Received July 5 2012, Revised July 30 2012, Accepted January 30 2013
Copyright ⵑ 2013 by the Korean Society of Civil Engineers
ǣǣȀȀǤǤȀͳͲǤͳʹͷʹȀ ǤʹͲͳ͵Ǥ͵͵Ǥ͵ǤͳͳͲͷ
Ǥ ǤǤ
Ꮾ♿#⇍#ጎ㝳⸮ሲⴲ#ኞ❋ᦂḚ#㰒#♪ኞ#⢪ᆿᦂ⮎#↶㐖ᡒ#⮿㭣⍂⛛
ౖঅߦي ȵࢠ୨ ȵૈశ ȵଲ׆ઽ
Choi, Saerona*, Kim, Mijoeng**, Oh, Cheol***, Lee, Keeyong****
Effects of Weather and Traffic Conditions on Truck Accident Severity on Freeways
ABSTRACT
Understanding the characteristics of truck-involved crashes is of keen interest because such crashes are highly associated with greater potential leading to severer injury. The purpose of this study is to identify factors affecting injury severity of truck-involved crashes on freeways. In addition, a binary logistic regression technique is applied to identify causal factors affecting truck crash severity under normal and adverse weather conditions. Major findings from the analyses are discussed with truck operations strategies including speed enforcement, variable speed limit, and truck lane restriction, from the safety enhancement point of view. The results of this study would be useful for developing traffic control and operations strategies to reduce truck-involved crashes and injury severity in practice.
Key words : Truck accident, Injury severity, Binary logistic regression, Road weather conditions
Ⅹಾ
Ʊ☖ᦩᱥ⊂໕ᨱᕽ⪵ྜྷ₉šಉƱ☖ᔍŁᝍbࠥ۵⪵ྜྷ₉᮹₉పᵲప, ྜྷඹᙹᘂ✚ᖒ, ⬥⧪₉ప᮹Ñᱽ᧞॒ŝšಉࡽ݅. ᅙᩑǍ۵Łᗮࠥ
ಽ⪵ྜྷ₉ᔍŁ᮹ᝍbࠥᨱၙ⊹۵ʑᔢၰࠥಽƱ☖ᯙᮥࠥ⇽⧉ᨱə༊ᱢᯕᯩ݅. ᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾᮥᯕᬊ⦹ᩍᔍŁᝍbࠥ᮹⪶ශ ᱢ᷾aᨱᩢ⨆ᮥၙ⊹۵ᯙᮥʑᔢᄥಽእƱᇥᕾ⦹ᩡ݅. ᇥᕾđŝᗮࠥ݉ᗮ, ᗮࠥšญᱥఖ, ⪵ྜྷ₉ᱥᬊ₉ಽ॒ŝzᮡƱ☖ඹšญᱥఖᯕ
ᔍŁᝍbࠥqᗭෝ᭥⦽ݡ₦ᮝಽᱽᦩࡹᨩ݅. ᅙᩑǍ᮹đŝ۵⨆⬥⪵ྜྷ₉ᔍŁၽᔾၰᔍŁᝍbࠥqᗭෝ᭥⦽Ʊ☖šᱽၰᬕᩢšಉᱥఖ
ᙹพᮁᬊ⦹í⪽ᬊࢁᙹᯩᮥäᮝಽ❱݉ࡽ݅.
áᔪᨕ ⪵ྜྷ₉ᔍŁ, ᔍŁᝍbࠥ, ᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾ, ࠥಽʑᔢ᳑Õ
1. ᕽು
ḡӽ2011֥ၽᔾ⦽Ʊ☖ᔍŁᵲ⪵ྜྷ₉ᔍŁಽᯙ⦽ᔍᯱa1,121ᮝಽᱥℕƱ☖ᔍŁᔍᯱᙹᯙ5,229᮹21%ෝ₉ḡ⦽
äᮝಽӹ┡ԍ݅. ⪵ྜྷ₉Ʊ☖ᔍŁၽᔾÕᙹ۵ⅾᔍŁÕᙹ221,711Õ᮹13% ᙹᵡᯙ29,143Õᯕ݅(ࠥಽƱ☖Ŗ݉). ᯕᵲŁᗮࠥಽᨱᕽ
ၽᔾ⦽⪵ྜྷ₉ᔍŁ۵1,034Õᮝಽⅾ2,640Õᵲ᧞40%ᨱݍ⦹໑, ᔍᯱ۵ⅾ265ᵲ39% ᙹᵡᯙ103ᮝಽӹ┡ԍ݅(⦽ǎࠥಽŖᔍ).
Ʊ☖ᦩᱥ ⊂໕ᨱᕽ ⪵ྜྷ₉ šಉ Ʊ☖ᔍŁ ᝍbࠥ۵ ࢱ aḡ ✚ᖒᮝಽ ᖅ⧁ ᙹ ᯩ݅. ℌṙ, ྜྷญ⦺᮹ ᬕ࠺ᨱթḡ ჶ⊺ᮥ ᱢᬊ⧕
ᅝ ভ ₉ప ∊࠭ ∊Ċపᮡ ྜྷℕ᮹ ᵲపᨱ እಡ⦹အಽ ⪵ྜྷ₉ ᔍŁ۵ ᬊ₉ ᔍŁᅕ݅ Ʊ☖ᔍŁ ᝍbࠥa ׳í ӹ┡ӽ݅(Evans
İࣀėॡ
et. al., 1993). ࢹṙ, ྜྷඹᙹᘂ✚ᖒᮥw۵⪵ྜྷ₉పᮡᝍੱ
۵ᰆÑญᬕ⧪ᮝಽᬕᱥᯱ⦝ಽᨱ᮹⦽᳙ᮭᬕᱥၽᔾa܆ᖒᯕ
׳Ł, ᭥⨹ᔢ⫊ ၽᔾᨱࠥ ݡ ܆ಆᯕ qᗭ⦹í ࡽ݅(Cantor et al. 2008). ᕽᯕ్⦽⪵ྜྷ₉ᔍŁqᗭၰᝍbࠥᱡ⦹ෝ
᭥⦽Ʊ☖ඹšญᱥఖ᮹⦥ᖒᮡᯕၙǎԕᐱอᦥܩǎᨱᕽ
ࠥ ݡࢱࡹŁ ᯩ݅.
ᅙᩑǍᨱᕽ۵Łᗮࠥಽᨱᖅ⊹ࡽ⥥áḡʑෝ☖⦹ᩍᙹḲࡽ
ᗮࠥ, Ʊ☖పᯱഭ᪡ʑᔢℎᨱᕽᙹḲࡽvᬑvᖅᯱഭෝእḲĥࡽ
Ʊ☖ᔍŁ⍡ᯕᜅ᮹Ŗeᱢ႑ĞᮥŁಅ⦹ᩍๅ⋎⧉ᮝಽ៉ᔍŁ ၽᔾḢᱥ᮹ʑᔢၰƱ☖ᔢ⫊ᮥӹ┡ԕ۵ᰁᰍᱢᯙᯙᮥᇥᕾ⦹
Łᯱ⦹ᩡ݅. ੱ⦽, ʑᔢ᳑ÕᮥŁಅ⦽⪵ྜྷ₉ᔍŁᝍbࠥ☖ĥ༉⩶
ᮥǍ⇶⧉ᮝಽ៉ᔍŁᝍbࠥ᮹⪶ශᱢ᷾aᨱᩢ⨆ᮥၙ⊹۵ᯙ
ᮥʑᔢᄥಽእƱᇥᕾ⧉ᮝಽ៉ᔍŁᝍbࠥqᗭݡ₦ᮥᱽᦩ⦹Ł
ᯱ ⦹ᩡ݅.
ᅙᩑǍ᮹2ᰆᨱᕽ۵ᅙᩑǍ᪡šಉࡽǎԕʑ᳕ᩑǍෝ
á☁⦹ᩡᮝ໑, 3ᰆᨱ۵ᇥᕾߑᯕ░Ǎ⇶ၰ☖ĥ༉⩶Ǎ⇶ŝᱶᨱ
ݡ⧕ᱽ⦹ᩡ݅. 3ᰆᨱ۵ᅙᩑǍ᮹ᇥᕾđŝෝʑᚁ⦹ᩡᮝ໑, 4ᰆᨱ۵ᇥᕾđŝෝ☖⦹ᩍᮡ⪵ྜྷ₉ᔍŁᝍbࠥᱡqᮥ᭥⦽
⪵ྜྷƱ☖ šญᱥఖᮥ ᱽᦩ⦹ᩡ݅.
2. ʑ᳕ᩑǍá☁
ǎᨱᕽ۵ ⪵ྜྷ₉ ᔍŁ ၽᔾශ ၰ ᔍŁᝍbࠥ qᗭෝ ᭥⦽
יಆ᮹ᯝ⪹ᮝಽŁᗮࠥಽ⪵ྜྷ₉Ʊ☖ᔍŁၽᔾᬱᯙၰᔍŁᝍb
ࠥ᷾aᯙᮥᇥᕾ⦹ʑ᭥⦽ᩑǍaᙹ⧪ࡹᨩ݅. ⪵ྜྷ₉ᬕᩢšಉ
ʑ᳕ᩑǍ۵Ʊ☖ඹෝɁḩ⦹Łᦩᱶᱢᮝಽšญ⦹ʑ᭥⦽ᱥఖᯙ
⪵ྜྷ₉ ᱥᬊ₉ಽ᮹ ↽ᱢ ᬕᩢʑჶ ࠥ⇽ ၰ ⬉ŝ⠪aෝ ᭥⦹ᩍ
⩥ᰆ⨹ߑᯕ░ၰဍ౩ᯕᖹʑၹᙹḲᯱഭෝ⪽ᬊ⦽ᇥᕾᮥ
ᙹ⧪⦹ᩡ݅(Fontaine., 2008, El-Tantawy et al., 2009, Fontaine et al., 2009). ݅ෙᱲɝჶᮝಽ۵࠺ᱢᗮࠥᱽ⦽ᮥᯕᬊ⦽⪵ྜྷ₉
šญᱥఖᮥ ᱽ⦹ʑࠥ ⦹ᩡ݅(Korkut et al., 2010).
Ʊ☖ᦩᱥ⊂໕ᨱᕽ᮹⪵ྜྷ₉ᔍŁෝᇥᕾ⦽ǎᩑǍᨱᕽ۵
⪵ྜྷ₉šಉᔍŁ᮹ᔍŁᝍbࠥᩢ⨆ᯙᮥȽ⦹ʑ᭥⦽ᇥᕾ
ᮥᙹ⧪⦹ᩡᮝ໑, ☖ĥᱢᯙᇥᕾʑჶᮥᯕᬊ⦹ᩍ⪵ྜྷ₉ᔍŁᩩ
⊂༉⩶, ⪵ྜྷ₉ᔍŁᝍbࠥ༉⩶ᮥᱽ⦹ʑࠥ⦹ᩡ݅(Golob et al., 1987, Zhu et al., 2011, Duncan et al., 1998, Khattak et al., 2003, Chang et al., 1999, Khorashadi et al., 2005, Lemp et al., 2011). ✚⯩, ᔍŁᝍbࠥᩢ⨆ᯙŝšಉ⧕ᕽ۵᳙ᮭᬕᱥ
॒᮹ᬕᱥᯱᯙᱢᗭ᪡ ⪵ྜྷ₉ᔍŁᝍbࠥ᮹šĥෝࠥ⇽⦹ʑ
᭥⦽ᇥᕾᯕᙹ⧪ࡹᨩ݅(Cantor et al., 2010, Gander et al., 2006, Zhu et al., 2011, Häkkänen et al., 2001). ੱ⦽ ✚ᱶ ⪵ྜྷ₉
ᔍŁᮁ⩶(₉ಽᄥᔍŁ, ᱥᅖᔍŁ॒)ᮥᇥᕾ⦽ᩑǍࠥᙹ⧪ࡹᨩ݅
(Hallmark et al., 2009, Young et al., 2007).
⪵ྜྷ₉Ʊ☖ᬕᩢᨱᯩᨕƱ☖ᦩᱥᔢ⬉ŝᱢᯙᱥఖᮥࠥ⇽⦹ʑ
᭥⧕ᕽ۵ၙᱢᯙšᱱᨱᕽᅝভ⪵ྜྷƱ☖ᯱℕ᮹✚ᖒᮥᯕ⧕⦹
Ł┡₉᳦ŝ᮹ᔢ⪙᯲ᬊᮥᇥᕾ⧁⦥ᖒᯕᯩ݅. ✚⯩⪵ྜྷƱ☖ᮡ
ᬊ₉॒ŝ۵ݍญᔢᨦᱢ✚ᖒᮥaḡ໑, ☖⧪᮹đᱶᯕ}ᯙᱢ
⬉ᬊ᮹ᩢ⨆ᮥฯᯕၼ۵ᬊ₉ᬕᱥᯱᅕ݅e, ᦦ⬥॒ŝ
zᮡࠥಽᔢ⫊ᨱᕽᬕᱥ⦹۵ኩࠥa׳݅(USDOT, 2006, NIOSH, 2007). ✚⯩šಉᩑǍᨱᕽ۵vᬑ, vᖅŝzᮡᦦ⬥ᔢ⫊ᨱᕽ
ࠥಽ᮹ᗭ☖܆ಆᯕqᗭ⦽݅ŁಅᲙᯩᮝအಽ(Keay et al., 2005, Knapp et al., 2000, Shi et al., 2011) ᯝၹᱢᯙʑᔢ᳑Õŝvᬑ, vᖅ॒᮹ʑᔢ᳑ÕᮥbbŁಅ⦹ᩍ⪵ྜྷ₉ᔍŁෝᇥᕾ⧁⦥ᖒ ᯕ ᯩ݅.
ǎԕᨱᕽࠥ⪵ྜྷ₉Ʊ☖ᔍŁšಉᩑǍaᙹ⧪ࡹᨩ݅. Łᗮࠥಽ
⪵ྜྷ₉ᔍŁ ߑᯕ░ෝ ᯕᬊ⦹ᩍݡ⩶ ⪵ྜྷ₉ప ᔍŁ᮹ᬱᯙ ၰ
✚ᖒᮥḢᱲᱢᬱᯙŝ⪹Ğᱢᬱᯙᮝಽ ᇥඹ⦹ᩍᇥᕾ⧉ᮝಽ៉
ᔍŁ}ᖁݡ₦ᮥᱽ⦹ᩡᮝ໑(ᱶ།, 2007)ݡ⩶₉Ʊ☖ᔍŁ✚
ᖒၰྙᱽᱱᮥᇥᕾ⦹Łݡ⩶₉ᬕᱥᯱᖅྙ᳑ᔍෝ☖⦽}ᖁႊᦩ
ᮥᱽ⦹ᩡ݅(₥ჵᕾ, 2006). ੱ⦽, ᔍŁᯙᄥᔢšĥᙹෝࠥ⇽
⦹ᩍ⪵ྜྷ₉ᔍŁၽᔾŝᔢšᖒᯕ׳ᮡᔍŁᯙᯱෝᱽ⦹ᩡ݅(ʡ ᖒᬊ॒, 2001). ə్ӹʑ᳕ǎԕᩑǍᨱᕽ۵ᵝಽḲĥࡽᯱഭ(⠪
ɁᔍŁၽᔾÕᙹ॒)ෝᯕᬊ⦹ᩍ⪵ྜྷ₉ᔍŁၽᔾᬱᯙᄥ✚ᖒ
ᇥᕾᮥᙹ⧪⦹ᩡᮝ໑, ࠥಽƱ☖⪹Ğᨱᕽๅᬑᵲ⦽ᗭᯙʑᔢ ᔢ┽ෝ Łಅ⦽ ⪵ྜྷ₉ ᔍŁᇥᕾᮡ ၙእ⦽ ᝅᱶᯕ݅. ᕽ ᅙ
ᩑǍᨱᕽ۵ʑᔢၰƱ☖᳑ÕᮥŁಅ⦽⪵ྜྷ₉ᔍŁᇥᕾ᮹⦥ᖒ
ᮥᯙ⦹ŁǎԕŁᗮࠥಽᨱᕽᙹḲࡽʑᔢᯱഭ, ᔍŁᯱഭ, Ʊ☖ᯱ
ഭෝᯕᬊ, ⪵ྜྷ₉Ʊ☖ᔍŁᝍbࠥᩢ⨆ᯙᇥᕾᮥᙹ⧪⦹ᩡ݅.
3. ᇥᕾ}
ᅙᩑǍ᮹༊ᱢᯙ⪵ྜྷ₉ᔍŁᝍbࠥᨱၙ⊹۵ʑᔢၰƱ☖᳑
Õ᮹ᩢ⨆ᮥᇥᕾ⦹ʑ᭥⦹ᩍ, Fig. 1᮹ᇥᕾᱩ₉ᨱᩑǍෝ
ᙹ⧪⦹ᩡ݅. ᇥᕾᨱᔍᬊ⧁ߑᯕ░ᄁᯕᜅෝǍ⇶⦹Ł, ᇥᕾႊჶು
ၰࠦพᄡᙹෝᖅᱶ⦹ᩡ݅. ᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾᮥ⪽ᬊ⦹ᩍ
⪵ྜྷ₉ Ʊ☖ᔍŁ ᝍbࠥ᮹ ⪶ශᱢ ᷾aᨱ ᩢ⨆ᮥ ၙ⊹۵ ʑᔢ
ၰ Ʊ☖᳑Õ šಉᯙᮥ ࠥ⇽⦹ᩡ݅.
ᅙᩑǍ᮹ݡᔢ₉పᯙ⪵ྜྷ₉᮹ჵ᭥۵⦽ǎࠥಽŖᔍ᮹Łᗮࠥ
ಽ ₉᳦ᇥඹ ʑᵡᨱ ⪵ྜྷ₉ಽ ᱶ᮹ࡽ ₉᳦ᮥ Łಅ⦹ᩍ ᇥᕾᮥ
ᙹ⧪⦹ᩡᮝ໑₉᳦ᇥඹʑᵡᵲ⪵ྜྷ₉ʑᵡᮡTable 1ŝz݅.
ᅙᩑǍᨱᕽ۵ʑᔢ᳑Õᵲาᮭ, ⮱ฝ, እ, ٩ᮥŁಅ⦹ᩍᇥᕾ
ᮥ ᙹ⧪⦹ᩡ݅. ᦩ}᮹ Ğᬑ ᔍŁၽᔾ ⍡ᯕᜅ᮹ ᙹa ๅᬑ ᱢ ᨕᇥᕾŁಅ⦹ḡᦫᦹ݅. ੱ⦽, ᬕᱥᯱ᮹ᯙᖒၰי໕ษₑಆ
ᱡ⦹ෝᮁၽ⦹۵እ, ٩ᮥᯕᔢʑ⬥(Adverse weather condition)
Fig. 1. Process of analysis
Table 1. Truck classification criteria on freeway
Truck classification Vehicle weight Vehicle Specifications
Light Duty truck class 1 below 2.5 ton two axle truck, Track tread below 279.4mm
Light Duty truck class 2 2.5~5.5 ton two axle truck, Track tread exceed 279.4mm, track width below 1,800mm
Medium Duty truck class 1 5.5~10 ton two axle truck, Track tread exceed 279.4mm, track width exceed 1,800mm
Medium Duty truck class 2 10 ~20 ton three axle truck
Heavy Duty truck exceed 20 ton more than four axle
1) ⦽ǎࠥಽŖᔍ Łᗮࠥಽ ᔍŁᯱഭ(2008~2010֥)
2) ᅙᩑǍᨱᕽ۵ᬕᱥᯱ᮹ᯙᖒၰࠥಽי໕ษₑಆᨱᦥྕᩢ⨆ᯕᨧ۵ʑᔢᔢ┽ෝ‘ᱶᔢʑ⬥’ಽ, vᬑੱ۵vᖅಽᯙ⦹ᩍᬕᱥᯱ᮹ᯙᖒᮥ
ಽ, ə᮹าᮭ, ⮱ฝᮥᱶᔢʑ⬥(Normal weather condition)ಽ
ᱶ᮹⦹ᩍ ᇥᕾᮥ ᙹ⧪⦹ᩡ݅.
3.1 ܁ଲഉࣕଲਆ֜ౠ
ᅙᩑǍᨱᕽ۵⪵ྜྷ₉ᔍŁᝍbࠥ༉⩶Ǎ⇶ᮥ᭥⦹ᩍŁᗮࠥಽ
ᔍŁᯱഭ, Ʊ☖ᯱഭ, ʑᔢᯱഭෝᯕᬊ⦽☖⧊ߑᯕ░ᄁᯕᜅෝǍ⇶
⦹ᩡ݅. Ʊ☖ᔍŁᯱഭᨱӹ┡ӽŖeᱢ, eᱢ႑Ğŝᯝ⊹⦹ࠥಾ
Ʊ☖ᯱഭ(ᗮࠥၰƱ☖ప)᪡ʑᔢᯱഭ(vᬑపၰvᖅప)ෝๅ⋎⦹
ᩡ݅. ߑᯕ░ ᄁᯕᜅ Ǎ⇶ᱩ₉۵ ݅ᮭŝ z݅.
ℌṙ, ᅙᩑǍᨱᕽ۵⪵ྜྷ₉ᔍŁᨱၙ⊹۵ʑᔢၰƱ☖᳑Õ᮹
ᩢ⨆ᮥᇥᕾ⦹ʑ᭥⦽ᇥᕾݡᔢיᖁᮝಽԉ⧕ᖁ, ᩢ࠺ᖁ, ᵲᇡԕය ᖁᮥᖁᱶ⦹ᩡ݅. ᇥᕾݡᔢיᖁ᮹ᱥǍeᮥŁಅ⦹ᩡᮝ໑, ݡᔢי
ᖁᖁᱶʑᵡᮡvᬑ, vᖅᔍŁၽᔾᯕᰇᮡיᖁ, ┡יᖁݡእ
ŝᗮᔍŁaฯᮡיᖁ, ⪵ྜྷ₉ᔍŁaᰇᮡיᖁ॒ᮥŁಅ⦹ᩡ݅.
ࢹṙ, ↽ɝ3֥eݡᔢיᖁᨱᕽၽᔾ⦽⪵ྜྷ₉šಉᔍŁᯱഭ
ෝ ᙹḲ⦹ᩡ݅. ᔍŁᯱഭᨱᕽ ᅙᖁᯝၹǍe, ░ձ, Ʊప ᯕ᮹
ఉ⥥, IC, JC, ☉íᯕ✙ᨱᕽၽᔾ⦽ᔍŁ᮹Ğᬑ₉ప᮹ᨨiฝᯕ
ၽᔾ⦹۵ʑ⦹Ǎ᳑ಽᯙ⦹ᩍᔍŁ✚ᖒᯕᅙᖁǍeŝ݅အಽᱽ
⦹ᩡ݅. ŁᗮࠥಽᔍŁᯱഭ
1)ᨱᕽᔍŁᝍbࠥ۵ᔍᯱᙹၰᇡᔢ
ᯱᙹᨱ A, B, Cɪᮝಽ Ǎᇥࡹ໑ ʑᔢᔢ┽۵ าᮭ, ⮱ฝ, እ, ٩, ᦩ}, v⣮ᮝಽǍᇥࡹ۵ߑ, ᯝၹᱢᮝಽᯕ్⦽ᔍŁᝍbࠥ
ၰʑᔢᄥᔍŁߑᯕ░᮹ᇩɁ⩶ྙᱽaၽᔾ⦽݅. ᕽᅙᩑǍᨱ ᕽ۵ᯕ్⦽ߑᯕ░ᇩɁ⩶ྙᱽෝᅕ᪥⦹ŁᯱĞᇡᖁ, Şᙽ⪹ᖁ
॒᮹ ᔍŁ ⍡ᯕᜅෝ ⇵a⦹ᩍ ᔍŁᯱഭෝ Ǎᖒ⦹ᩡ݅.
ᖬṙ, ᔍŁᯱഭ᮹⍡ᯕᜅᄥeၰŖeᱢჵ᭥aᯝ⊹⦹۵
ʑᔢᯱഭၰáḡʑᯱഭෝๅ⋎⦹ᩡ݅. bᯱഭ᮹ᙹḲ݉᭥۵ʑ ᔢᯱഭ᮹ Ğᬑ 1e, áḡʑᯱഭ᮹ Ğᬑ 15ᇥᯕ݅.
֘ṙ, ᯱഭᙹḲᯕᔢ⊹ၰđ⊂⊹aၽᔾ⦽ᯱഭᨱݡ⦹ᩍ
ᅕᱶᮥ ᝅ⦹ᩡ݅. áḡʑᯱഭ᮹ ᗮࠥ ၰ Ʊ☖పᨱ ᯕᔢ⊹ ၰ
đ⊂⊹aၽᔾ⦽Ğᬑ, ࠺ᯝáḡʑ᮹ᱥ⬥eݡ᮹⠪Ɂsᮥ
ᯕᬊ⦹ᩍᅕᱶ⦹ᩡ݅. ᱥ⬥eݡᨱࠥᯕᔢ⊹ၰđ⊂⊹aၽᔾ
⦽ Ğᬑ, ੱ۵ ᅕᱶᯕ a܆⦹ࠥ ᅕᱶ⊹a ᔍŁ⍡ᯕᜅ ᄥಽ
50% aչ۵Ğᬑ⧕ݚᔍŁ᭥⊹᮹✚ᖒᮥၹᩢ⦹ḡ༜⦽݅Ł
❱݉⦹ᩍᔍŁ⍡ᯕᜅෝᔎᱽ⦹ᩡ݅. ʑᔢᯱഭ᮹Ğᬑᯕᔢ⊹ၰ
đ⊂⊹۵ၽᔾ⦹ḡᦫᦹᮝӹᔍŁᯱഭ᮹ʑᔢᔢ┽᪡ʑᔢᯱഭ᮹
vᙹప⊂ᱶsᯕᯝ⊹⦹ḡ ᦫ۵Ğᬑaၽᔾ⦹ᩡ݅. ᩩෝॅᨕ, ʑᔢᯱഭᨱ۵vᙹప⊂ᱶsᯕ᳕ᰍ⧉ᨱࠥᔍŁᯱഭᨱ۵าᮭᮝಽ
⢽ࡹ۵Ğᬑaၽᔾ⦹ᩡ۵ߑᯕ్⦽Ğᬑ ᔍŁᯱഭʑಾᔢ᮹
ྙᱽᱱᮝಽ ❭ᦦࡹᨕ ᔍŁ ⍡ᯕᜅෝ ᔎᱽ⦹ᩡ݅.
Table 2᪡zᯕǍ⇶ࡽߑᯕ░ᄁᯕᜅ᮹ᯱഭ}ᙹ۵ⅾ377}ᯕ ໑ʑᔢ᳑Õᨱᯕᵲᱶᔢʑ⬥
2)۵261}, እ۵97}, ٩ᮡ
19}ᯕ݅. ᝍbࠥᄥ}ᙹ۵ᝍb⦽ᔍŁa52}, Ğၙ⦽ᔍŁa325
}ಽ ӹ┡ԍ݅.
Table 2. Crash frequencies by freeway line, weather condition and injury severity
Freeway line
Case of accident
Weather Injury severity
Normal Rain Snow Fatal Non-fatal
Namhae 54 44 2 10 90
Youngdong 82 36 8 17 109
Jungbu naeryuk et al. 125 17 9 25 126
Total 261 97 19 52 325
Table 3. Accident occurrence probability of Logistic Model
Curve (X=1) Straight (X=0)
Fatal accident
occurrence probability ©Îá ćÎâÞķâĸ±ßÞķâĸ±ß ©×á ćÎâÞķßÞķß Non-fatal accident
occurrence probability Îà ©Îá ćÎâÞķâĸ±ßÎ Îà ©×á ćÎâÞķßÎ
3.2 ंজࢺ࣑ߨট୨
ᅙᩑǍᨱᕽ۵᳦ᗮᄡᙹaᝍb⦽ᔍŁ᪡Ğၙ⦽ᔍŁ᮹ᯕᇥ
⩶ᮝಽӹ┡ӹ໑, ⪵ྜྷ₉Ʊ☖ᔍŁᝍbࠥᨱᩢ⨆ᮥၙ⊹۵ʑᔢ
ၰƱ☖᳑Õᨱšಉࡽᯙᮥᇥᕾ⦹Łᯱᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾ
ᮥᱢᬊ⦹ᩡ݅. ᅙᩑǍᨱᕽ۵᳦ᗮᄡᙹಽᔍŁᝍbࠥෝŁಅ⦹ᩡ
ᮝ໑1ᮡƱ☖ᔍŁᝍbࠥᇥඹʑᵡA, Bᨱᗮ⦹۵ᔍᯱ1
ᯕᔢੱ۵ᇡᔢᯱ5ᯕᔢ᮹ᝍb⦽ᔍŁෝ᮹ၙ⦹໑, 0ᮡᇡᔢᯱ
1ᯕᔢ᮹ Ğၙ⦽ ᔍŁෝ ᮹ၙ⦽݅.
ᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾ(BLR)ᮡ᳦ᗮᄡᙹaჵᵝ⩶ᮝಽš⊂
ࡽߑᯕ░ෝᱢ⧊┍ভᮁᬊ⦹íᔍᬊࡹ۵ʑჶᮝಽ, ༉⩶᮹
᳦ᗮᄡᙹᯙᝍb⦽Ʊ☖ᔍŁෝ1ಽ, Ğၙ⦽Ʊ☖ᔍŁෝ0ᮝಽᖅᱶ
⦹۵Binary classification ྙᱽᨱ⬉ŝᱢᮝಽ᮲ᬊa܆⦹݅. ੱ⦽
odds-ratio, Wald ☖ĥప॒ᮥᯕᬊ⦹ᩍ᳦ᗮᄡᙹ᮹⪶ශᱢ᷾aᨱ
☖ĥᱢᮝಽᮁ᮹⦽ᩢ⨆ᮥၙ⊹۵ࠦพᄡᙹ❱݉ᮁᬊ⦹íᔍᬊ
⧁ᙹᯩ݅. ᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾ᮹ʑᅙᙹᮡ(1)ŝz݅.
©ÞƗ á ÎçƖ
ÎìzìƖ
Ƈß á ć Î âãƄÞƖ
Ƈìĸ
Ƈßä
ãƄÞƖ
Ƈìĸ
Ƈßä
(1)
©ÞƗ á ÎçƖ
ÎìzìƖ
Ƈß = Fatal accident occurrence probability Ɩ
Ƈ= Factors effecting truck accident
ĸ
Ƈ= Estimated parameters
༉⩶ԕᄡᙹ᮹ĥᙹ᮹ᇡ⪙a᧲ᯙĞᬑ⧕ݚᄡᙹ۵ᝍb⦽
ᔍŁၽᔾ᮹ ⪶ශᱢ ᷾aᨱ ᩢ⨆ᮥ ၙ⊽݅Ł ⧕ᕾ⧁ ᙹ ᯩᮝ໑, ᇡ⪙aᮭᯙĞᬑᝍb⦽ᔍŁၽᔾ⪶ශᮥqᗭ┅۵äᮥ᮹ၙ⦽
݅. ಽḡᜅ❒ ⫭ȡᇥᕾ᮹ đŝྜྷ ᵲ ⦹ӹᯙ ࠦพᄡᙹ᮹ ᔑእ
(Odds ratio)۵݅ෙᄡᙹaŁᱶࡹᨩᮥভ⧕ݚࠦพᄡᙹ᮹᭥⨹
ࠥෝᖅ⧁ᙹᯩ݅. ᩩෝॅᨕ‘⍅ቭᩍᇡ(curve)’ ᄡᙹ۵ʑ⦹Ǎ᳑
ałᖁᯝভ1ಽ, Ḣᖁᯝভ0ᮝಽ⎵ঊࡽᄡᙹᯙߑ, ᔑእa
1 ᯕᔢᯝĞᬑᝍb⦽ᔍŁၽᔾ᮹⪶ශᱢ᷾aᨱᮁ᮹⦽ᩢ⨆ᮥ
ၙ⊹໑, ᄡᙹsᯕ 1 ੱ۵ 0ᯝ ভ bb᮹ Ʊ☖ᔍŁၽᔾ ⪶ශᮡ
Table 3᮹ ᙹᮥ ⪽ᬊ⦹ᩍ ࠥ⇽⧁ ᙹ ᯩ݅.
3.3 ࣡ড୨
ᇥᕾᮥ᭥⦽᳦ᗮᄡᙹ۵ᯕᇥ⩶ᮝಽӹ┡ӹ۵ᔍŁᝍbࠥᯕ݅.
ࠦพᄡᙹ۵Ʊ☖ᔍŁᯱഭᨱӹ┡ӽᯙᱢ✚ᖒ, ʑ⦹Ǎ᳑✚ᖒ, Ʊ☖
✚ᖒ, ⪹Ğ✚ᖒᨱݡ⦽ᄡᙹෝᖅᱶ⦹ᩡ݅. ᯙᱢ✚ᖒᨱᕽ۵ᖒᄥ, ᩑಚᮥŁಅ⦹ᩡŁ, ʑ⦹Ǎ᳑✚ᖒᨱᕽ۵᪅สᩍᇡ, ԕญสᩍᇡ,
⍅ቭ, ᔍŁ᭥⊹(Ʊప, ░ձ, ᅙᖁᯝၹǍe)ෝŁಅ⦹ᩡ݅. Ʊ☖✚ᖒ ᨱᕽ۵ᔍŁ᭥⊹↽ɝᱲᔢඹᇡáḡʑᨱᕽᙹḲࡹᨕ15ᇥeĊᮝ ಽᙹḲࡽᗮࠥၰƱ☖పŝᔢ⦹ඹᇡᗮࠥ₉ᯕ, ᗮࠥ᮹ᄡ࠺ĥᙹ, Ʊ☖ప-ᬊపእෝŁಅ⦹ᩡ݅. ݡᔢיᖁ᮹Ǎeᄥᱽ⦽ᗮࠥෝŁಅ
⦹ᩍ ᔢඹᇡ 15ᇥᱥ ᗮࠥa ᱽ⦽ᗮࠥෝ Ⅹŝ⦽ Ğᬑᨱࠥ ᯕෝ
ᄡᙹ⪵⦹ᩡ݅. ᱽ⦽ᗮࠥ۵ʑᔢᔢ┽ෝŁಅ⦹ᩍ⡎ᬑ⡎ᖅ॒
eݚ 20mm ᯕᔢ᮹ v⦽ እ٩ᯕ ԕต Ğᬑ ᱽ⦽ᗮࠥ᮹ 50%
ᙹᵡᮥᱢᬊ⦹໑, əᯕ⦹᮹እ٩ᯕԕตĞᬑ20% ᙹᵡᮥᱢᬊ⦹
۵ࠥಽƱ☖ჶ⧪Ƚ⊺ᱽ19᳑᮹ჶಚᮥᱢᬊ⦹ᩍᖅᱶ⦹ᩡ݅.
⪹Ğ✚ᖒᨱᕽ۵ᵝ, ᵝᵲᩍᇡෝŁಅ⦹ᩡᮝ໑, ᵝ᮹Ğᬒ
⠪Ɂᯝ⇽, ᯝ༑eᮥŁಅ⦹ᩍᖅᱶ⦹ᩡ݅. 2011֥ᬵ⠪Ɂᯝ⇽, ᯝ༑eᮡ Table 4᪡ z݅.
༊⩶ᄡᙹᨱݡ⦽ᖅᱶᮡƱ☖ᔍŁᝍbࠥ᷾aᨱᔢݡᱢᮝ ಽฯᮡᩢ⨆ᮥၙ⋁äᮝಽ❱݉ࡹ۵Ḳ݉ᮥ1ಽ, ə౨ḡᦫᮡ
Ḳ݉ᮥ0ᮝಽ⎵ঊ⦹ᩡ݅. ᩑᗮ⩶ᄡᙹ۵bᄡᙹ᮹✚ᖒᮥၹᩢ⦹
Table 4. Annual average sunrise and sunset
Month Sunrise Sunset
1 07:35 17:31
2 07:15 18:03
3 06:35 18:32
4 05:50 19:00
5 05:17 19:26
6 05:05 19:45
7 05:16 19:42
8 05:40 19:15
9 06:06 18:32
10 06:34 17:48
11 07:05 17:17
12 07:30 17:10
http://astro.kasi.re.kr/
Table 5. Summary of database
Normal condition Adverse condition Total Description
Variables Fatal 60 17 77 Weather condition : Normal or adverse Injury severity : Fatal or non-fatal
Non-fatal 201 99 300
Dependent variable injury severity 1 0 1 0 - 0: non-fatal, 1: fatal
Independent variables
Nominal variable
day_night 1 39 95 7 29 170
0: day, 1: night ; regarding sunrise and sunset
0 21 106 10 70 207
week 1 51 168 15 80 314 0: weekend (Saturday, Sunday), 1: weekday (MonFri)
0 9 33 2 19 63
gender 1 60 200 16 96 372
0: female, 1: male
0 0 1 1 3 5
grade_up 1 21 70 5 34 130
0: non-up grade, 1: up grade
0 39 131 12 65 247
grade_dn 1 21 83 9 37 150
0: non-down grade, 1: down grade
0 39 118 8 62 227
curve 1 21 81 10 44 156
0: non-curve, 1: curve
0 39 120 7 55 221
location 1 4 12 2 2 20
0: mainline, 1: bridge or tunnel
0 56 189 15 97 357
Continuous variable
age 46.17 45.30 45.00 45.10 - median of age group
up_sp15b 91.77 91.74 80.06 81.59 -
15-min average speed prior to accident occurrence (archived from adjacent upstream detection station)
up_speeding 1.12 0.48 4.29 6.92 -
amount of speeding when up_sp15b exceeds speed limit (When up_sp15b does not exceed speed limit, up_speeding is set to be ‘0’) df_sp15b 7.65 7.97 9.18 8.72 - difference between up_sp15b and dn_sp15b
sp_cv 0.06 0.07 0.12 0.08 - coefficient of variation of speed v/c ratio 0.22 0.23 0.26 0.25 - volume/capacity ratio
ᩍ ᖅᱶ⦹ᩡ݅.
☖ᔢᱢᮝಽ☖ĥʑჶᮥᯕᬊ⦽༉⩶}ၽࠦพᄡᙹeᔢš ᖒᯕ׳ᮡᄡᙹෝzᯕ⚍᯦⧁Ğᬑ݅ᵲŖᖁᖒ
3)ྙᱽaၽᔾ⧁
ᬑಅaᯩ݅. ᕽᅙᩑǍᨱᕽ۵݅ᵲŖᖁᖒྙᱽෝᩩႊ⦹ʑ
᭥⦹ᩍࠦพᄡᙹeᔢššĥෝᇥᕾ⦹ᩍᔢšĥᙹa0.7 ᯕᔢᮝಽ
׳íӹ┡ӹ۵ᄡᙹॅᮡᇥᕾᨱᕽᱽ⦹ᩡ݅. ᩩෝॅᨕ, ᔢ⦹ඹ ᇡƱ☖పšಉᄡᙹ۵Ʊ☖ప - ᬊపእ᪡᮹׳ᮡᔢšᖒᮝಽᱽ
ࡹᨩ݅.
ᔢšᇥᕾđŝෝၵ┶ᮝಽᅙᩑǍᨱᕽ↽᳦ᱢᮝಽᔍᬊ⦽ࠦพ ᄡᙹᨱݡ⦽ᄡᙹᖅᱶႊჶၰʑᚁ☖ĥෝTable 5ᨱᱽ⦹ᩡ݅.
ࠦพᄡᙹᵲ༊⩶ᄡᙹᨱݡ⧕ᕽ۵ ᳦ᗮᄡᙹᯙᔍŁᝍbࠥ᮹
Ḳ݉ᄥ⍡ᯕᜅᙹෝᱽ⦹ᩡᮝ໑, ᩑᗮ⩶ᄡᙹ᮹ĞᬑᔍŁᝍbࠥ
Ḳ݉ᄥ ⠪Ɂsᮥ ᱽ⦹ᩡ݅.
Table 6. Factors affecting injury severity by weather conditions
Normal weather condition model Adverse weather condition model Coef. S.E. t P>|t | odds. Coef. S.E. t P>|t | odds.
day_night 0.9153 0.3749 2.44 0.015 2.4975 0.3741 0.7205 0.52 0.604 1.4536 weekend 0.2753 0.4487 0.61 0.540 1.3169 1.0026 0.9617 1.04 0.297 2.7254 gender 0.0055 0.0152 0.36 0.716 1.0056 -0.0098 0.0306 -0.32 0.748 0.9902 age -0.0056 0.4090 -0.01 0.989 0.9944 1.2294 1.0569 1.16 0.245 3.4193 grade_dn -0.2745 0.4059 -0.68 0.499 0.7599 1.6945 0.9954 1.70 0.089 5.4439 curve -0.0737 0.3307 -0.22 0.824 0.9290 0.5372 0.6389 0.84 0.400 1.7112 location 0.3456 0.6483 0.53 0.594 1.4128 3.4761 1.5798 2.20 0.028 32.3341 up_sp15b -0.0089 0.0161 -0.56 0.578 0.9911 0.0876 0.0424 2.06 0.039 1.0916 up_speeding 0.1280 0.0649 1.97 0.048 1.1366 -0.1139 0.0653 -1.74 0.081 0.8924 df_sp15b 0.0420 0.0285 1.47 0.141 1.0428 -0.0472 0.0401 -1.18 0.240 0.9539
sp_cv -10.1785 5.5820 -1.82 0.068 3.810-5 20.8062 8.2802 2.51 0.012 1.09109 v/c ratio 0.7905 1.1142 0.71 0.478 2.2046 0.3260 2.0998 0.16 0.877 1.3854 constant -1.2574 1.8208 -0.69 0.490 - -12.0710 4.5035 -2.68 0.007 -
Log likelihood -132.9925 -37.8285
Number of observation 261 116
LR ŌÏ(14) 15.58 21.01
Pseudo «Ï 0.0554 0.2174
4. ᇥᕾđŝ
᳦ᗮᄡᙹaჵᵝ⩶ᮝಽš⊂ࡽߑᯕ░ෝᱢ⧊┍ভᮁᬊ⦹í
ᔍᬊࡹ۵ʑჶᯙᯕ⧎ಽḡᜅ❒⫭ȡᇥᕾᮥᯕᬊ⦹ᩍ⪵ྜྷ₉Ʊ☖
ᔍŁ᮹ᝍbࠥᨱᩢ⨆ᮥၙ⊹۵ࠥಽƱ☖✚ᖒᇥᕾᮥᙹ⧪⦹ᩡ݅.
ʑᔢ᳑Õᨱ⪵ྜྷ₉ᔍŁᝍbࠥᨱၙ⊹۵ᩢ⨆ᯙᨱ₉ᯕa
ᯩᮥäᮝಽ❱݉⦹ᩍᱶᔢʑ⬥ၰᯕᔢʑ⬥ᨱݡ⦽ᇥᕾđŝෝ
bbᱽ⦹Łbđŝᨱᕽ☖ĥᱢᮝಽᮁ᮹⦹íࠥ⇽ࡽᄡᙹॅᮥ
እƱᇥᕾ⦹ᩡ݅. ੱ⦽, bʑᔢᄥ༉⩶᮹☖ĥᱢᮁ᮹ᖒŝࢱ༉⩶ᯕ
☖ĥᱢᮝಽ₉ᯕaᯩ۵ḡእƱᇥᕾ⦹ᩡ݅. ᇥᕾđŝ۵Table 6ᨱ
ᱽ⦹ᩡ݅.
4.1 ୨ঃ׆บਏਕԨܑઽේ૬ंজէր
ᱶᔢʑ⬥⇵ᱶ༉⩶᮹ᱥℕᱢ⧊ࠥ(Overall Goodness)ෝӹ
┡ԕ۵ Ō
Ï۵15.58ಽᯱᮁࠥa12ᯝভ Ō
Ï᮹5%᮹ᙹᵡᯙ21.0 ᅕ᯲݅ᮝအಽ᳦ᗮᄡᙹaࠦพᄡᙹᨱᮁ᮹⦽₉ᯕaᨧ݅۵
ȡྕaᖅᮥʑb⦹ᩡ݅. ༉⩶᮹ᖅಆᮥӹ┡ԕ۵ Ň
Ï(ᬑࠥእ)۵
0.0554 ಽ እƱᱢ ԏí ӹ┡ԍ݅.
ᱶᔢʑ⬥ᨱᕽ۵☖ĥᱢᮝಽᮁ᮹⦹íӹ┡ӽࠦพᄡᙹ۵‘ᵝ
’, ‘ᱽ⦽ᗮࠥⅩŝs’, ‘ᗮࠥ᮹ᄡ࠺ĥᙹ’᮹P-valuea0.1 ᯕ⦹ಽ
ӹ┡ӹᝍb⦽ᔍŁ᮹ၽᔾ⪶ශ᷾aᨱ☖ĥᱢᮝಽᮁ᮹⦽ᩢ⨆ᮥ
ၙ⊹۵ᄡᙹಽࠥ⇽ࡹᨩ݅. ‘ᵝ’ᄡᙹ᮹odds-ratio۵2.4975ಽ
ӹ┡ӹ, eᯝভᝍb⦽ᔍŁaၽᔾ⧁⪶ශᯕᵝeᅕ݅᧞2.5႑
᷾a⦹໑, ‘ᱽ⦽ᗮࠥⅩŝs’ ᄡᙹ۵odds-ratioa1.1366ᮝಽӹ┡
ԍᮝ໑, ᱽ⦽ᗮࠥⅩŝsᯕ1kph ᷾a⧁ভษ݅ᝍb⦽ᔍŁᯝ
⪶ශᮡ ᧞ 1.14႑ ᷾a⦹ᩡ݅.
‘ ᗮࠥᄡ࠺ĥᙹ’۵ĥᙹa-10.1785ಽᗮࠥ᮹ᄡ࠺ĥᙹaqᗭ
⧁ᙹಾᔍŁ᮹ᝍbࠥ۵᷾a⦹۵đŝaӹ┡ԍ݅. ᯝၹᱢᮝಽ
₉పeᗮࠥ₉ෝ᮹ၙ⦹۵ᗮࠥ᮹ᄡ࠺ĥᙹ, ᷪ₉పॅ᮹Ŗe ᱢᯙᗮࠥ ⢽ᵡ⠙₉a ⓕভ ᔍŁၽᔾ }ᩑᖒၰ ᔍŁᝍbࠥ۵
᷾a⦹íࡹӹᅙ༉⩶ᨱᕽ۵ၹݡ᮹đŝaࠥ⇽ࡹᨩ݅. ᅙᩑǍᨱ ᕽ۵ᯕ᪡ zᮡ đŝaᯱഭ᮹ ⦽ĥಽ ࠥ⇽ࡽäᮝಽ ❱݉⦹Ł
ߑᯕ░ᄁᯕᜅ᮹ ᔢᖙ⦽ á☁ෝ ᙹ⧪⦹ᩡ݅. ᗮࠥ᮹ ᄡ࠺ĥᙹ۵
ᗮࠥ᮹⢽ᵡ⠙₉ෝᗮࠥ᮹⠪Ɂᮝಽӹ٩sᮝಽᔑ⇽ࡹ໑, ᇥᯱᯙ
ᗮࠥ᮹⢽ᵡ⠙₉a ᯲Ł ᇥ༉ᯙᗮࠥ᮹ ⠪Ɂᯕ ⓕĞᬑ ᗮࠥ᮹
ᄡ࠺ĥᙹa᯲ᦥḥ݅. ᅙ༉⩶ᨱᕽᗮࠥᄡ࠺ĥᙹa᯲ᮥভᔍŁᝍ bࠥa ׳í ӹ┡ӽ äᮡ ᱶᔢʑ⬥ ᯝၹᱢᮝಽ ₉ప ᗮࠥa
Łᗮᮝಽӹ┡ӹ໑, ᯕভᗮࠥ᮹⢽ᵡ⠙₉a᯲ࠥᔍŁᝍbࠥ
a ᷾a⧁ ᙹ ᯩᮭᮥ ᮹ၙ⦹۵ đŝ ❱݉ࡽ݅.
đŝᱢᮝಽᱶᔢʑ⬥᳑Õᨱᕽ۵eᯝভ, ᱽ⦽ᗮࠥⅩŝ
ၽᔾ⦽ ⪵ྜྷ₉ Ʊ☖ᔍŁ۵ ᝍbࠥa ׳í ӹ┡ӽ݅.
Table 7. Model Comparison
Normal weather condition model Adverse weather condition model
Model comparison
log-likelihood for integrated model using all data -184.2061
Comparison 26.77
Prob > ŌÏ 26.77 > 25.00
Goodness of Fit test
Number of observation 261 116
covariate patterns 260 116
Pearson ŌÏ 255.48 119.53
Prob > ŌÏ 0.3420 0.1269
4) ᵝᨕḥ ⢽Ḳᯕ aᱶࡽ ᨕਅ ᱥḲᇥ⡍᪡ ᯝ⊹⦹۵ḡ á᷾⦹۵ ႊჶ. á àÏÞ¥¥Þ§ ßà ¥¥Þ ßß N: null ༉⩶, A: Alternative ༉⩶
5) ᅙ ᩑǍᨱᕽ۵ ࢱ ༉⩶᮹ Log likelihood᮹ እƱෝ ☖⦹ᩍ ༉⩶᮹ ☖ĥᱢ ₉ᯕa ᯩ۵ḡ á᷾⦹ᩡ݅.
ƍƋƎſƐƇƑƍƌá àÏÞ¥¥ à ¥¥ à ¥¥ ß ᱥℕ ༉⩶, A: ᱶᔢʑ⬥ ༉⩶, B: ᯕᔢʑ⬥ ༉⩶
