✵ ■♥tr♦❞✉❝t✐♦♥

▲▲❇❚ ❡①❛♠♣❧❡✿ ❈❊▼❙ ❡①❝❤❛♥❣❡ ♣r♦❣r❛♠

• ❣❡♥❡r❛t❡ ♦❜❥❡❝t ❝♦✈❛r✐❛t❡s ✭❞✉♠♠② ❝♦❞✐♥❣✮✿

❃ ▲❆❚ ❁✲ ❝✭✵✱ ✶✱ ✶✱ ✵✱ ✶✱ ✵✮ ❃ ❊❈ ❁✲ ❝✭✶✱ ✵✱ ✶✱ ✵✱ ✵✱ ✵✮ ❃ ▼❙ ❁✲ ❝✭✵✱ ✶✱ ✵✱ ✵✱ ✶✱ ✵✮ ❃ ❋❙ ❁✲ ❝✭✵✱ ✵✱ ✵✱ ✶✱ ✵✱ ✶✮

• ♠❛❦❡ ❛ ❞❛t❛ ❢r❛♠❡ ❢♦r ♦❜❥❡❝t ❝♦✈❛r✐❛t❡s✱ ♥❛♠❡ ♦❜❥❡❝ts

❃ ❖❇❏ ❁✲ ❞❛t❛✳❢r❛♠❡✭▲❆❚✱ ❊❈✱ ▼❙✱ ❋❙✮ ❃ ❝✐t✐❡s ❁✲ ❝✭✧▲❖✧✱ ✧P❆✧✱ ✧▼■✧✱ ✧❙●✧✱ ✧❇❆✧✱ ✧❙❚✧✮

• ♠❛❦❡ ❛ ❞❡s✐❣♥ ♠❛tr✐①

❃ ❞❡s✳♥✶ ❁✲ ❧❧❜t✳❞❡s✐❣♥✭❝♣❝✱ ✻✱ ♦❜❥❝♦✈s ❂ ❖❇❏✱ ❝❛t✳s❝♦✈s ❂ ✧❙❊❳✧✱ ✰ ♦❜❥♥❛♠❡s ❂ ❝✐t✐❡s✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✶✶ ■♥tr♦❞✉❝t✐♦♥

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮

• ✜t ♠♦❞❡❧ ✉s✐♥❣ ❣♥♠✭✮

❃ ♠♦❞ ❁✲ ❣♥♠✭② ⑦ ▲❆❚ ✰ ▼❙ ✰ ❋❙ ✰ ❙❊❳✿✭▲❆❚ ✰ ▼❙ ✰ ❋❙✮✱ ❡❧✐♠✐♥❛t❡ ❂ ♠✉✿❙❊❳✱ ✰ ❢❛♠✐❧② ❂ ♣♦✐ss♦♥✱ ❞❛t❛ ❂ ❞❡s✳♥✶✮

• ♠♦❞❡❧ r❡s✉❧ts

❃ ♠♦❞ ❈❛❧❧✿ ❣♥♠✭❢♦r♠✉❧❛ ❂ ② ⑦ ▲❆❚ ✰ ▼❙ ✰ ❋❙ ✰ ❙❊❳✿✭▲❆❚ ✰ ▼❙ ✰ ❋❙✮✱ ❡❧✐♠✐♥❛t❡ ❂ ♠✉✿❙❊❳✱ ❢❛♠✐❧② ❂ ♣♦✐ss♦♥✱ ❞❛t❛ ❂ ❞❡s✳♥✶✮ ❈♦❡❢❢✐❝✐❡♥ts ♦❢ ✐♥t❡r❡st✿ ▲❆❚ ▼❙ ❋❙ ▲❆❚✿❙❊❳✷ ▼❙✿❙❊❳✷ ❋❙✿❙❊❳✷ ✲✵✳✼✹✾✼✷ ✵✳✵✷✸✺✺ ✲✶✳✵✵✼✹✷ ✲✵✳✷✾✻✸✹ ✵✳✷✼✺✵✽ ✵✳✶✻✹✺✼ ❉❡✈✐❛♥❝❡✿ ✶✸✷✷✳✵✵✾ P❡❛rs♦♥ ❝❤✐✲sq✉❛r❡❞✿ ✶✷✵✸✳✹✺✵ ❘❡s✐❞✉❛❧ ❞❢✿ ✺✹ Ps②❝❤♦❝♦ ✷✵✶✶ ✶✷

■♥tr♦❞✉❝t✐♦♥

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮

• ❝❛❧❝✉❧❛t❡ t❤❡ ✇♦rt❤

❃ ✇♠❛t ❁✲ ❧❧❜t✳✇♦rt❤✭♠♦❞✮ ❃ ✇♠❛t ❙❊❳✶ ❙❊❳✷ ▲❖ ✵✳✻✷✽✻✽✻✸✾ ✵✳✻✺✷✸✵✼✼✵ P❆✱❇❆ ✵✳✶✹✼✶✷✻✶✼ ✵✳✶✹✻✷✾✽✽✵ ▼■ ✵✳✶✹✵✸✺✼✼✽ ✵✳✵✽✵✺✶✶✼✽ ❙●✱❙❚ ✵✳✵✽✸✽✷✾✻✺ ✵✳✶✷✵✽✽✶✼✷ ❛ttr✭✱✧♦❜❥t❛❜❧❡✧✮ ▲❆❚ ▼❙ ❋❙ ① ✶ ✵ ✵ ✵ ▲❖ ✷ ✶ ✵ ✵ ▼■ ✸ ✶ ✶ ✵ P❆✱ ❇❆ ✹ ✵ ✵ ✶ ❙●✱ ❙❚

• ♣❧♦t t❤❡ ✇♦rt❤

❃ ♣❧♦t✇♦rt❤✭✇♠❛t✱ ②❧❛❜ ❂ ✧❡st✐♠❛t❡❞ ✇♦rt❤✧✱ ❧♦❣ ❂ ✧②✧✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✶✸ ■♥tr♦❞✉❝t✐♦♥

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮

estimated worth

Preferences

0.1 0.2 0.3 0.4 0.6 SEX1 SEX2

• SG,ST

MI PA,BA LO

• MI

SG,ST PA,BA LO

Ps②❝❤♦❝♦ ✷✵✶✶ ✶✹ ■♥tr♦❞✉❝t✐♦♥

❚❤❡ ♣❛tt❡r♥ ♠♦❞❡❧ ✐♥ ♣r❡❢♠♦❞

▸ ✉s❡r✲❢r✐❡♥❞❧② ❢✉♥❝t✐♦♥ ✭r❡str✐❝t❡❞ ❢✉♥❝t✐♦♥❛❧✐t②✮✿

♣❛ttP❈✳❢✐t✭♦❜❥✱ ♥✐t❡♠s✱ ❢♦r♠❡❧ ❂ ⑦✶✱ ❡❧✐♠ ❂ ⑦✶✱ ♦❜❥✳♥❛♠❡s ❂ ◆❯▲▲✱ ✉♥❞❡❝ ❂ ❋❆▲❙❊✱ ✐❛ ❂ ❋❆▲❙❊✮

▸ ❛♥❛❧♦❣♦✉s ❢♦r r❛♥❦✐♥❣s ✭♣❛tt❘✳❢✐t✮

❛♥❞ r❛t✐♥❣s ✭♣❛tt▲✳❢✐t✮

▸ ❝❛❧❝✉❧❛t❡ t❤❡ π✬s ✭λ✬s✮ ❢r♦♠ t❤❡ ❡st✐♠❛t❡❞ ♠♦❞❡❧

♣❛tt✳✇♦rt❤✭♦❜❥✱ ♦❜❥✳♥❛♠❡s ❂ ◆❯▲▲✱ ♦✉t♠❛t ❂ ✧✇♦rt❤✧✮

▸ ♣❧♦t t❤❡ π✬s ✭λ✬s✮ ❢r♦♠ t❤❡ ♣❛tt✳✇♦rt❤✭✮ ♦✉t♣✉t

♣❧♦t✇♦rt❤✭✇♦rt❤♠❛t✱ ♠❛✐♥ ❂ ✧Pr❡❢❡r❡♥❝❡s✧✱ ②❧❛❜ ❂ ✧❊st✐♠❛t❡✧✱ ♣s②♠❜ ❂ ◆❯▲▲✱ ♣❝♦❧ ❂ ◆❯▲▲✱ ②❧✐♠ ❂ r❛♥❣❡✭✇♦rt❤♠❛t✮✮

▸ ❢♦r ♠♦r❡ s♣❡❝✐❛❧✐s❡❞ ♠♦❞❡❧s✿ ❣❡♥❡r❛t❡ ❛ ❞❡s✐❣♥ ♠❛tr✐①

♣❛tt✳❞❡s✐❣♥✭♦❜❥✱ ♥✐t❡♠s ❂ ◆❯▲▲✱ ♦❜❥♥❛♠❡s ❂ ✧✧✱ r❡s♣t②♣❡ ❂ ✧♣❛✐r❝♦♠♣✧✱ ❜❧♥❘❡✈❡rt ❂ ❋❆▲❙❊✱ ❝♦✈✳s❡❧ ❂ ✧✧✱ ❜❧♥■♥t❝♦✈s ❂ ❋❆▲❙❊✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✶✺

P❛rt ■■✿ ▼♦❞❡❧ ❊①t❡♥s✐♦♥s

• ❤❡t❡r♦❣❡♥❡✐t② ✐♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s ✭❧❛t❡♥t ❝❧❛ss❡s✮

✭❆♥♥❛❧s ♦❢ ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ✷✵✶✵✮

• ♠✐ss✐♥❣ ♦❜s❡r✈❛t✐♦♥s

✭✉♥❞❡r r❡✈✐s✐♦♥✱ ✷✵✶✶✮

• ♠✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s ✐♥ t❤❡ ▲▲❇❚✿

♠✉❧t✐❞✐♠❡♥s✐♦♥❛❧ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s r❡♣❡❛t❡❞ ♠❡❛s✉r❡♠❡♥ts

✭❜❡✐♥❣ ✇r✐tt❡♥✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✶✻

◆P▼▲

❊①t❡♥s✐♦♥ ✶✿ ❍❡t❡r♦❣❡♥❡✐t② ✐♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s

• r❡s♣♦♥s❡s ✈❛r② ❜❡t✇❡❡♥ r❡s♣♦♥❞❡♥ts
• ♠❡❛s✉r❡❞ ❝♦✈❛r✐❛t❡s ❝❛♥ ❜❡ t❛❦❡♥ ✐♥t♦ ❛❝❝♦✉♥t
• ♦t❤❡r ✉♥♠❡❛s✉r❡❞ ♦r ✉♥♠❡❛s✉r❛❜❧❡ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ t❤❡ r❡✲

s♣♦♥❞❡♥ts ♠✐❣❤t ❛✛❡❝t t❤❡ r❡s♣♦♥s❡ ✐♥ ♣r❛❝t✐❝❡ ♠❛✐♥❧② ✷ s✐t✉❛t✐♦♥s✿

• ✉♥❦♥♦✇♥ ♦r ♥♦t ❛✈❛✐❧❛❜❧❡ s✉❜❥❡❝t ✈❛r✐❛❜❧❡s
• ✈❡r② ❝♦♠♣❧❡① s✐t✉❛t✐♦♥s ♠❛❦❡ ♠♦❞❡❧ ✜t

✉♥tr❛❝t❛❜❧❡

O1 O2 O3 O4 O3 O4 O1 O2

Ps②❝❤♦❝♦ ✷✵✶✶ ✶✼ ◆P▼▲

❘❛♥❞♦♠ ❡✛❡❝ts ♠♦❞❡❧ ✐♥tr♦❞✉❝❡ r❛♥❞♦♠ ❡✛❡❝ts ❢♦r ❡❛❝❤ r❡s♣♦♥❞❡♥t ✭♣❛tt❡r♥ ℓ✮ ✇❡ ♥❡❡❞ J r❛♥❞♦♠ ❡✛❡❝t ❝♦♠♣♦♥❡♥ts δjℓs t❤❡ ❧✐♥❡❛r ♣r❡❞✐❝t♦r ✐s ηℓs = ∑

j<j

yjk;ℓs(λjs + δjℓs − λks − δkℓs) ❧♦❝❛t✐♦♥ ♦❢ ♣r❡❢❡r❡♥❝❡ ♣❛r❛♠❡t❡r ❢♦r ✐t❡♠ j ✇✐❧❧ ❜❡ s❤✐❢t❡❞ ✉♣ ♦r ❞♦✇♥ ❢♦r ❡❛❝❤ r❡s♣♦♥s❡ ♣❛tt❡r♥ ✐♥ ❡❛❝❤ s✉❜❥❡❝t ❝♦✈❛r✐❛t❡ ❣r♦✉♣ t❤❡ ❧✐❦❡❧✐❤♦♦❞ ❜❡❝♦♠❡s L = ∏

ℓs

(∫

∞ −∞ ...∫ ∞ −∞ P(yℓs∣δℓs) g(δℓs) dδ1ℓs dδ2ℓs ... dδJ−1;ℓs) nℓs

✇❤❡r❡ g(δℓs) ✐s t❤❡ ♠✉❧t✐✈❛r✐❛t❡ ♣r♦❜❛❜✐❧✐t② ❞❡♥s✐t② ❢✉♥❝t✐♦♥ ♦r ♠✐①✐♥❣ ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ r❛♥❞♦♠ ❡✛❡❝ts ✈❡❝t♦r✳

Ps②❝❤♦❝♦ ✷✵✶✶ ✶✽ ◆P▼▲

◆♦♥♣❛r❛♠❡tr✐❝ ❛♣♣r♦❛❝❤ ❛❧t❡r♥❛t✐✈❡ ❛♣♣r♦❛❝❤ ✭◆P▼▲✱ ❆✐t❦✐♥✱ ✶✾✾✻✮✿ r❡♣❧❛❝❡ ♠✉❧t✐✈❛r✐❛t❡ ❞✐str✐❜✉t✐♦♥ ❜② s❡r✐❡s ♦❢ ♠❛ss ♣♦✐♥t ❝♦♠♣♦✲ ♥❡♥ts ✇✐t❤ ✉♥❦♥♦✇♥ ♣r♦❜❛❜✐❧✐t② ❛♥❞ ✉♥❦♥♦✇♥ ❧♦❝❛t✐♦♥ → ♠❛ss ♣♦✐♥t ❛♣♣r♦❛❝❤ ✐s ❛ ♠✐①t✉r❡ ♠♦❞❡❧✱ ✇❤❡r❡ ♠✉❧t✐♥♦♠✐❛❧ ✭✜①❡❞ ❡✛❡❝ts✮ ♠♦❞❡❧ ✐s r❡♣❧❛❝❡❞ ❜② ♠✐①t✉r❡ ♦❢ ♠✉❧t✐♥♦♠✐❛❧s ✐❢ ♥✉♠❜❡r ♦❢ ❝♦♠♣♦♥❡♥ts ✐s ❦♥♦✇♥✱ s❛② R✱ ✇❡ ❣❡t R ✈❡❝t♦rs ♦❢ ♠❛ss✲♣♦✐♥ts ❧♦❝❛t✐♦♥s δr = (δ1r,δ2r,...,δJ−1;r) ❛♥❞ ✉♥❦♥♦✇♥ ❝♦♠♣♦♥❡♥t ♣r♦❜❛❜✐❧✐t② qr ❚❤❡ ❧✐❦❡❧✐❤♦♦❞ ♥♦✇ ❜❡❝♦♠❡s L = ∏

ℓs

(

R

∑

r=1

qr Pℓsr(yℓs∣δr))

nℓs

✇❤❡r❡ ∑

ℓ

Pℓsr = 1, ∀s,r

Ps②❝❤♦❝♦ ✷✵✶✶ ✶✾ ◆P▼▲

❊st✐♠❛t✐♦♥ ✉s✐♥❣ t❤❡ ❊▼ ❛❧❣♦r✐t❤♠ ✈✐❡✇ ♣r♦❜❧❡♠ ❛s ♠✐ss✐♥❣ ❞❛t❛ ♣r♦❜❧❡♠✿ ❧❛t❡♥t ❝❧❛ss ♠❡♠❜❡rs❤✐♣ ✐♥❞✐❝❛t♦r zℓsr ∈ {0,1} ❢♦r ❡❛❝❤ ℓs ❝♦♠❜✐✲ ♥❛t✐♦♥ zℓsr = 1 ✐❢ ℓs ∈ r E(zℓsr) = wℓsr wℓsr ❛r❡ t❤❡ ♣♦st❡r✐♦r ♣r♦❜❛❜✐❧✐t✐❡s ♦❢ ❝❧❛ss ♠❡♠❜❡rs❤✐♣ zℓsr ✐s ♠✐ss✐♥❣

▸ ❊✲st❡♣✿

r❡❝❛❧❝✉❧❛t❡s t❤❡ w✬s ❣✐✈❡♥ ❝✉rr❡♥t ♣❛r❛♠❡t❡r ❡st✐♠❛t❡s ❢♦r t❤❡ q✬s ❛♥❞ λ✬s

▸ ▼✲st❡♣✿

♠❛①✐♠✐s❡s t❤❡ ♠✉❧t✐♥♦♠✐❛❧ ❧✐❦❡❧✐❤♦♦❞ ✇✳r✳t✳ λ✬s ❛♥❞ δ✬s ❝❛rr✐❡❞ ♦✉t t❤r♦✉❣❤ ❧♦❣❧✐♥❡❛r ♠♦❞❡❧ ✇✐t❤ ✇❡✐❣❤ts wℓsr

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✵

◆P▼▲

❚❤❡ ◆P▼▲ ♠♦❞❡❧ ✐♥ ♣r❡❢♠♦❞

♣❛tt♥♣♠❧✳❢✐t✭ ❢♦r♠✉❧❛✱ ★ ❢♦r♠✉❧❛ ❢♦r ❢✐①❡❞ ❡❢❢❡❝ts r❛♥❞♦♠ ❂ ⑦✶✱ ★ ❢♦r♠✉❧❛ ❢♦r r❛♥❞♦♠ ❡❢❢❡❝ts ❦ ❂ ✶✱ ★ ♥✉♠❜❡r ♦❢ ♠❛ss✲♣♦✐♥ts ✭❝❧❛ss❡s✮ ❞❡s✐❣♥✱ ★ ❞❡s✐❣♥ ♠❛tr✐① t♦❧ ❂ ✵✳✺✱ ★ t♦ ❝♦♥tr♦❧ t❤❡ ❊▼✲❛❧❣♦r✐t❤♠ st❛rt♣ ❂ ◆❯▲▲✱ ❊▼♠❛①✐t ❂ ✺✵✵✱ ❊▼❞❡✈✳❝❤❛♥❣❡ ❂ ✵✳✵✵✶✱ ♣r✳✐t ❂ ❋❆▲❙❊ ✮

♣❛tt♥♣♠❧✳❢✐t✭✮ ✐s ❛ ✇r❛♣♣❡r ❢✉♥❝t✐♦♥ ❢♦r ❛❧❧❞✐stP❈✭✮ ✇❤✐❝❤ ✐♥ t✉r♥ ✐s ❛ ♠♦❞✐✜❝❛t✐♦♥ ♦❢ ❛❧❧❞✐st✭✮ ❢r♦♠ t❤❡ ♥♣♠❧r❡❣ ♣❛❝❦❛❣❡ ✭❊✐♥❜❡❝❦✱ ❉❛r♥❡❧❧✱ ❛♥❞ ❍✐♥❞❡✱ ✷✵✵✼✮ ♠♦❞✐✜❝❛t✐♦♥ ❛❧❧♦✇s ❢♦r ♠✉❧t✐♣❧❡ r❛♥❞♦♠ ❡✛❡❝t t❡r♠s ♠♦r❡ ✢❡①✐❜✐❧✐t② ✐♥ ❝❤♦♦s✐♥❣ st❛rt✐♥❣ ✈❛❧✉❡s

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✶ ◆P▼▲

◆P▼▲ ❡①❛♠♣❧❡✿ ❙♦✉r❝❡s ♦❢ ❙❝✐❡♥❝❡ ✐♥❢♦r♠❛t✐♦♥

❊✉r♦❜❛r♦♠❡t❡r ✺✺✳✷ ▼❛②✲❏✉♥❡ ✷✵✵✶ ◗✉❡st✐♦♥ ✺✳ ❍❡r❡ ❛r❡ s♦♠❡ s♦✉r❝❡s ♦❢ ✐♥❢♦r♠❛t✐♦♥ ❛❜♦✉t s❝✐❡♥t✐✜❝ ❞❡✈❡❧♦♣♠❡♥ts✳ P❧❡❛s❡ r❛♥❦ t❤❡♠ ❢r♦♠ ✶ t♦ ✻ ✐♥ t❡r♠s ♦❢ t❤❡✐r ✐♠♣♦rt❛♥❝❡ t♦ ②♦✉ ✭✶ ❜❡✐♥❣ t❤❡ ♠♦st ✐♠♣♦rt❛♥t ❛♥❞ ✻ t❤❡ ❧❡❛st ✐♠♣♦rt❛♥t✮ ❛✮ ❚❡❧❡✈✐s✐♦♥ ✳✳✳✳✳ ❜✮ ❘❛❞✐♦ ✳✳✳✳✳ ❝✮ ◆❡✇s♣❛♣❡rs ❛♥❞ ♠❛❣❛③✐♥❡s ✳✳✳✳✳ ❞✮ ❙❝✐❡♥t✐✜❝ ♠❛❣❛③✐♥❡s ✳✳✳✳✳ ❡✮ ❚❤❡ ✐♥t❡r♥❡t ✳✳✳✳✳ ❢✮ ❙❝❤♦♦❧✴❯♥✐✈❡rs✐t② ✳✳✳✳✳

✶✷✷✶✻ ❝♦♠♣❧❡t❡ r❛♥❦✐♥❣s ♦❢ t❤❡ ✻ ♦❜❥❡❝ts✿ ❚❱✱ ❘❛❞✐♦✱ ✳ ✳ ✳ s✉❜❥❡❝t ❝♦✈❛r✐❛t❡s✿ ❆●❊ ✭✹ ❧❡✈❡❧s✿ ✶✺✲✷✹✱ ✷✺✲✸✾✱ ✹✵✲✺✹ ❛♥❞ ✺✺✰✮ ❙❊❳ ✭✷ ❧❡✈❡❧s✿ ♠❛❧❡✱ ❢❡♠❛❧❡✮

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✷ ◆P▼▲

❊①❛♠♣❧❡✿ ▼♦❞❡❧ s❡❧❡❝t✐♦♥

• ✜♥❞ ✜tt✐♥❣ ✜①❡❞ ❡✛❡❝ts ♠♦❞❡❧✿ ❆●❊ ✰ ❙❊❳
• ✜t ❆●❊ ✰ ❙❊❳ r❛♥❞♦♠ ❡✛❡❝ts ♠♦❞❡❧ ✇✐t❤ ✐♥❝r❡❛s✐♥❣ ♥✉♠❜❡r

♦❢ ♠❛ss ♣♦✐♥ts

• ❡❛❝❤ ♠♦❞❡❧ ✇❛s ✜tt❡❞ ✺✵ t✐♠❡s ✇✐t❤ ❞✐✛❡r❡♥t st❛rt✐♥❣ ✈❛❧✉❡s
• ♠♦❞❡❧ ✇✐t❤ s♠❛❧❧❡s ❇■❈ ✇❛s s❡❧❡❝t❡❞ ✭∗✮

✭❛✮ ✇✐t❤♦✉t ❝♦✈❛r✐❛t❡s ✭❜✮ ✇✐t❤ ❆●❊ ❛♥❞ ❙❊❳ ◆♦✳ ♦❢ ◆♦✳ ♦❢ ◆♦✳ ♦❢ ♠❛ss ♣❛r❛✲ ♣❛r❛✲ ♣♦✐♥ts r ❉❡✈✐❛♥❝❡ ♠❡t❡rs ❇■❈ ❉❡✈✐❛♥❝❡ ♠❡t❡rs ❇■❈ ✶ ✷✶✷✾✸ ✶✸ ✷✶✹✵✻ ✶✼✽✶✺ ✸✸ ✶✽✶✵✵ ✷ ✶✷✹✾✹ ✶✽ ✶✷✻✺✵ ✶✵✼✸✶ ✸✽ ✶✶✵✻✵ ✸ ✶✵✷✺✷ ✷✸ ✶✵✹✺✶ ✾✵✺✻ ✹✸ ✾✹✷✽ ✹ ✾✼✾✷ ✷✽ ✶✵✵✸✺ ✽✽✸✻ ✹✽ ✾✷✺✷ ✺ ✾✺✹✹ ✸✸ ✾✽✸✵ ✽✼✷✾ ✺✸ ✾✶✽✼ ✻ ✾✸✽✼ ✸✽ ✾✼✶✻ ✽✻✻✼ ✺✽ ∗ ✾✶✼✵ ✼ ✾✸✵✷ ✹✸ ✾✻✼✹ ✽✻✸✻ ✻✸ ✾✶✽✷ ✽ ✾✷✼✼ ✹✽ ✾✻✾✸ ✽✻✷✸ ✻✽ ✾✷✶✷ Ps②❝❤♦❝♦ ✷✵✶✶ ✷✸ ◆P▼▲

❘❡s✉❧ts

Estimate

Male Class 1

0.05 0.10 0.15 0.20 0.30 0.40 15−24 25−39 40−54 55+

• Rad

Press TV SciJ WWW Edu

• Rad

TV Press WWW Edu SciJ

• Rad

TV WWW Press Edu SciJ

• Rad

WWW TV Press Edu SciJ Estimate

Male Class 6

0.05 0.10 0.15 0.20 0.30 0.40 15−24 25−39 40−54 55+

• Edu

WWW SciJ Press Rad TV

• Edu

WWW SciJ Press Rad TV

• Edu

WWW SciJ Press Rad TV

• WWW

Edu SciJ Press Rad TV

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✹

▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❊①t❡♥s✐♦♥ ✷✿ ▼✐ss✐♥❣ ♦❜s❡r✈❛t✐♦♥s ✐♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s ♠✐ss✐♥❣ ♦❜s❡r✈❛t✐♦♥s ❝❛♥ ♦❝❝✉r ❢♦r s❡✈❡r❛❧ r❡❛s♦♥s✿ ❜② ❞❡s✐❣♥✱ r❡s♣♦♥❞❡♥t ❞♦❡s♥✬t ❦♥♦✇✱ ✐s ✉♥✇✐❧❧✐♥❣✱ ❢❛t✐❣✉❡✱ ❡t❝✳ ✐❢ ◆❆ ♦❝❝✉rs ❛t r❛♥❞♦♠ ✕ ❡❛s✐❧② ❤❛♥❞❧❡❞ ✐♥ ▲▲❇❚ s✐♥❝❡ m(yjk) ❞❡♣❡♥❞ ♦♥❧② ♦♥ ♦❜s❡r✈❡❞ ✈❛❧✉❡s ❜✉t ✇❡ ✇❛♥t t♦ ✉s❡ ♣❛tt❡r♥ ♠♦❞❡❧s ❢♦r s❡✈❡r❛❧ r❡❛s♦♥s ❤♦✇ ❝❛♥ ✇❡ t❛❦❡ ❛❝❝♦✉♥t ♦❢ ✐♥❝♦♠♣❧❡t❡ r❡s♣♦♥s❡ ♣❛tt❡r♥s❄

• ❡❛❝❤ ❞✐✛❡r❡♥t ♠✐ss✐♥❣ ♣❛tt❡r♥ ❣✐✈❡s ❛ ❞✐✛❡r❡♥t ❞❡s✐❣♥ ♠❛tr✐①

✭s♠❛❧❧❡r t❤❛♥ ❞❡s✐❣♥ ♠❛tr✐① ❢♦r ♥♦♥✲♠✐ss✐♥❣ ❞❛t❛✮

• ❧✐❦❡❧✐❤♦♦❞ ✐s ❝♦♠♣✉t❡❞ ❢♦r ❡❛❝❤ ♦❢ t❤❡s❡ ✏❞✐✛❡r❡♥t✑ t❛❜❧❡s

✏✐♥❞✐✈✐❞✉❛❧✑ ❝♦♥tr✐❜✉t✐♦♥s t♦ t❤❡ ❧✐❦❡❧✐❤♦♦❞

• t♦t❛❧ ❧✐❦❡❧✐❤♦♦❞ ✭✇❤✐❝❤ ✐s t❤❡♥ ♠❛①✐♠✐s❡❞✮

✐s t❤❡ ♣r♦❞✉❝t ♦❢ ❛❧❧ t❤❡ ✏✐♥❞✐✈✐❞✉❛❧✑ ❝♦♥tr✐❜✉t✐♦♥s

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✺ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❉❛t❛ str✉❝t✉r❡

♦❜s❡r✈❡❞ ♣❛tt❡r♥s ❝♦♠♣❧❡t❡ ♣❛tt❡r♥s ◆❆ ♣❛tt❡r♥s y12 y13 y23 (12) (13) (23) (12) (13) (23) ❜❧♦❝❦ ✶ ❬❪ 1 1 1 1 1 1 1 1 −1 1 1 −1 1 −1 1 1 −1 1 1 −1 −1 1 −1 −1 −1 1 1 −1 1 1 −1 1 −1 −1 1 −1 −1 −1 1 −1 −1 1 −1 −1 −1 −1 −1 −1 ❜❧♦❝❦ ✷✿ ❬✷✸❪ 1 1 ◆❆ 1 1 1 1 1 1 −1 1 1 −1 ◆❆ 1 −1 1 1 1 −1 −1 1 −1 1 ◆❆ −1 1 1 1 −1 1 −1 1 −1 −1 ◆❆ −1 −1 1 1 −1 −1 −1 1 ❜❧♦❝❦ ✸ ⋮ ⋮ ⋮

• Pobs(1,1,◆❆) = Pcompl(1,1,1) + Pcompl(1,1,−1)

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✻ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

▼♦❞❡❧❧✐♥❣ ♠✐ss✐♥❣ ✈❛❧✉❡s ❝♦♠♣❧❡t❡ ❞❛t❛ ✐s t❛❜❧❡ ✇✐t❤ 22ℓ ❝❡❧❧s ❝❡❧❧ ♣r♦❜❛❜✐❧✐t② ✐s P{Y = y,R = r; π,ψ} ◆❆ ♠♦❞❡❧✿ P{Y = y,R = r; π,ψ} = P{Y = y; π}P{R = r∣Y = y; ψ} = f(y)q(r∣y) ❝❡❧❧ ♣r♦❜❛❜✐❧✐t✐❡s ❢♦r ✐♥❝♦♠♣❧❡t❡ ✭♦❜s❡r✈❡❞ ❞❛t❛✮✿ P{y12,y13,y23; π,ψ} = f(y12,y13,y23; π) q(0,0,0 ∣ y12,y13,y23;ψ) P{y12,y13,◆❆; π,ψ} = ∑y23f(y12,y13,y23; π) q(0,0,1 ∣ y12,y13,y23;ψ) P{y12,◆❆,y23; π,ψ} = ∑y13f(y12,y13,y23; π) q(0,1,0 ∣ y12,y13,y23;ψ) ⋮ t❤✐s ✐s ❛ ❝♦♠♣♦s✐t❡ ❧✐♥❦ ❛♣♣r♦❛❝❤ ✭❚❤♦♠♣s♦♥ ✫ ❇❛❦❡r✱ ✶✾✽✶✮✿ ❡①t❡♥❞✐♥❣ ●▲▼s✿ µi = cih(γ) = ∑cikh(ηk) ci✬s ❛r❡ ❦♥♦✇♥ ❢✉♥❝t✐♦♥s ✭❈▲ ❢✉♥❝t✐♦♥s✮

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✼ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

▼✐ss✐♥❣ ❞❛t❛ ♠❡❝❤❛♥✐s♠s ✭❘✉❜✐♥✱ ✶✾✼✻✮ ❧❡t y = (yobs,ymis) ❛♥❞ Rjk ❜❡ ❛♥ ◆❆ ✐♥❞✐❝❛t♦r ✭✐❢ ◆❆✿ Rjk = 1✮ ▼✐ss✐♥❣ ❝♦♠♣❧❡t❡❧② ❛t r❛♥❞♦♠ ✭▼❈❆❘✮✿ ■❢ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❞✐str✐❜✉t✐♦♥ P{R = r ∣ Y = y; ψ} ✐s ✐♥❞❡♣❡♥❞❡♥t ♦❢ Y ✱ ✐✳❡✳ P{R = r ∣ Y = y; ψ} = P{R = r; ψ}✳ ▼✐ss✐♥❣ ❛t r❛♥❞♦♠ ✭▼❆❘✮✿ ■❢ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❞✐str✐❜✉t✐♦♥ ❞❡♣❡♥❞s ♦♥ t❤❡ ♦❜s❡r✈❡❞✱ ❜✉t ♥♦t ♦♥ t❤❡ ♠✐ss✐♥❣ ✈❛❧✉❡s✱ P{R = r ∣ Y = y; ψ} = P{R = r ∣ Yobs = yobs; ψ}✳ ▼✐ss✐♥❣ ♥♦t ❛t r❛♥❞♦♠ ✭▼◆❆❘✮✿ ■❢ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❞✐str✐❜✉t✐♦♥ ❞❡♣❡♥❞s ♦♥ ❜♦t❤ t❤❡ ♦❜s❡r✈❡❞ ❛♥❞ t❤❡ ♠✐ss✐♥❣ ✈❛❧✉❡s✱ P{R = r ∣ Y = y; ψ} = P{R = r ∣ Yobs = yobs,Ymis = ymis; ψ}✳

Ps②❝❤♦❝♦ ✷✵✶✶ ✷✽

▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❊st✐♠❛t✐♦♥ ♦❢ t❤❡ ♦✉t❝♦♠❡ ♠♦❞❡❧ f(y) t♦t❛❧ ❧✐❦❡❧✐❤♦♦❞ ✐s ♣r♦❞✉❝t ♦❢ ❧✐❦❡❧✐❤♦♦❞s ❢♦r ❡❛❝❤ ◆❆ ♣❛tt❡r♥ ❜❧♦❝❦ ❬⋅❪ L(λ;y) = L[ ] ⋅ L[12]⋯L[12][13]⋯L[12...J] ✐♥❞✐✈✐❞✉❛❧ ❝♦♥tr✐❜✉t✐♦♥s ❛r❡✿ L[ ] = ∏

y∈Y[ ]

P(y;π,ψ)ny = ∏

y∈Y[ ]

⎛ ⎝ exp{η(y12,y13,...,yJ−1,J)} ∑y∈Y[ ] exp{ηy} ⎞ ⎠

ny

❛♥❞✱ ❡✳❣✳✱ L[12] = ∏

y∈Y[12]

⎛ ⎝ exp{η(1,y13,...,yJ−1,J)} + exp{η(−1,y13,...,yJ−1,J)} ∑y∈Y[ ] exp{ηy} ⎞ ⎠

ny Ps②❝❤♦❝♦ ✷✵✶✶ ✷✾ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❙♦♠❡ ♥♦♥r❡s♣♦♥s❡ ♠♦❞❡❧s✿ q(r ∣y)

▸ ✉♥❞❡r ▼❈❆❘ ❛ss✉♠♣t✐♦♥✿

♠♦❞❡❧ ✶✿ P{Rjk = rjk} = eαjkrjk/(1 + eαjk)✱ rjk ∈ {0,1} ♠♦❞❡❧ ✷✿ ❝♦♠♠♦♥ α✱ ✐✳❡✳✱ αjk = α ♠♦❞❡❧ ✸✿ r❡♣❛r❛♠❡t❡r✐s❡ αjk ✇✐t❤ αj + αk

▸ ✉♥❞❡r ▼◆❆❘ ❛ss✉♠♣t✐♦♥✿ ✭✐♥❝❧✉❞❡ ❞❡♣❡♥❞❡♥❝❡ ♦♥ y✮

♠♦❞❡❧ ✶✿ P{Rjk = rjk∣Yjk = yjk} = e(αjk+yjkjβjk)rjk/(1 + eαjk+yjkβjk) ♠♦❞❡❧ ✷✿ ❝♦♠♠♦♥ α ❛♥❞ β ♠♦❞❡❧ ✸✿ ❛❞❞✐t✐♦♥❛❧❧② r❡♣❛r❛♠❡t❡r✐s❡ βjk ✇✐t❤ βj + βk ❊st✐♠❛t✐♦♥✿ ❧✐♥❡❛r ♣r❡❞✐❝t♦rs ♦❢ ♦✉t❝♦♠❡ ♠♦❞❡❧ ηy ❛r❡ ❡①t❡♥❞❡❞ t♦ ηy + ηr∣y ❛♣❛rt ❢r♦♠ t❤❛t✱ t❤❡ ♣r♦❝❡❞✉r❡ r❡♠❛✐♥s t❤❡ s❛♠❡ ❛s ❢♦r t❤❡ ♣✉r❡ ♦✉t❝♦♠❡ ♠♦❞❡❧

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✵ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❚❤❡ ♠✐ss✐♥❣ ♦❜s❡r✈❛t✐♦♥s ♠♦❞❡❧ ✐♥ ♣r❡❢♠♦❞ s♦♠❡ ♥♦♥r❡s♣♦♥s❡ ♠♦❞❡❧s ❢♦r ♠✐ss✐♥❣ ♦❜s❡r✈❛t✐♦♥s ❛r❡ ❤❛♥❞❧❡❞ ✉s✐♥❣ ❢✉rt❤❡r ❛r❣✉♠❡♥ts ✐♥ t❤❡ ♣❛tt❡r♥ ♠♦❞❡❧ ❢✉♥❝t✐♦♥s

♣❛ttP❈✳❢✐t✭♦❜❥✱ ♥✐t❡♠s✱ ❢♦r♠❡❧ ❂ ⑦✶✱ ❡❧✐♠ ❂ ⑦✶✱ r❡s♣t②♣❡ ❂ ✧♣❛✐r❝♦♠♣✧✱ ♦❜❥✳♥❛♠❡s ❂ ◆❯▲▲✱ ✉♥❞❡❝ ❂ ❋❆▲❙❊✱ ✐❛ ❂ ❋❆▲❙❊✱ ◆■t❡st ❂ ❋❆▲❙❊✱ ◆■ ❂ ❋❆▲❙❊✱ ▼■❙❝♦♠♠♦♥ ❂ ❋❆▲❙❊✱ ▼■❙♠♦❞❡❧ ❂ ✧♦❜❥✧✱ ▼■❙❛❧♣❤❛ ❂ ◆❯▲▲✱ ▼■❙❜❡t❛ ❂ ◆❯▲▲✱ ♣r✳✐t ❂ ❋❆▲❙❊✮ ◆■t❡st ✳ ✳ ✳ s❡♣❛r❛t❡ ❡st✐♠❛t✐♦♥ ❢♦r ❝♦♠♣❧❡t❡ ❛♥❞ ✐♥❝♦♠♣❧❡t❡ ♣❛tt❡r♥s ◆■ ✳ ✳ ✳ ❧❛r❣❡ t❛❜❧❡ ✭❝r♦ss❝❧❛ss✐✜❝❛t✐♦♥ ✇✐t❤ ◆❆ ♣❛tt❡r♥s✮ ▼■❙❝♦♠♠♦♥ ✳ ✳ ✳ ✜ts ❛ ❝♦♠♠♦♥ ♣❛r❛♠❡t❡r ❢♦r ◆❆ ✐♥❞✐❝❛t♦rs✱ ✐✳❡✳✱ α = αj = αk ▼■❙❛❧♣❤❛ ✳ ✳ ✳ s♣❡❝✐✜❝❛t✐♦♥ t♦ ✜t ♣❛r❛♠❡t❡rs ❢♦r ◆❆ ✐♥❞✐❝❛t♦rs ✉s✐♥❣ αij ♦r αi+αj ▼■❙❜❡t❛ ✳ ✳ ✳ ✜ts ♣❛r❛♠❡t❡rs ❢♦r ▼◆❆❘ ♠♦❞❡❧✱ ❛♥❛❧♦❣♦✉s t♦ ▼■❙❛❧♣❤❛

s❛♠❡ ❛r❣✉♠❡♥ts ❛✈❛✐❧❛❜❧❡ ❢♦r ♣❛tt❘✳❢✐t✭✮ ❛♥❞ ♣❛tt▲✳❢✐t✭✮

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✶ ▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

▼✐ss✐♥❣ ✈❛❧✉❡s ❡①❛♠♣❧❡✿ ❆tt✐t✉❞❡s t♦✇❛r❞s ❢♦r❡✐❣♥❡rs

❙✉r✈❡② ❛t t❤❡ ❱✐❡♥♥❛ ❯♥✐✈❡rs✐t② ♦❢ ❊❝♦♥♦♠✐❝s✭❲❡❜❡r✱ ✷✵✶✵✮ ✾✽ st✉❞❡♥ts r❛t❡❞ ❢♦✉r ❡①tr❡♠❡ st❛t❡♠❡♥ts ❛❜♦✉t ❤②♣♦t❤❡t✐❝❛❧ ❝♦♥s❡q✉❡♥❝❡s ♦❢ ♠✐❣r❛t✐♦♥ t❤r♦✉❣❤ ❛ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥ ❡①♣❡r✐♠❡♥t ✶✮ ❝r✐♠❘❛t❡ ❋♦r❡✐❣♥❡rs ✐♥❝r❡❛s❡ ❝r✐♠❡ r❛t❡s ✷✮ ♣♦s✐t✐♦♥ ❋♦r❡✐❣♥❡rs t❛❦❡ ❛✇❛② tr❛✐♥✐♥❣ ♣♦s✐t✐♦♥s ✸✮ s♦❝❇✉r❞ ❋♦r❡✐❣♥❡rs ❛r❡ ❛ ❜✉r❞❡♥ ❢♦r t❤❡ s♦❝✐❛❧ ✇❡❧❢❛r❡ s②st❡♠ ✹✮ ❝✉❧t✉r❡ ❋♦r❡✐❣♥❡rs t❤r❡❛t❡♥ ♦✉r ❝✉❧t✉r❡ ❃ ▼❈❆❘ ❁✲ ♣❛ttP❈✳❢✐t✭✐♠♠✐❣✱ ✹✱ ✉♥❞❡❝ ❂ ❚✮ ❃ ▼◆❆❘ ❁✲ ♣❛ttP❈✳❢✐t✭✐♠♠✐❣✱ ✹✱ ✉♥❞❡❝ ❂ ❚✱ ▼■❙❛❧♣❤❛ ❂ ❝✭❚✱ ❚✱ ❚✱ ❚✮✱ ✰ ▼■❙❜❡t❛ ❂ ❝✭❚✱ ❚✱ ❚✱ ❚✮✮ Ps②❝❤♦❝♦ ✷✵✶✶ ✸✷

▼✐ss✐♥❣ ❖❜s❡r✈❛t✐♦♥s

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮

estimated worth

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0.1 0.2 0.3 0.4 0.5 MCAR MNAR

• culture

position socBurd crimRate

• culture

position socBurd crimRate

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✸ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

❊①t❡♥s✐♦♥ ✸✿ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s ✕ r❡♣❡❛t❡❞ ♦❜s❡r✈❛t✐♦♥s ♦❢ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥s ♦✈❡r t✐♠❡ ✕ ❝r♦ss✲s❡❝t✐♦♥❛❧ ❝♦♠♣❛r✐s♦♥s ❛❝❝♦r❞✐♥❣ t♦ ❞✐✛❡r❡♥t ❛ttr✐❜✉t❡s ❢♦r♠✉❧❛t✐♦♥ ❛s ♣❛tt❡r♥ ♠♦❞❡❧ str❛✐❣❤t❢♦r✇❛r❞ ❛ r❡s♣♦♥s❡ ♣❛tt❡r♥ ✐s {y121,...,y12T,...,yjk1,...yjkT,...,y(J−1)J1,...,y(J−1)JT} ❤♦✇❡✈❡r ♣❛tt❡r♥ ♠♦❞❡❧ ✐♥tr❛❝t❛❜❧❡✿ ❡✳❣✳✱ ✺ ✐t❡♠s ❛t ✸ t✐♠❡ ♣♦✐♥ts r❡s✉❧ts ✐♥ 230 ♣❛tt❡r♥s ✐❞❡❛✿ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ▲▲❇❚ ❛♥❞ ♣❛tt❡r♥ ♠♦❞❡❧ ❛ss✉♠✐♥❣✿ ✕ ✐♥❞❡♣❡♥❞❡♥❝❡ ❜❡t✇❡❡♥ ❝♦♠♣❛r✐s♦♥s ✭▲▲❇❚✮ ✕ ♣❛tt❡r♥s ✇✐t❤✐♥ ❝♦♠♣❛r✐s♦♥s ✭t✐♠❡ ♣♦✐♥ts✮

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✹ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

▼✉❧t✐✈❛r✐❛t❡ ▲▲❇❚ ❡①t❡♥❞✐♥❣ t❤❡ ▲▲❇❚ ✇❡ ❣❡t lnm(jk)(yjk1⋯yjkT ) = µ(jk) +

T

∑

t=1

yjkt(λjt − λkt) + ∑

s<t

yjksyjktζ(jk)(st) ❢♦r ✷ t✐♠❡ ♣♦✐♥ts ❛♥❞ ❢♦r ❛ ❝❡rt❛✐♥ ❝♦♠♣❛r✐s♦♥ (jk) lnm(jk)(++) = µ(jk) + λj1 − λk1 + λj2 − λk2 + ζ(jk) lnm(jk)(−+) = µ(jk) − λj1 + λk1 + λj2 − λk2 − ζ(jk) lnm(jk)(+−) = µ(jk) + λj1 − λk1 − λj2 + λk2 − ζ(jk) lnm(jk)(−−) = µ(jk) − λj1 + λk1 − λj2 + λk2 + ζ(jk)

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✺ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

❲✐t❤✐♥✲❝♦♠♣❛r✐s♦♥ ❞❡♣❡♥❞❡♥❝❡ ❢♦r ✷ t✐♠❡ ♣♦✐♥ts t❤❡r❡ ❛r❡ (J

2) ✇✐t❤✐♥✲❝♦♠♣❛r✐s♦♥ ❞❡♣❡♥❞❡♥❝✐❡s

❢♦r T t✐♠❡ ♣♦✐♥ts t❤❡r❡ ❛r❡ (T

2) × (J 2) s✉❝❤ ❞❡♣❡♥❞❡♥❝✐❡s

✐♥t❡r♣r❡t❛t✐♦♥ ♦❢ ζ(jk)(st)

t✐♠❡ ✷ (1 ≻ 2) (2 ≻ 1) + − t✐♠❡ ✶ (1 ≻ 2) + m++ m+− (2 ≻ 1) − m−+ m−−

lnOR(jk) = ln m++m−− m+−m−+ = 4ζ(jk) r❡str✐❝t✐♦♥s ♦♥ ζ(jk)(st) ❛❧❧♦✇ ❢♦r ♠♦❞❡❧❧✐♥❣ t❤❡ ❛ss♦❝✐❛t✐♦♥ str✉❝✲ t✉r❡

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✻

▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

▼♦❞❡❧❧✐♥❣ ❝❤❛♥❣❡ s♣❡❝✐❢②✐♥❣ ❛ ❞❡s✐❣♥ ♠❛tr✐① W ❢♦r t❤❡ ♦❜❥❡❝ts ❛❧❧♦✇s ❢♦r ❛ r❡♣❛✲ r❛♠❡t❡r✐s❛t✐♦♥ r❡✢❡❝t✐♥❣ ❝❡rt❛✐♥ ✏❝❤❛♥❣❡✑✲❤②♣♦t❤❡s❡s ❡✳❣✳✱ ✸ ♦❜❥❡❝ts ✷ t✐♠❡ ♣♦✐♥ts✱ δj = λj2 − λj1 W = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ λ11 λ21 λ31 δ1 δ2 δ3 λ11 ✶ ✵ ✵ ✵ ✵ ✵ λ21 ✵ ✶ ✵ ✵ ✵ ✵ λ31 ✵ ✵ ✶ ✵ ✵ ✵ λ12 ✶ ✵ ✵ ✶ ✵ ✵ λ22 ✵ ✶ ✵ ✵ ✶ ✵ λ32 ✵ ✵ ✶ ✵ ✵ ✶ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ♦t❤❡r ❝❤♦✐❝❡s ♦❢ W ❛❧❧♦✇ ❢♦r ❞✐✛❡r❡♥t ❤②♣♦t❤❡s❡s✱ ❡✳❣✳✱ δ1 = δ2

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✼ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

❊①❛♠♣❧❡✿ Ps②❝❤❛❝♦✉st✐❝s ❢♦r ❞❡t❛✐❧s ❛s❦ ❋❧♦r✐❛♥ ✇❡ ✜t ❛ ♠♦❞❡❧ ✇✐t❤ ✽ ♦❜❥❡❝ts ❛♥❞ ✺ t✐♠❡♣♦✐♥ts

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✽ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮✿ ❛ss♦❝✐❛t✐♦♥ str✉❝t✉r❡

t✐♠❡ ♣♦✐♥ts 12 13 23 14 24 34 15 25 35 45

mo ph st wst mat dol dts mo ph st wst mat dol dts

z−values

−3 −2 −1 1 2 3

NA

Ps②❝❤♦❝♦ ✷✵✶✶ ✸✾ ▼✉❧t✐✈❛r✐❛t❡ r❡s♣♦♥s❡s

❊①❛♠♣❧❡ ✭❝♦♥t✬❞✮✿ ✇♦rt❤ ♣❧♦ts

Estimate

without dependencies

0.02 0.05 0.10 0.20 1 2 3 4 5

• mo

ph dol wst

• ri

dts st mat

• mo

ph wst

• ri

dts dol st mat

• mo

ph wst

• ri

dts dol mat st

• mo

ph

• ri

wst dts dol st mat

• mo

ph

• ri

wst dts dol st mat Estimate

with dependencies

0.02 0.05 0.10 0.20 1 2 3 4 5

• mo

ph dol dts wst st

• ri

mat

• mo

ph wst

• ri

dts dol st mat

• mo

ph wst dts mat

• ri

dol st

• ph
• ri

mo dts wst dol st mat

• ph
• ri

mo wst dts dol st mat

Ps②❝❤♦❝♦ ✷✵✶✶ ✹✵

❙♦♠❡ ❘❡❢❡r❡♥❝❡s

❆✐t❦✐♥✱ ▼✳ ✭✶✾✾✻✮✳ ❆ ❣❡♥❡r❛❧ ♠❛①✐♠✉♠ ❧✐❦❡❧✐❤♦♦❞ ❛♥❛❧②s✐s ♦❢ ♦✈❡r❞✐s♣❡rs✐♦♥ ✐♥ ❣❡♥❡r❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧s✳ ❙t❛t✐st✐❝s ❛♥❞ ❈♦♠♣✉t✐♥❣✱ ✻✿✷✺✶✕✷✻✷✳ ❇r❛❞❧❡②✱ ❘✳ ❛♥❞ ❚❡rr②✱ ▼✳ ✭✶✾✺✷✮✳ ❘❛♥❦ ❆♥❛❧②s✐s ♦❢ ■♥❝♦♠♣❧❡t❡ ❇❧♦❝❦ ❉❡✲ s✐❣♥s✳ ■✳ ❚❤❡ ▼❡t❤♦❞ ♦❢ P❛✐r❡❞ ❈♦♠♣❛r✐s♦♥s✳ ❇✐♦♠❡tr✐❦❛✱ ✸✾✿✸✷✹✕✸✹✺✳ ❈❤♦✐s❡❧✱ ❙✳ ❛♥❞ ❲✐❝❦❡❧♠❛✐❡r✱ ❋✳ ✭✷✵✵✼✮✳ ❊✈❛❧✉❛t✐♦♥ ♦❢ ♠✉❧t✐❝❤❛♥♥❡❧ r❡♣r♦❞✉❝❡❞ s♦✉♥❞✿ ❙❝❛❧✐♥❣ ❛✉❞✐t♦r② ❛ttr✐❜✉t❡s ✉♥❞❡r❧②✐♥❣ ❧✐st❡♥❡r ♣r❡❢❡r❡♥❝❡✳ ❚❤❡ ❏♦✉r♥❛❧ ♦❢ t❤❡ ❆❝♦✉st✐❝❛❧ ❙♦❝✐❡t② ♦❢ ❆♠❡r✐❝❛✱ ✶✷✶✿✸✽✽✳ ❉✐ttr✐❝❤✱ ❘✳✱ ❍❛t③✐♥❣❡r✱ ❘✳✱ ❛♥❞ ❑❛t③❡♥❜❡✐ss❡r✱ ❲✳ ✭✶✾✾✽✮✳ ▼♦❞❡❧❧✐♥❣ t❤❡ ❡✛❡❝t ♦❢ s✉❜❥❡❝t✲s♣❡❝✐✜❝ ❝♦✈❛r✐❛t❡s ✐♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥ st✉❞✐❡s ✇✐t❤ ❛♥ ❛♣♣❧✐❝❛t✐♦♥ t♦ ✉♥✐✈❡rs✐t② r❛♥❦✐♥❣s✳ ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ✹✼✿✺✶✶✲✺✷✺✳ ❉✐ttr✐❝❤✱ ❘✳✱ ❍❛t③✐♥❣❡r✱ ❘✳✱ ❛♥❞ ❑❛t③❡♥❜❡✐ss❡r✱ ❲✳ ✭✷✵✵✷✮✳ ▼♦❞❡❧❧✐♥❣ ❞❡♣❡♥❞❡♥❝✐❡s ✐♥ ♣❛✐r❡❞ ❝♦♠♣❛r✐s♦♥ ❡①♣❡r✐♠❡♥ts✳ ❈♦♠♣✉t❛t✐♦♥❛❧ ❙t❛t✐st✐❝s ❛♥❞ ❉❛t❛ ❆♥❛❧②s✐s✱ ✹✵✿✸✾✕✺✼✳ ❋r❛♥❝✐s✱ ❇✳✱ ❉✐ttr✐❝❤✱ ❘✳✱ ❛♥❞ ❍❛t③✐♥❣❡r✱ ❘✳ ✭✷✵✶✵✮✳ ▼♦❞❡❧✐♥❣ ❤❡t❡r♦✲ ❣❡♥❡✐t② ✐♥ r❛♥❦❡❞ r❡s♣♦♥s❡s ❜② ♥♦♥♣❛r❛♠❡tr✐❝ ♠❛①✐♠✉♠ ❧✐❦❡❧✐❤♦♦❞✿ ❍♦✇ ❞♦ ❊✉r♦♣❡❛♥s ❣❡t t❤❡✐r s❝✐❡♥t✐✜❝ ❦♥♦✇❧❡❞❣❡❄ ❚❤❡ ❆♥♥❛❧s ♦❢ ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ✹✭✹✮✿✷✶✽✶✕✷✷✵✷✳ ❚❤♦♠♣s♦♥✱ ❘✳ ❛♥❞ ❇❛❦❡r✱ ❘✳ ✭✶✾✽✶✮✳ ❈♦♠♣♦s✐t❡ ❧✐♥❦ ❢✉♥❝t✐♦♥s ✐♥ ❣❡♥❡r✲ ❛❧✐③❡❞ ❧✐♥❡❛r ♠♦❞❡❧s✳ ❆♣♣❧✐❡❞ ❙t❛t✐st✐❝s✱ ✸✵✿✶✷✺✕✶✸✶✳ Ps②❝❤♦❝♦ ✷✵✶✶ ✹✶