Relationship between Interstate Highway Accidents and Heterogeneous Geometrics by Random Parameter Negative Binomial Model - A case of Interstate Highway in Washington State, USA

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Received April 11, 2013/ revised May 20, 2013/ accepted June 10, 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

ǣǣȀȀǤǤȀͳͲǤͳʹ͸ͷʹȀǤʹͲͳ͵Ǥ͵͵Ǥ͸ǤʹͶ͵͹ ǤǤǤ

㰓἞⶿#⁦⟖Ἲ#ኞᷢ㬚#ⴊⴲ㬫⁦㯓⮎#ⴖ㬚#ጎ㝳♪ኞ⯾#Ꮾ㬖ጪ⸮⯾ⴖ#ኾኂ - ↶ጫ#Ⲋ⢯㛲#⺺(᲼) ኞ❋ᦂḚἺ#⻏⢪⳺Ḛ

ࢮࢢ෹

Park, Minho*

Relationship between Interstate Highway Accidents and

Heterogeneous Geometrics by Random Parameter Negative Binomial Model - A case of Interstate Highway in Washington State, USA

ABSTRACT

The objective of this study is finding the relationship between interstate highway accident frequencies and geometrics using Random Parameter Negative Binomial model. Even though it is impossible to take account of the same design criteria to the all segments or corridors on the road in reality, previous research estimated the fixed value of coefficients without considering each segment's characteristic. The drawback of the traditional negative binomial is not to explain the integrated variations in terms of time and the distinct characters specific segment has. This results in under-estimation of the standard error which inflates the t-value and finally, affects the modeling estimation. Therefore, this study tries to find the relationship of accident frequencies with the heterogeneous geometrics using 9-years and 7-interstate highway data in Washington State area. 16-types of geometrics are used to derive the model which is compared with the traditional negative binomial Model to understand which Model is more suitable. In addition, by calculating marginal effect and elasticity, heterogeneous variables' effect to the accidents are estimated. Hopefully, this study will help to estiblish the future policy of geometrics.

Key words : Accident model, Random parameter negative binomial regression analysis, Interstate highway geometrics, Heterogeneity

Ⅹಾ

ᯕᩑǍ۵⪶ශᱢ༉ᙹෝŁಅ⦽ᮭᯕ⧎⫭ȡᇥᕾᮥᯕᬊ⦹ᩍŁᗮࠥಽᨱᕽ᮹ᔍŁ᪡ʑ⦹Ǎ᳑᪡᮹šĥෝ❭ᦦ⦹۵ߑ༊ᱢᯕᯩ݅. Łᗮࠥಽᨱ ᕽ᮹ʑ⦹Ǎ᳑۵༉ुǍeᨱ࠺ᯝ⦽ᖅĥ᫵ᗭaᱢᬊࡹʑᨱ۵⩥ᝅᱢᮝಽᇩa܆⧉ᨱࠥᇩǍ⦹Ł, ḡɩʭḡ᮹ᩑǍᨱᕽ۵༉⩶ᮥ☖⧕ࠥ⇽ࡹ

۵ĥᙹsᯕǍeᨱᖅ⊹ࡽʑ⦹Ǎ᳑᮹✚ᖒᨱšĥᨧᯕ⧎ᔢŁᱶࡽsᮝಽ⇵ᱶࡹᨕ᪵݅. Łᱶࡽsᮥᯕᬊ⦽ᯝၹᱢᯙᮭᯕ⧎༉⩶ᮡ᜽eᱢ ᄡ⪵ੱ۵bݡᔢǍeᯕaḡŁᯩ۵Łᮁ⦽✚ᖒᨱ঑ෙᄡ⪵ෝ☖⧊⦹ᩍᖅ໦⦹ḡ༜⦽݅۵݉ᱱᯕᯩᮝ໑, ᯕಽᯙ⧕⇵ᱶࡽĥᙹ᮹⢽ᵡ᪅

₉aŝᗭ⇵ᱶࡹᨕt-sᯕᇡ⣡ಅḡíࡹ໑, əđŝ༉⩶᮹ᖅ໦ಆᯕਉᨕḡíࡽ݅. ঑௝ᕽ, ᯕᩑǍᨱᕽ۵ᬭᝒ▕ᵝᨱ᭥⊹⦹Łᯩ۵7}᮹

Łᗮࠥಽᨱᕽၽᔾ⦽9֥࠺ᦩ᮹ᔍŁᯱഭၰʑ⦹Ǎ᳑ᯱഭෝᯕᬊ⦹ᩍǍeᄥಽᔢᯕ⦽ʑ⦹Ǎ᳑aᔍŁᨱၙ⊹۵ᩢ⨆ᮥ᦭ᦥᅕŁᯱ⦽݅. ⅾ

16}᮹ʑ⦹Ǎ᳑šಉᄡᙹa༉⩶ࠥ⇽ᨱᯕᬊࡹᨩᮝ໑, ʑ᳕᮹ᮭᯕ⧎༉⩶ŝ᮹እƱෝ☖⧕ᯕᩑǍᨱᕽᱽ᜽⦹۵༉⩶ᯕƱ☖ᔍŁ᪡ʑ⦹Ǎ

᳑᪡᮹šĥ❭ᦦᨱ޵ᬒᱢ⧊⧉ᮥᅕᯕŁᯱ⦽݅. əญŁ, bᄡᙹ᮹⦽ĥ⬉ᬊၰ┥ಆᖒᇥᕾᮥ☖⧕ᯕḩᖒᮥaḡ۵ʑ⦹Ǎ᳑aᔍŁᨱၙ⊹

۵ᩢ⨆ᮥᱽ᜽⦹Łᯱ⦽݅. ᯕ۵⨆⬥ʑ⦹Ǎ᳑šಉᱶ₦ᙹพᨱࠥᬡᯕࢁäᮝಽ❱݉ࡽ݅.

áᔪᨕ ᔍŁ༉⩶, ⪶ශᱢ༉ᙹෝŁಅ⦽ᮭᯕ⧎⫭ȡᇥᕾ, Łᗮࠥಽʑ⦹Ǎ᳑, ᯕḩᖒ

İࣀėॡ

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Fig. 1. Research Flow

1. ᕽು

1.1 ઴֜ଭࢼլࢫࡧୡ

᪅௽ʑe࠺ᦩƱ☖ᔍŁ᮹✚ᖒᮥ❭ᦦ⦹ʑ᭥⧕ฯᮡᩑǍॅᯕ

ḥ⧪ࡹᨕ᪵ᮝ໑, ݡ⢽ᱢᯙᩑǍaƱ☖ᔍŁ᪡ࠥಽʑ⦹Ǎ᳑᪡᮹

šĥ❭ᦦᯕ݅. ᯕ్⦽ᩑǍॅᮥ☖⧕ᕽƱ☖ᔍŁᨱᩢ⨆ᮥၙ⊹۵

ࠥಽʑ⦹Ǎ᳑᫵ᗭෝ❭ᦦ⦹ᩍᯕෝ}ᖁ⧉ᮝಽ៉Ʊ☖ᔍŁෝᵥ ᯕ۵ יಆᮥ ⦹ᩍ᪵݅. ᯕ్⦽ יಆᮡ ᵝಽ ☖ĥ༉⩶ᮥ ☖⧕ᕽ

ᯕ൉ᨕᲙ ᪵ᮝ໑, ᯕෝ ᭥⧕ ᔍᬊࡽ ᵝ᫵☖ĥ༉⩶ᮡ aᔑ༉⩶

(Count Model)ᯕ໑, ᖁ⩶⫭ȡ༉⩶(Linear Regression Model),

⡍ᦥᘂ(Poisson Model) əญŁᮭᯕ⧎༉⩶(Negative Binomial Model)ᯕ ݡ⢽ᱢᯙ aᔑ༉⩶ᯕ݅.

⦹ḡอ ᯕ్⦽ ༉⩶ॅᮡ ༉ु š⊂s(ࠥಽǍe ⪚ᮡ Ʊ₉ಽ

॒)ᨱݡ⦽⇵ᱶࡽ༉ᙹ(parameter)aŁᱶࡹᨕᯩ݅Łaᱶ⦹Ł

ᖅ⊹⩶┽ᨱšĥᨧᯕ࠺ᯝ⦽sᯕᱢᬊࡹᨕᔍᬊࡹᨕ᪵݅. ࠥಽʑ

⦹Ǎ᳑᮹Ğᬑ, ⩥ᝅᱢᮝಽ࠺ᯝ⦽ʑ⦹Ǎ᳑aࠥಽᱥℕᨱᱢᬊࢁ

ᙹaᨧᮭᨱࠥᇩǍ⦹Ł, ḡɩʭḡ༉⩶ᨱᱢᬊࡽᄡᙹॅᮡᯕ్⦽

⩥ᝅᮥŁಅ⦹ḡᦫᮡ₥ᔍᬊࡹŁᯩ۵ᝅᱶᯕ݅. əđŝ, ༉⩶ᮥ

☖⧕⇵ᱶࡽĥᙹ᮹⢽ᵡ᪅₉sᯕŝᗭ⇵ᱶࡹᨩᮝ໑, ᯕ۵ĥᙹ᮹

t- sᮥŝࠥ⦹íᇡ⣡ญíࡹᨕ༉⩶᮹ᖅ໦ಆᯕਉᨕḡíࡹ۵

đŝෝ Ⅹ௹⦹í ࡽ݅.

঑௝ᕽ, ᯕჩᩑǍᨱᕽ۵ࠥಽ᮹bǍeᄥಽᔢᯕ⧁ᙹᯩ۵

ʑ⦹Ǎ᳑᮹ᯕḩᖒ(heterogeneity)ᮥŁಅ⦹ᩍʑ⦹Ǎ᳑᪡Ʊ☖ᔍ Ł᪡᮹ šĥෝ ❭ᦦ⦹Łᯱ ⦽݅.

1.2 ઴֜ଭٛ૳

ᯕ ᩑǍᨱᕽ۵ ʑ᳕᮹ ᮭᯕ⧎༉⩶(Fixed Parameter Model, ᯕ⦹FPM)ŝᯕᩑǍᨱᕽᱽ᜽⦹Łᯱ⦹۵ࠥಽʑ⦹Ǎ᳑᮹ᯕḩᖒ

ᮥŁಅ⦽ᮭᯕ⧎༉⩶(Random Parameter Model, ᯕ⦹RPM)᮹

እƱෝ☖⧕ᅕ݅⩥ᝅᱢᯙႊჶᮥᱽ᜽⦹Łᯱ⦽݅. ᯕࢱaḡ

⩶┽᮹༉⩶ᮡࠥ⇽ࡽĥᙹsၰĥᙹsॅ᮹┥ಆᖒ, ⦽ĥ⬉ŝ᪡

⧉̹RMSE(Root Mean Square Error : ⠪ɁᱽŒɝ᪅₉), MAPE (Mean Absolute Perchange Error : ⠪Ɂ႒ᇥᮉ᪅₉᮹⠪Ɂ), əญ ŁMAE(Mean Absolute Error : ⠪Ɂᱩݡ᪅₉)ႊჶᨱ᮹⧕እƱ

ࡹᨩ݅. ᯱᖙ⦽ ᩑǍ ᙹ⧪ᱩ₉۵ Fig. 1ᨱ ᱽ᜽ࡹᨕ ᯩ݅.

1.3 ઴֜ଭ࣐଍

1.3.1 վԩୡ࣐଍

ၙ ᬭᝒ▕ ᵝ(Washington State)ᨱ ᭥⊹⦽ 7}᮹ Łᗮࠥಽ

(interstate highway) : I-5, 82, 90, 182, 205, 405, əญŁ

705(1,528 mile ⴉ2,458 km)

1.3.2 ਏԩୡ࣐଍

9֥(1999~2007֥) ࠺ᦩ᮹ŁᗮࠥಽƱ☖ᔍŁ, Ʊ☖పၰʑ⦹

Ǎ᳑ ᯱഭ

1.3.3 ٛ૳ୡ࣐଍

ࠥಽǍeᨱ ᖅ⊹ࡽ ʑ⦹Ǎ᳑᮹ ᯕḩᖒᮥ Łಅ⦽ ᮭᯕ⧎༉⩶

ࠥ⇽ ၰ b ᄡᙹᄥ ᔍŁᨱ ၙ⊹۵ ᩢ⨆ᇥᕾ

2. ʑ᳕ྙ⨭Łₑ

2.1 ֗ധॷճࡦ෴

ʑ᳕᮹ᔍŁ༉⩶ᮡᮁ⩶ᄥಽⓍí3aḡ⩶┽-ᖁ⩶⫭ȡ᜾, ⡍ᦥ ᘂ⫭ȡ᜾, ᮭᯕ⧎⫭ȡ᜾ಽӹ٥ᨕḥ݅. ᬑᖁᖁ⩶⫭ȡ᜾ᮡᔍŁ

ၽᔾᨱᩢ⨆ᮥၙ⊹۵ᯙᯱॅᮥᇥᕾ⦹۵aᰆ݉ᙽ⦽ʑჶᯕ໑,

݅ᮭŝ zᯕ ӹ┡ԝ ᙹ ᯩ݅.

y _i = ⱕ + ⱖx i + ⱙ i (1)

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ᩍʑᕽ, y i : Ǎeiᨱᕽ᮹ᔍŁÕᙹ, ᔍᔢᯱᙹੱ۵ᔍŁᮉ(᳦ᗮ ᄡᙹ)

ⱕ᪡ ⱖ : ᔢᙹ᪡ ⫭ȡĥᙹ(⇵ᱶs) x _i : Ǎe iᨱᕽ᮹ ᔍŁ᫵ᯙ(ࠦพᄡᙹ) ⱙ i : ⪶ශ᪅₉⧎ N~(0, ⱦ ² )

ᔍŁ༉⩶ᵲaᰆ݉ᙽ⦽ႊჶᯕʕ⦹ḡอ, ĥᙹ⇵ᱶᨱᔍᬊࡹ۵

ᄡᙹsᯕ᷾a⧁ᙹಾᇥᔑs ੱ⦽᷾a⦹íࡹᨕᖁ⩶⫭ȡ᜾᮹

ʑᅙaᱶᯙ࠺ᇥᔑᖒ(Homoscedastisity)ᮥ᭥႑⦹íࡽ݅. əđ ŝᄡᙹ᮹ᮁ᮹ᙹᵡᨱᄡ⪵ෝᵝíࡹ໑, ᯕ۵ᄡᙹᨱݡ⦽☖ĥᱢ

ᮁ᮹ᖒᮥԏ⇵íࡽ݅. ᐱอᦥܩ௝Ʊ☖ᔍŁᙹ᪡zᮡ᧲᮹ᄡᙹᨱ

ݡ⧕ᮭ(Negative)᮹ᔍŁᙹෝᩩ⊂⦽݅۵݉ᱱᯕᯩ݅. ✚⯩Ʊ☖

ᔍŁ᮹ ✚ᖒᯙ ✚ᱶʑe ࠺ᦩ ᔍŁa ၽᔾ⦹ḡ ᦫᦹÑӹ ԏᮡ

ᔍŁÕᙹᨱݡ⧕ᖁᮭ᮹sᮥᩩ⊂⦹íࡽ݅(Jovanis and Chang, 1986). ੱ⦽, Miaou et al.(1993)ᮡʑ᳕᮹ᖁ⩶༉⩶ᮡᔑၽᱢ(sporadic) ᯕŁ ྕ᯲᭥(random)ಽ ၽᔾ⦹۵ ᔍŁ᮹ ༉⩶⪵ᨱ۵ ᱢ⧊⦹ḡ

ᦫ݅Łᵝᰆ⦹ᩡ݅. ᯕ్⦽ᮭ᮹ᔍŁᩩ⊂sᨱݡ⦽ྙᱽෝ⧕đ⦹

ʑ᭥⦽⦽aḡႊჶᮝಽ0᮹sᮥӹ┡ԕ۵ᔍŁෝᱽÑ⦹Ł

ᇥᕾ⦹۵ʑჶ(Left-Truncating the Accident Frequency at Zero)

ᮥᔍᬊ⧁ᙹᯩᮝӹ, ᯕ۵༉⩶⇵ᱶᨱᔍᬊࡹ۵⢽ᅙᙹaᵥᨕॅ

ᐱอᦥܩ௝, ༉⩶᮹}ֱᯕ┡༉⩶ᨱእ⧕ᩕᦦ⧕ḥ݅. ᯕ్⦽

ྙᱽᱱᮥ⧕đ⦹Łᯱ, Jovanis and Chang(1986), əญŁJoshua and Garber(1990) ॒ᮡᔍŁÕᙹෝᯕᔑᱢ⪶ශᄡᙹ(Discrete Random Variable)ಽ⧕ᕾ⦹۵⡍ᦥᘂ⫭ȡ᜾(Poisson Regression)ᮥᱽᦩ

⦹ᩡᮝ໑, ⡍ᦥᘂ⫭ȡ᜾᮹ ᯝၹ᜾ᮡ ݅ᮭŝ z݅.

©Þƌ _Ƈ ß á ć ƃ ^àŁ ƌØ _ Ł ^ƌ

^Ƈ

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ᩍʑᕽ, P(n i ) : ᔍŁ nᯕ ḡᱱ iᨱᕽ ၽᔾ⧁ ⪶ශ

ⱟ : ⠪ɁᔍŁၽᔾÕᙹ(=exp(ⱖX i )) ⱖ : ⇵ᱶࡽ ĥᙹ

⡍ᦥᘂ༉⩶ᮡ“ᇥᔑŝ⠪Ɂᯕz݅.”௝۵ᵲ᫵⦽ʑᅙᱥᱽa

ᯩ݅. ⦹ḡอ, ᝅᱽၽᔾ⦹۵Ʊ☖ᔍŁ۵ݡᇡᇥ᮹Ğᬑ, ᇥᔑsᯕ

⠪Ɂsᅕ݅ⓑŝᇥᔑ(Overdispersion)᮹⩶┽ෝᅕᯕíࡹᨕ⡍ᦥ ᘂ༉⩶ᯕᱢ⧊⦹ḡᦫᮡĞᬑaၽᔾ⦹íࡽ݅. ᯕෝᅕ᪥⦹ʑ

᭥⧕ᮭᯕ⧎⫭ȡ᜾(Negative Binomial Regression Model)ᯕᵝ ಽᔍᬊࡹŁᯩ݅. ᮭᯕ⧎ᇥ⡍ᨱ۵ᔍŁᙹ(ⱟi)᪡᪅₉⧎(ⱙi)ᯕ⡍⧉

ࡹ໑ ᯕ۵ ݅ᮭ᜾ŝ z݅.

ⱟ i = exp( ⱖX i + ⱙ i ) (3)

ᩍʑᕽ, exp(ⱙi) : ⠪Ɂᯕ1ᯕŁᇥᔑᯕⱕᯙqษᇥ⡍ෝ঑෕۵

᪅₉⧎

ᮭᯕ⧎༉⩶ᮡ⡍ᦥᘂ༉⩶᮹⪶ᰆࡽ⩶┽ᯕ໑, อ᧞᪅₉⧎᮹

ⱕsᯕ ☖ĥᱢᮝಽ 0ŝ ݅ෙ Ğᬑᨱ۵ ᮭᯕ⧎ ༉⩶ᯕ ᱢ⧊⦹໑, ၹݡ᮹Ğᬑ(ⱕ=0)ᨱ۵⡍ᦥᘂ༉⩶ᯕᱢ⧊⦹íࡽ݅. Engel (1984), Lawless (1987), Maher (1991) əญŁMiaou (1994)۵Ʊ☖ᔍŁ

᪡ʑ⦹Ǎ᳑᪡᮹šĥ❭ᦦᮥ᭥⦽ᩑǍᨱᕽᮭᯕ⧎༉⩶ᯕᖁ⩶

ੱ۵ ⡍ᦥᘂ ༉⩶ᅕ݅ ᬑᙹ⦹݅۵ ᩑǍđŝෝ ၽ⢽⦹ᩡ݅.

2.2 ֗ധॷճ૕׆෇֜୺૕ଭւծ

Ʊ☖ᔍŁ᪡ʑ⦹Ǎ᳑᪡᮹šĥᨱš⦽ᩑǍ۵ฯᮡᩑǍᯱॅᨱ

᮹⧕ᯕ൉ᨕᲙ᪵۵ߑ, ᩑǍᨱᔍᬊࡽʑ⦹Ǎ᳑۵Ʊ☖పᮥ⡍⧉⦹

ᩍʙᨕˉ⡎(Ogden, 1997), ₉ᖁᙹ᪡₉ᖁմᯕ, əญŁᱽ⦽ᗮࠥ

2005), ᜽Ñ, Ǎ႑(Caliendo et al., 2007), ᯙ░ℕᯙḡఉ⥥(Montella et al., 2008)॒ᮥᔍŁᨱၙ⊹۵ᄡᙹಽ₥┾⦹ᩍᵝಽᮭᯕ⧎༉⩶ᮝ ಽ ᇥᕾᮥ⦹ᩡ݅. ⦹ḡอ, ⇵ᱶࡽĥᙹsॅᯕࠥಽ᮹Ǎeᨱšĥᨧᯕ

༉ुǍeᨱݡ⧕Łᱶࡽsᮝಽࠥಽ᮹bǍeᯕaḩᙹᯩ۵

bb᮹ᯕḩᱢᯙ✚ᖒᨱš⦽a܆ᖒᮡ႑ᱽ⦹ᩡ݅۵݉ᱱᯕᯩ݅.

ᯕ్⦽ᯕḩᖒŝšಉࡽᩑǍ⊂໕ᨱᕽ۵Shankar et al.(1998)ᮡ

2 aḡ⩶┽᮹༉⩶-Random Effects Negative Binomial (RENB) ŝCross-sectional Negative Binomialᮥᯕᬊ⦹ᩍ, RENB ༉⩶

ᯕᔢᙹsᨱᕽᯕḩᖒᯕࠥ⇽ࡹࠥಾ⦹ᩡᮝ໑, Chin et al.(2003)ᮡ

ᝒa⡍෕᮹Ʊ₉ಽᨱᕽၽᔾ⦽ᔍŁෝᯕᬊ⦹ᩍ, š⊂ࡹḡᦫᮡ

ᯕḩᖒ(Unobserved Heterogeneity)ŝ᜽ĥᩕᔢš(serial correlation)

ᮥ ݅൉ʑ᭥⧕RENB༉⩶ᮥᱢᬊ⦹ᩡ݅. Washington et al.(2010)

ᮡ ĥᙹsᯕš⊂sᨱ঑௝݅᧲⦽sᮥӹ┡ԕḡอ, Łᱶࡽsᯕ௝

Łaᱶ⦹ᩍᯕෝᱽ᧞⧁Ğᬑ, ᯝšᖒᯕᨧŁ(inconsistent) ⠙ᵲࡽ

(unbiased) đŝa ࠥ⇽ࢉᮥ ᷾໦⦹ᩡ݅.

3. ᯱഭǍ⇶

3.1 ंজ࣐଍

ᯕᩑǍᨱᕽᔍᬊࡽƱ☖ᔍŁ, Ʊ☖పၰʑ⦹Ǎ᳑ᯱഭ۵ⅾ

9 ֥࠺ᦩ᮹ၙǎᬭᝒ▕ᵝ(Washington State)ᨱᗮ⦽Łᗮࠥಽ (interstate highway)ෝݡᔢᮝಽᇩɁ⩶➉ձߑᯕ┡(Unbalanced Panel Data) ¹⁾ ⩶᜾ᮝಽǍ⇶ࡹᨩ݅. ߑᯕ░Ǎ⇶ᨱ⡍⧉ࡽŁᗮࠥ

1)ʑ⦹Ǎ᳑᮹Ğᬑ, 9֥࠺ᦩ}ᖁ⪚ᮡᄡĞࡽᯱഭ᮹ᙹḲᯕᇩa܆⦹ᩍ

(4)

Fig. 2. Interstate Highway in Washington State

Table 1. Number of Segments and Miles by Route and Direction

Route

Increasing Direction

Interchange Segment Non-interchange Segment Miles(Kilometers) Segments Miles(Kilometers) Segments 5 104.84(168.69) 138 171.78(276.39) 139 82 27.51(44.26) 33 105.06(169.04) 34 90 65.73(105.76) 83 231.79(372.95) 83

182 7.08(11.39) 8 8.11(13.05) 9

205 4.14(6.66) 5 6.43(10.35) 6

405 13.53(21.77) 19 16.77(26.98) 20

705 0.5(0.80) 1 1(1.61) 2

Total 223.33(375.43) 287 540.94(870.37) 293

Route

Decreasing Direction

Interchange Segment Non-interchange Segment Miles(Kilometers) Segments Miles(Kilometers) Segments 5 104.48(168.11) 138 172.13(276.96) 140

82 26.5(42.64) 33 106.07(170.67) 34

90 65.28(105.04) 85 232.24(373.67) 85

182 7.55(12.15) 8 7.64(12.29) 9

205 4.06(6.54) 5 6.51(10.47) 6

405 13.84(22.27) 20 16.46(26.48) 21

705 0.55(0.88) 2 0.95(1.53) 2

Total 222.26(357.62) 291 542.00(872.08) 297

ಽ۵I-5, I-82, I-90, I-182, I-205, I-405, əญŁI-705᮹7}

יᖁᯕ໑, ᅕ݅ᯱᖙ⦽יᖁ᮹ʙᯕၰ᭥⊹۵Fig. 2ᨱӹ┡ӹᯩ݅.

༉ु Łᗮࠥಽ۵ ႊ⨆ᄥಽ ᅙᖁǍeŝ ᯙ░ℕᯙḡ Ǎeᮝಽ

Ǎᇥࡹᨕᯩ۵ߑ, ᯕ۵ʑᅙᱢᮝಽࢱǍe᮹ʑ⦹Ǎ᳑aᔢᯕ⦹ʑ

ভྙᯥŝ࠺᜽ᨱƱ☖ᔍŁᇥᕾᨱᕽᵝ᫵⦽᫵ᯙᯙƱ☖పᯕᯙ░

ℕᯙḡෝʑᵡᮝಽၵѭʑভྙᯕ݅. Ǎeᇥ⧁᮹Ğᬑ, ੱ݅ෙ

⩶┽ಽa܆(ʑ⦹Ǎ᳑aᄡĞࡹ۵ḡᱱ॒)⦹ḡอ, ᯕᩑǍᨱᕽ۵

ᯕḩᖒᮥŁಅ⦹ᩡʑভྙᨱ༉⩶ᨱᕽࠥ⇽ࡹ۵ĥᙹs॒ᮥ☖⧕

ᖅ໦ᯕࡹᨕḡ໑, Milton ॒(2008)᮹ᩑǍᨱᕽࠥʑᚁࡹᨕᯩ݅.

ᯙ░ℕᯙḡǍeᮡᅙᖁᨱᕽᯙ░ℕᯙḡಽ᮹ᇥඹᇡ᜽ᱱᨱᕽ

ᯙ░ℕᯙḡᨱᕽᅙᖁᮝಽ᮹⧊ඹᇡ᜽ᱱʭḡ᮹Ǎeᯕ໑, ᅙᖁǍ eᮡə᫙᮹Ǎeᮝಽᱶ᮹⦹ᩡ݅. ᯕ్⦽ᱥᱽ᳑Õ⦹ᨱⅾ7}י ᖁ᮹1,528mile(2,458km)Ǎeᯕ1,168}᮹ǍeᮝಽǍᇥࡹᨩᮝ ໑, Ǎe᮹יᖁᄥႊ⨆ᄥ}ᙹၰʙᯕ۵Table 1ᨱӹ┡ӹᯩ݅.

ᅙᩑǍᨱᕽᔍᬊࡽʑ⦹Ǎ᳑ᨱݡ⦽ᯱഭ۵ᱶ᮹ࡽbb᮹Ǎeᨱ

ݡ⦽sᮝಽᄡ⪹ࡹᨕᱢᬊࡹᨩ݅. əญŁƱ☖పŝᔍŁ۵9֥࠺

ᦩ b ֥ࠥᄥಽ ᱢᬊࡹᨩ݅.

3.2 Թ࣢ୀ߹ंজ

Table 2 ۵ᯕᩑǍᨱᕽᔍᬊࡽ⪶ශᱢ༉ᙹෝŁಅ⦽ᮭᯕ⧎

༉⩶ᨱᔍᬊࡽᄡᙹᨱݡ⦽☖ĥsᮥӹ┡ԕŁᯩ݅. ᵝ᫵⦽ᄡᙹಽ

ᄡᙹ, Ǎe᮹ʙᯕၰƱ☖పᯕᔍᬊࡹᨩᮝ໑, ֥eᔍŁÕᙹ᮹

⠪Ɂsᮡ10.70 ⢽ᵡ⠙₉۵18.92 əญŁ↽ݡsᮡ388Õᮥᅕᩍ ᵝŁ ᯩ݅.

ᮁḡࡹ۵Ŕࠥᯩ۵ၹ໕, ݍ௝ḡ۵ĞᬑࠥŁಅ⦹ʑ᭥⧕ᯕᩑǍᨱ ᕽ۵Ǎeᄥʙᯕእᮉಽᱶ᮹⦹ᩡ݅. ঑௝ᕽʑ⦹Ǎ᳑a࠺ᯝ⦹í

ᮁḡࡹ۵Ǎeᨱᕽ᮹↽ݡsᮡ1ᮥչḡᦫᮝ໑, ᔢᯕ⦽ʑ⦹Ǎ᳑

aǍeԕᨱ݅ᗭ᳕ᰍ⦹޵௝ࠥǍeԕᨱᕽ᮹⧊ᮡ↽ݡsᯙ1ᮥ

չḡᦫíࡽ݅. Łᗮࠥಽෝݡᔢᮝಽᇥᕾᯕḥ⧪ࡹᨩʑভྙᨱ

2 ₉ᖁࠥಽ۵ฯᯕ᳕ᰍ⦹ḡᦫᮝ໑, ʙᯕ۵0.52᮹⠪Ɂsŝ0.494 ᮹⢽ᵡ⠙₉sᮥaḥ݅. 3₉ᖁࠥಽ᮹Ğᬑᨱ۵0.336, 0.461, 4 ₉ᖁᮡ0.135, 0.331 əญŁ5₉ᖁࠥಽ᮹Ğᬑᨱ۵0.002, 0.043 ᮹ ⠪Ɂsŝ ⢽ᵡ⠙₉sᮥ aḥ݅.

ʙᨕˉ᮹Ğᬑᨱ۵5aḡ᮹Ğᬑ(2-feet ᯕ⦹, 3~4, 5~9, 10, 10-feet ᯕᔢ)ಽǍᇥ⦹ᩡᮝ໑, ₉ᖁᙹ᪡ษ₍aḡಽǍeԕᨱᕽ

₉ḡ⦹۵ እᮉಽ ᱶ᮹⦹ᩡ݅.

Ǎeԕᨱᕽ⬂݉łᖁ᮹}ᙹ۵⠪Ɂᱢᮝಽ1.805}a᳕ᰍ⦹۵

äᮝಽ❭ᦦࡹᨩᮝ໑, ↽ݡ37}᮹⬂݉łᖁᯕ᳕ᰍ⦹۵äᮝಽ

ӹ┡ԍ݅. ੱ⦽, aᰆ Ṉᮡ ⬂݉łᖁᮡ ⠪Ɂᱢᮝಽ 0.182mile (0.29km) ᮹ ʙᯕෝ aḡŁ ᯩᮝ໑, ၹ໕ aᰆ ʕ ⬂݉łᖁᮡ

0.275mile(0.44km)᮹⠪Ɂsᮥaḡ۵äᮝಽ❭ᦦࡹᨩ݅. ⬂݉

łᖁ᮹↽ᗭƱb᮹⠪Ɂsᮡ12.186°ᯕ໑, ↽ݡƱbᮡ21.080°᮹

⠪Ɂsᮥ aḡ۵ äᮝಽ ӹ┡ԍ݅.

᳦݉łᖁ᮹Ğᬑᨱ۵3.125}᮹łᖁᯕǍeԕᨱᕽ⠪Ɂᱢᮝಽ

᳕ᰍ⦹໑, ↽ݡ}ᙹ۵30}ᯙäᮝಽ❭ᦦࡹᨩ݅. ᳦݉łᖁŝšಉ

1.385%᮹ ⠪Ɂsŝ ⢽ᵡ⠙₉sᮥ aḡ۵ äᮝಽ ӹ┡ӽ ၹ໕,

(5)

Table 2. Statistics of Accident, Geometrics and ADT Variables

Variable Variable Description Mean Std.Dev. Minimum Maximum

ACC Number of Accidents per year 10.703 18.917 0 388

NLN2 Portion of segment with 2 lanes 0.525 0.494 0 1

LSHW2 2-ft(60cm) left-shoulder width segment proportion 0.175 0.337 0 1

LSHW34 3- to 4-ft(90~120cm) left-shoulder width segment proportion 0.199 0.387 0 1 LSHW59 5- to 9-ft(150~270cm) left-shoulder width segment proportion 0.133 0.320 0 1

LSHW10 10-ft(300cm) left-shoulder width segment proportion 0.472 0.478 0 1

LSHW1126 Over 10-ft(over 300cm) left-shoulder width segment proportion 0.020 0.132 0 1

RSHW2 2-ft(60cm) right-shoulder width segment proportion 0.178 0.341 0 1

RSHW34 3- to 4-f(90~120cm)t right-shoulder width segment proportion 0.207 0.392 0 1 RSHW59 5- to 9-f(150~270cm)t right-shoulder width segment proportion 0.121 0.308 0 1

RSHW10 10-ft(300cm) right-shoulder width segment proportion 0.464 0.477 0 1

RSHW1124 Over 10-ft(over 300cm) right-shoulder width segment proportion 0.030 0.155 0 1

NHORZ Number of hirizontal curves in segment 1.807 2.459 0 37

MINHLMI Shortest horizontal curve-in-segment length (miles) 0.182(0.29km) 0.193 0 1.219 MAXHLMI Longest horizontal curve-in-segment length (miles) 0.275(0.44km) 0.277 0 2.402 MINHDEL Smallest horizontal curve-in-segment central angle (degrees) 12.186 14.692 0 98.426 MAXHDEL Largest horizontal curve-in-segment central angle (degrees) 21.080 21.001 0 111.294

NVERT Number of vertical curves in segment 3.125 3.210 0 30

MINVCRVG Smallest absolute vertical curve gradient (%) 1.232 1.385 0 7.430

MAXVCRVG Largest absolute vertical curve gradient (%) 2.780 2.075 0 10

LENGTH Segment length (miles) 1.309(2.11km) 1.753 0.01 20.380

AADT Annual Average Daily Traffic Volume 13043.300 8378.490 916.45 44223.800

↽ݡǍ႑᮹Ğᬑᨱ۵2.78%᮹⠪Ɂsŝ2.075%᮹⢽ᵡ⠙₉sᮥ

aḡ۵ äᮝಽ ӹ┡ԍ݅.

ݡᔢǍe᮹⠪Ɂʙᯕ۵1.309mile(2.11km)ᯕ໑, Ǎeԕᩑ⠪

ɁᯝƱ☖ప(ႊ⨆ᄥ₉ᖁᄥ)ᮡ⠪Ɂ13,043ݡಽӹ┡ԍᮝ໑, ↽ݡ Ʊ☖పᮡ44,223ݡಽ᳑ᔍࡹᨩ݅. Ǎe᮹ʙᯕ᪡Ʊ☖పᮡಽəs ᮝಽ ᄡ⪹ࡽ sᯕ ༉⩶ᨱ ᱢᬊࡹᨩ݅.

4. ༉⩶᮹Ǎ⇶ၰđŝᇥᕾ

4.1 คࠔୡࡦ৤ࠜճߙ෉ଣଲාࡦ෴

(Random Parameter Negative Binomial)

ᯕ ᩑǍᨱᕽ ᱽ᜽⦹Łᯱ ⦹۵ ⪶ශᱢ ༉ᙹෝ Łಅ⦽ ᮭᯕ⧎

༉⩶ᯕʑ᳕᮹ᮭᯕ⧎༉⩶ŝ݅ෙaᰆⓑ✚Ḷᮡĥᙹs(ⱖ)ᯕ

Łᱶࡹᨕᯩḡᦫ݅۵äᯕ݅. ᯝၹᱢᮝಽࠦพᄡᙹ(x)۵š⊂ࡹÑ ӹᙹḲࡽᯱഭᨱᱽ᧞ࡹᨕᯩʑভྙᨱࠦพᄡᙹಽᇡ░ᯕᬊa܆

⦽ ↽ݡ⦽᮹ ᱶᅕෝ ᨜۵äᨱ ༉ߙย᮹ ༊ᱢᯕ ᯩᮝ໑, ᯕ్⦽

šᱱᨱᕽbĥᙹෝŁᱶࡽsᯕᦥܩ௝, Ŗeᄥ(i) ⪚ᮡ᜽eᄥ(t)ಽ

݅᧲⦹݅Łaᱶ⦹ᩍᱲɝ⦽݅໕ᯕḩᖒᮥŁಅ⦽ĥᙹsᮥࠥ⇽

⧁ᙹᯩíࡽ݅. ᩩෝॅ໕, ᨕ۱✚ᱶᇥ⡍a⪶ශ༉ᙹ᮹ĥᗮᱢᯙ

ᄡ⪵ෝaᰆ᯹ӹ┡ԙ݅௝Łaᱶ⦹۵äᯕ໑, ᯕ్⦽aᱶᨱʑၹ

⦽ᬑࠥ⧉ᙹ(likelihood function)۵Łᱶࡽĥᙹaᦥܭᄡ⪵⦹۵

ĥᙹಽᇡ░ĥᔑࡽ⪶ශᮥʑၹᮝಽ⧕ᕽ݅ᮭŝzᯕᙹᱶࢁᙹ

ᯩí ࡽ݅.

ⱖ it = ⱖ + ⶸh i + ⰿw it (4)

ᩍʑᕽ, haᗮ⦽ࢱჩṙ⧎ᮡh i ᨱᗮ⦽ᄡᙹॅ᮹⠪Ɂsᨱ

ݡ⦽ᯕḩᖒᮥӹ┡ԕ໑, ᖙჩṙ⧎ᮡ⠪Ɂᮝಽᇡ░᮹⪶ශ⠙₉ (random deviation)ෝӹ┡ԕíࡽ݅. ঑௝ᕽ, Eq. (4)۵⪶ශᱢ

ᯕḩᖒ(parameter heterogeniety)ᮥӹ┡ԕ۵ ʑᅙᱢᯙ᜾ᯕ໑,

(6)

Table 3. Modeling Estimation Results for Fixed-and Random-Parameters Negative Binomial Models

Variable Fixed Parameter Model (FPM) Random Parameter Model (RPM) Coefficient t-value Coefficient t-value Exposure and Context

Constant -8.409 -73.556 -7.624 -73.294

Logarithm of Length of segment in miles 0.743 68.992 0.787 83.210

Standard deviation of parameter distribution - 0.087 11.882

Logarithm of ADT 1.143 99.726 1.036 98.715

Interchange indicator(1 if segment is an interchange segment; 0 otherwise) -0.027 -1.991 -0.051 -4.418 Number of Lanes by Length Proportion

Three-lane cross-section segment proportion 0.375 15.947 0.473 23.879

Four-lane cross-section segment proportion 0.902 33.995 0.856 38.592

Five-lane cross-section segment proportion 0.785 3.456 1.190 7.868

Left Shoulder Width by Length Proportion

3- to 4-ft(90~120cm) left-shoulder-width proportion -0.273 -8.528 -0.231 -8.430

5- to 9-ft(150~270cm) left-shoulder-width proportion -0.496 -18.081 -0.393 -18.274

10-ft(300cm) left-shoulder-width proportion -0.416 -20.219 -0.300 -16.131

Right Shoulder Width by Length Proportion

3- to 4-ft(90~120cm) right-shoulder-width proportion -0.286 -8.347 -0.279 -10.380 5- to 9-ft(150~270cm) right-shoulder-width proportion -0.319 -13.737 -0.344 -14.733

10-ft(300cm) right-shoulder-width proportion -0.395 -17.875 -0.320 -18.813

Horizontal-Vertical Curvature

Number of horizontal curves in segment 0.029 7.080 0.019 6.150

Shortest horizontal curve-in-segment length in miles -0.625 -12.484 -0.514 -12.109

Largest degree of curvature in segment 0.006 13.850 0.005 13.023

Largest vertical curve gradient in segment 0.020 5.327 0.029 8.955

Dispersion parameter for negative binomial distribution

Dispersion parameter 0.348 51.092 5.960 41.550

Number of observations 10512

Log-likelihood with constant only -105,377.5

Log-likelihood at convergence -29,210.79 -28,315.69

쩐2 0.722 0.731

✚⯩ߙ┡(ⶸ)۵ĥᙹ(ⱖ)ᨱᩢ⨆ᮥၙ⊹۵᫙ᔾᄡᙹ(exogenous variable)ෝ⡍⧉⦹໑, อ᧞ᄡᙹ⠪Ɂsԕᨱᯕḩᖒᯕ᫙ᔾᄡᙹಽ

᳕ᰍ⦹ḡᦫ۵݅໕, ᯕ⧎ᮡᔍ௝ḡíࢁäᯕ݅. ᷪ, ༉ुᯕḩᖒᮡ

ᖙჩṙ⧎ᨱ᮹⧕ᕽ༉⩶⪵ࡹᨕḡíࡽ݅. ᯕ۵ᔍᬊࡽࠦพᄡᙹ᮹

✚ᖒᨱ঑ෙᇥ⡍᮹⩶┽ෝၵ┶ᮝಽᱢᬊࢁäᯕ໑, อ᧞ࠦพᄡᙹ

᮹⩶┽aᯕ⧎ᄡᙹ(dummy variable)௝໕, Ɂᯝ(uniform)ᇥ⡍a,

ᩑᗮᄡᙹ(continuous variable)௝໕ᱶȽ(normal) ੱ۵ಽəᱶȽ

(lognormal)ᇥ⡍aࢁäᯕ݅. ঑௝ᕽ, ᖙჩṙ⧎ᯕ☖ĥᱢᮝಽ

(7)

ᮁ᮹⦹໕, ĥᙹsᯕ⢽ᵡ⠙₉sŝ⧉̹bǍeᄥಽᔢᯕ⦽sᯕ(ᯕ ḩᖒᮥaḥ݅) ⇵ᱶࡹ໑, ☖ĥᱢᮝಽᮁ᮹⦹ḡᦫᮝ໕, ᯝၹᱢᯙ

ᮭᯕ⧎༉⩶ᯕᱢᬊࡹᨕĥᙹsᯕǍeᨱᔢšᨧᯕŁᱶࡽsᮝಽ

⇵ᱶࡽ݅.

4.2 էրंজ

ᯕᩑǍᨱᕽ۵ Table 2ᨱᕽᱽ᜽ࡽ ᄡᙹॅᮥ ⪶ශᱢ༉ᙹෝ

ᯕᬊ⦽ ᮭᯕ⧎༉⩶ᨱ ᯕᬊ⦹ᩡ݅. ᳦ᗮᄡᙹ۵ ᬭᝒ▕ ᵝ 7}᮹

Łᗮࠥಽᨱᕽၽᔾ⦽Ʊ☖ᔍŁÕᙹෝࠦพᄡᙹಽ۵ʑ⦹Ǎ᳑, Ʊ

☖పၰǍe᮹ʙᯕಽᖅᱶ⦹ᩡᮝ໑, ☖ĥ⥥ಽəఉᯙLIMDEPᮥ

ᯕᬊ⦹ᩍʑ᳕ᩑǍᨱᕽᵝಽᔍᬊࡹ۵ᮭᯕ⧎༉⩶(FPM)ŝᅙ

ᩑǍᨱᕽ ᱽ᜽⦹Łᯱ ⦹۵ ⪶ශᱢ ༉ᙹෝ ᯕᬊ⦽ ᮭᯕ⧎ ༉⩶

(RPM) ᮥࠥ⇽⦹ᩡ݅. ⡍ᦥᘂ༉⩶ŝᮭᯕ⧎༉⩶᮹ᖁ┾ᨱᯩᨕᕽ

ᦿᕽᖅ໦⦽ߑಽŝᇥᔑs(ⱕ)ᯕ0.348, t-sᯕ51.092ᯥᮥᅕᩍ

☖ĥᱢᮝಽ0ŝ݅෕݅۵ᮁ᮹ᖒᮥᅕᯕʑভྙᨱࠥ⇽ࡽ༉⩶ᮡ

⡍ᦥᘂᇥ⡍ᅕ݅ᮭᯕ⧎ᇥ⡍ෝ঑෕۵äᮝಽӹ┡ӹđŝᱽ᜽۵

ᮭᯕ⧎༉⩶ᨱ ᮹⦽ đŝอ ᱽ᜽⦹Łᯱ ⦽݅.

༉⩶᮹ࠥ⇽ᮡHalton drawsෝᯕᬊ⦽↽ݡᬑࠥჶᮥᔍᬊ⦹ᩡ

ᮝ໑, Bhat (2003) əญŁMilton et al. (2008)᮹םྙᨱᕽᱶ⪶⦽

ĥᙹ⇵ᱶᮥ⧁ᙹᯩ݅Łᨙɪࡽ200 Halton Drawsෝᱢᬊ⦹ᩡ݅.

ĥᙹ⇵ᱶ᮹ੱ݅ෙႊჶᮝಽᯕᬊࢁᙹᯩ۵Random Drawsࠥ

ᯩḡอĥᙹsᮥᙹಕ⦹ʑ᭥⧕Halton Draws ႊჶᨱእ⧕ฯᮡ

Draws a⦥᫵⦹ᩍ⬉ᮉᱢᯕḡ༜⦹݅Ł᦭ಅᲙᯩ݅(Train, 2003).

əญŁ ᯕ ᩑǍᨱᕽ ᱽ᜽⦹۵ ⪶ශᱢ ༉ᙹෝ Łಅ⦽ ᮭᯕ⧎

༉⩶᮹ĥᙹ⇵ᱶ᜽, ᩍ్⩶┽᮹⪶ශᇥ⡍(ᱶȽ, ಽəᱶȽ, Ɂᯝᇥ

⡍)ෝŁಅ⧁ᙹᯩ۵ߑ, ᯕᵲᱶȽᇥ⡍a☖ĥᱢᮝಽaᰆᮁ⬉⦽

sᮥ ᅕᯕ۵ äᮝಽ ӹ┡ԍ݅.

ࠥ⇽ࡽĥᙹ᮹⦽ĥ⬉ŝ(Marginal Effect)aTable 4ᨱᱽ᜽ࡹ

ᨕᯩ݅. ᯕෝ☖⧕ʑ⦹Ǎ᳑᮹݉᭥(unit)ᄡ⪵aᔍŁၽᔾᨱၙ⊹۵

ᔢݡᱢᯙᩢ⨆ᮥ᦭ᙹᯩ݅. əญŁᯕᬊࡽᄡᙹ᮹✚ᖒᨱ঑௝ᕽ

┥ಆᖒ(Elsaticity)ᮥ ᱽ᜽⦹Łᯱ ⦽݅.

ࠥ⇽ࡽ༉⩶᮹ᱥℕᱢᯙᖅ໦ಆᮡಽə-ᬑࠥ⧉ᙹsᯕ-105,377.5 ᨱᕽ -28,315.69ಽ ᬑࠥእ(ⱥ ² ) a 0.731ಽ ᯝၹᱢᯙ ᮭᯕ⧎༉⩶

(-29,210.79, ⱥ ² =0.722)ᨱእ⧕ᔢݡᱢᮝಽ᳑ɩӹᮡᖅ໦ಆᮥ

aḡ۵ äᮝಽ ӹ┡ԍ݅.

ᦿᕽᖅ໦⦽ߑಽ ⪶ශᱢ ༉ᙹෝᯕᬊ⦽ ᮭᯕ⧎ ༉⩶᮹Ğᬑ,

⇵ᱶࡽĥᙹ᮹⢽ᵡ⠙₉a☖ĥᱢᮝಽᮁ᮹⦽Ğᬑ(s.dⴊ0, t-value ⴍ1.96)ᨱᔍᬊࢁᙹᯩᮝ໑(RPM), อ᧞⇵ᱶࡽĥᙹ᮹⢽ᵡ⠙₉ a☖ĥᱢᮝಽᮁ᮹⦹ḡᦫᮝ໕(s.d=0, t-value<1.96) ⇵ᱶࡽĥᙹ aᯝၹᱢᯙᮭᯕ⧎༉⩶᮹Ğᬑ⃹ౝ, Ǎeᨱšĥᨧᯕ༉ुǍeᨱ

ݡ⧕ᕽ ࠺ᯝ⦽ sᮥ aḡí ࡽ݅(FPM).

Table 3ᨱ঑෕໕, Ǎe᮹ʙᯕaʙᨕḡíࡹ໕ᔍŁၽᔾ⪶ශᯕ

׳ᦥḱᮥ ᦭ ᙹ ᯩ݅. RPMᨱᕽ۵ ⠪Ɂsᯕ 0.787 ⢽ᵡ⠙₉۵

0.087ᯕ໑t-sᨱ᮹⦹໕ᔢݚ⯩׳ᮡᮁ᮹⧉ᮥᅕᯥᮥ᦭ᙹᯩ݅.

RPM ᮹┥ಆᖒ⊂໕ᨱᕽ1%᮹Ǎeʙᯕ᷾a۵0.787%᮹ᔍŁ᷾

aᨱᩢ⨆ᮥᵝ۵äᮝಽӹ┡ԍ݅. əญŁFPMᨱᕽ۵0.743%᮹

ᩢ⨆ᯕᯩ۵äᮝಽӹ┡ԍ݅. ᯕ۵י⇽పᯕฯᦥḩᙹಾᔍŁၽᔾ

⪶ශᯕ ׳ᦥḥ݅۵ ʑ᳕᮹ ᩑǍ᪡ ᯝ⊹⧉ᮥ ᦭ ᙹ ᯩ݅. ੱ⦽, Ǎe ʙᯕ᮹ Ğᬑ ☖ĥᱢᮝಽ ᮁ᮹⦽ ⢽ᵡ᪅₉ sᮥ ᅕᯕʑᨱ

ᔍŁᨱݡ⦽ᩢ⨆ᮡǍeᨱ঑௝݅෕íӹ┡ԁᙹᯩᮝ໑, ↽ݡ

1168 }᮹ ݅ෙ sᮥ aḡí ࡽ݅.

Ʊ☖పੱ⦽Ǎe᮹ʙᯕ᪡ษ₍aḡಽƱ☖పᯕ᷾a⧁ᙹಾ

ᔍŁၽᔾᨱᩢ⨆ᮥฯᯕᵝ۵äᮝಽӹ┡ԍ݅. FPMᨱᕽ۵1%᮹

Ʊ☖ప᷾aa1.143%᮹ᔍŁ᷾aಽᯕᨕḱᮥ᦭ᙹᯩ݅. ၹ໕, RPM ᨱᕽࠥᔢݚ⯩ᮁ᮹⦽1.036᮹⠪Ɂsŝ0.008᮹⢽ᵡ⠙₉s

ᮥaḡ۵äᮝಽӹ┡ԍ݅. ┥ಆᖒ⊂໕ᨱᕽࢱaḡĞᬑᨱᕽ

༉ࢱ┥ಆᱢᯥᮥᅕᯕ۵ߑ, 1%᮹Ʊ☖ప᷾a۵1.143%(FPM)᪡

1.036%(RPM)᮹ᔍŁ᷾aᨱᩢ⨆ᮥၙ⊹۵äᮝಽӹ┡ԍ݅. Ǎ e᮹ʙᯕ᮹Ğᬑ᪡ษ₍aḡಽי⇽పᯕ᷾a⧁ᙹಾᔍŁ᷾aᨱ

ࠥᩢ⨆ᮥၙ⊹۵äᯥᮥ᦭ᙹᯩ݅. ⢽ᵡ⠙₉ᨱᕽᮁ᮹⦽sᮥ

ӹ┡ԕʑভྙᨱ↽ݡ1168ǍeᨱᕽƱ☖ᔍŁᨱbʑ݅ෙᩢ⨆

(%)ᮥ ၙ⊹۵ äᮝಽ ᅝ ᙹ ᯩ݅.

ᯙ░ℕᯙḡ Ǎe᮹ Ğᬑ, ᅙᖁǍeᨱ እ⧕ ᔍŁၽᔾᯕ ᯲í

ၽᔾ⧉ᮥ ᦭ ᙹ ᯩ݅.

₉ᖁᙹ᮹Ğᬑᨱ۵2₉ᖁᮥaḥǍeᮥᱽ᫙⦽ӹນḡǍeᨱ ᕽ☖ĥᱢᮝಽᮁ᮹⦽đŝෝᅕᩡ݅. ᬑᖁǍeԕᨱᕽ₉ᖁᙹa

ฯᦥḩᙹಾᔍŁၽᔾࠥ᷾a⧉ᮥ᦭ᙹᯩ݅. ᯕ۵Ǎe᮹ʙᯕ

ၰƱ☖పŝ⧉̹י⇽పᯕ᷾a⦹۵⊂໕ᨱᕽᔍŁၽᔾᨱࠥᩢ⨆

ᮥၙ⊹۵äᮝಽ❱݉ࡽ݅. əญŁ, ⦽ĥ⬉ŝ᮹šᱱᨱᕽ۵4₉ᖁ ᨱᕽ 5₉ᖁ እᮉᨱ ঑௝ ə ᷾a⬉ŝa ᔢݡᱢᮝಽ 3₉ᖁᨱᕽ

4 ₉ᖁᮝಽ᮹᷾aእᮉᨱእ⧕᯲Ñӹၙእ⧉ᮥᅕᩍǍeԕ4₉ᖁ ᮹ እᮉᯕ Ʊ☖ᦩᱥ ၰ ⚍ᯱእᬊ᮹ ⊂໕ᨱᕽ ⬉ᮉᱢᯙ äᮝಽ

❱݉ࡽ݅.

᫝἞ʙᨕˉ⡎᮹Ğᬑ, 2-ft(60cm)ၙอ᮹ʙᨕˉ⡎ᮥᱽ᫙⦽

ӹນḡᨱᕽᮁ᮹⦽đŝaࠥ⇽ࡹᨩᮝ໑, ʙᨕˉ⡎ᯕմᨕḩᙹಾ

Ʊ☖ᔍŁa qᗭ⧉ᮥ ᦭ ᙹ ᯩ݅.

3-4ft(90~120cm) ᪡10ft(300cm)ᯕᔢ᮹Ğᬑᨱᕽ۵RPM᮹

⢽ᵡ⠙₉aᮁ᮹⧉ᮥ᦭ᙹᯩ݅. ᬑᖁ3-4ft۵78.9%᮹Ǎeᨱᕽ

ᔍŁÕᙹ᮹qᗭa, ӹນḡ21.1%᮹ǍeᨱᖁᔍŁÕᙹa᷾a⦽

݅. 10ft ᯕᔢ᮹ʙᨕˉ⡎ᮥaḥĞᬑᨱ۵97%᮹ǍeᨱᕽᔍŁÕ ᙹ᮹qᗭa, 3%᮹ǍeᨱᕽᔍŁÕᙹa᷾a⦹۵äᮝಽӹ┡ӹ, ᬕᱥᯱ᮹ᇡᵝ᮹⪚ᮡ₉ప᮹ྙᱽ॒ᮝಽᯙ⦽₉ᖁᯕ┩॒᮹ᩩᔢ

⊹༜⦽ᔢ⫊᮹Ğᬑᨱࠥᯕෝႊḡ⧁ᙹᯩ۵∊ᇥ⦽⡎᮹᪥∊ḡᩎ

aᔍŁၽᔾÕᙹqᗭᨱฯᮡʑᩍ⧉ᮥ᦭ᙹᯩ݅. ⦹ḡอ, ⦽ĥ⬉

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Table 4. Average Marginal Effects for Fixed-and Random- Parameters Negative Binomial Models

Fixed Parameter Model Random Parameter Model

LNLEN 7.788 4.251

LNADT 11.971 5.597

INTERCHANGE -0.287 -0.275

NLN3 3.932 2.556

NLN4 9.454 4.625

NLN5 8.219 5.429

LSHW34 -2.858 -1.245

LSHW59 -5.193 -2.125

LSHW10 -4.359 -1.623

RSHW34 -2.998 -1.504

RSHW59 -3.343 -1.860

RSHW10 -4.134 -1.726

NHORZ 0.302 0.105

MINHLMI -6.544 -2.777

MAXHDEL 0.066 0.026

MAXVCRVG 0.208 0.156

ŝ⊂໕ᨱᖁ10ft ᯕᔢ᮹Ğᬑa5-9ft(150~270cm)Ğᬑᅕ݅ᔢݡ

⬉ŝaᵥᨕऽ۵äᮝಽᅕᯕ۵ߑ, ᔍ⫭ᱢእᬊ॒᮹Ğᱽᱢ⊂໕ᨱ ᕽ 5-9ft᮹ ʙᨕˉ ⡎ᮥ aḥ ʙᨕˉa ޵ᬒ ⬉ᮉᱢᯥᮥ ᦭ ᙹ

ᯩ݅.

᪅ෙ἞ʙᨕˉ⡎᮹Ğᬑࠥ, ᫝἞ʙᨕˉ⡎ŝษ₍aḡಽ2-ft Ǎeᮡ ᮁ᮹⦹ḡ ᦫᮡ đŝෝ ᅕᯕ۵ ၹ໕, ӹນḡ Ğᬑᨱᕽ۵

ᮁ᮹⦽đŝaࠥ⇽ࡹᨕ᪅ෙ἞ʙᨕˉ᮹⡎ᯕմᨕḩᙹಾᔍŁၽ ᔾᮡᵥᨕऽ۵ᔍᝅᮥᅕᯙ݅. 5-9ft⡎᮹Ğᬑᨱᕽ⠪Ɂsŝ⢽ᵡ⠙

₉a☖ĥᱢᮝಽᮁ᮹⧉ᮥᅕᩍ, bǍeษ݅݅ෙsᮥaḱᮥ

᦭ᙹᯩᮝ໑, Ñ᮹ݡᇡᇥ᮹Ǎe(99.6%)ᨱᕽᔍŁÕᙹaqᗭ⦹

۵äᮥ᦭ᙹᯩ݅. ⦽ĥ⬉ŝ⊂໕ᨱᕽ۵᫝἞ʙᨕˉ⡎᮹Ğᬑ᪡

ݍญ10-ftᯕᔢ᮹ʙᨕˉ⡎ᮥaḥǍeᨱᕽ۵ᔍŁqᗭᨱݡ⦽

⬉ŝa۹ᨕӹÑӹ(FPM᮹Ğᬑ), ᔢݡᱢ⬉ŝⓍʑa᫝἞ʙᨕˉ ᮹ Ğᬑᅕ݅ ᳑ɩ ᵥᨕे(RPM᮹ Ğᬑ)ᮥ ᦭ ᙹ ᯩ݅. ࠥಽ᮹

᫝἞ʙᨕˉ⡎ŝݍญ᪅ෙ἞ʙᨕˉ⡎ᨱ۵ᗮࠥᱽ⦽॒᮹⢽ḡ❱,

᜽ᖅྜྷ ⪚ᮡ ݉ᗮᮥ ᭥⦽ ᙽₑ₉॒᮹ ∊࠭ᔍŁෝ ᮁၽ᜽┍ ᙹ

ᯩ۵ ᯙᯱa ᳕ᰍ⦹ʑ ভྙᨱ մᮡ ᨕˉ⡎ᯕ ᔍŁqᗭ ⬉ŝᨱ

ⓑ ᩢ⨆ᮥ ၙ⋁äᮝಽ ᔍഭࡽ݅.

Ǎeԕᨱ ᳕ᰍ⦹۵ ⬂݉łᖁ᮹ }ᙹ᮹ Ğᬑ, łᖁ᮹ }ᙹa

᷾a⧁ᙹಾ ᔍŁÕᙹࠥ ᷾a⧉ᮥ ᅕᩍᵡ݅. ၹ໕, ᳦݉ łᖁ᮹

}ᙹ۵☖ĥᱢᮝಽᮁ᮹⦹ḡᦫᮭᮥӹ┡ԕᨕƱ☖ᔍŁၽᔾᨱ۵

⬂݉łᖁ᮹ Ğᬑa ޵ ฯᮡ ᩢ⨆ᮥ ᵝ۵ äᮥ ᦭ ᙹ ᯩ݅.

Ṉᮡ⬂݉łᖁ᮹ʙᯕaʙᨕḱᨱ঑௝ᔍŁၽᔾᮥqᗭ᜽┅۵

äᮝಽӹ┡ԍ݅. ྜྷುǍeԕᨱᕽ1-mile(1.609km) ʙᯕ᮹⬂݉

łᖁ᮹݉᭥᷾a۵⩥ᝅᱢᮝಽᇩa܆⦹ḡอ, əᨱ঑ෙ⦽ĥ⬉ŝ

⊂໕ᨱᕽ۵ Ʊ☖ᔍŁᨱ ݡ⦽ qᗭ⬉ŝෝ ᅕᩍᵡ݅.

Ǎeԕᨱ᳕ᰍ⦹۵⬂݉łᖁ᮹↽ݡƱb᮹Ğᬑ, Ʊb᮹Ⓧʑa

᷾a⧁ᙹಾƱ☖ᔍŁၽᔾᨱᩢ⨆ᮥᵝ۵äᮝಽӹ┡ԍ݅. ᯕ۵

⬂݉łᖁǍe᮹Ʊbᯕ᷾a⧁ᙹಾłᖁǍe᮹ࠥಽᖁ⩶᮹⩶┽

aḢᖁ⪵ࢉᨱ঑ෙ₉పᗮࠥ᮹᷾aᨱ঑ෙᩢ⨆ᮝಽ❱݉ࡽ݅.

঑௝ᕽ, ࠥಽǍeԕᨱᕽ⬂݉łᖁ᮹↽ݡƱbၽᔾᮥ↽ᗭ⪵⦹۵

ႊ⨆᮹ ᖅĥa ⦥᫵⧁ äᯕ݅.

↽ݡ᳦݉Ǎ႑᮹Ğᬑ, ᱩݡsᮝಽᔑ⇽ࡹᨩᮝ໑, Ǎ႑a᷾a⧁

ᙹಾᔍŁÕᙹࠥ᷾a⧉ᮥᅕᩍᵡ݅. ᳦݉Ǎ႑a1ⰺ᷾a⧉ᨱ঑௝

ᕽᔍŁၽᔾᨱ۵FPMᨱᕽ۵0.208, RPMᨱᕽ۵0.156᮹᷾aᨱ

ᩢ⨆ᮥ ၙ⊹۵ äᮝಽ ӹ┡ԍ݅.

4.3 ࡦ෴ण֗

FPM ༉⩶ŝRPM ༉⩶᮹⇵ᱶsእƱෝ᭥⧕3aḡႊჶᮝಽ

⇵ᱶsᮥ እƱ⦹ᩡ݅. RMSEෝ ᱽ᫙⦽ ⇵ᱶᨱᕽ۵ ၙእ⦹ḡอ

ᅕ݅ ӹᮡ ⇵ᱶsᮥ ᅕᯥᮥ ᦭ ᙹ ᯩ݅.

Table 5. Prediction Accuracy

FPM RPM

RMSE (Root Mean Seuare Mean) 18.01 13.13 MAPE (Mean Absolute Perchange Error) 0.00332 0.00322

MAE (Mean Absolute Error) 5.473 5.429

5. đುၰ⨆⬥ᩑǍŝᱽ

ᯕჩᩑǍᨱᕽ۵ʑ᳕ᨱᔍᬊࡹ޹ᯝၹᱢᯙᮭᯕ⧎༉⩶ᨱᕽ

ᅕ݅ၽᱥࡽ⩶┽᮹⪶ශᱢ༉ᙹෝŁಅ⦽ᮭᯕ⧎༉⩶ᮥᱽ᜽⦹ᩍ

Ʊ☖ᔍŁ᪡ʑ⦹Ǎ᳑᪡᮹šĥෝ❭ᦦ⦹ᩡ݅. ʑ᳕᮹ᮭᯕ⧎༉⩶

ᮡbࠥಽǍeᨱᖅ⊹ࡽʑ⦹Ǎ᳑᮹᳦ඹၰᖅ⊹⩶┽a࠺ᯝ⦹ḡ

ᦫᮭᨱࠥᇩǍ⦹Ł, Ǎe᮹ᯕḩᖒᮥŁಅ⦹ḡ༜⦽݉ᱱᮝಽᯙ⧕

ᔍŁᩩ⊂᜽ᔍŁ᮹ᩩ⊂sᨱݡ⦽ᇩ⪶ᝅᖒ(uncertainity)᪡ᯥ᮹ ᖒ(randomness)ᮥԕ⡍⦹Łᯩᨩ݅. ᯕ్⦽ᯕᮁಽ, }ᖁᯕ⦥᫵⦽

Ǎeᯕ⚍ᯱᬑᖁᙽ᭥ᨱᕽၡಅӹ, ᱢᱩ⦽ᩩᔑᯕᇥ႑ࡹḡ༜⦹ᩍ

}ᖁ ᔍᨦᯕ ᱽভ ᯕ൉ᨕḡḡ ༜⦹۵ ᬱᯙᯕ ࡹʑࠥ ⧩ᨩ݅.

ᯕෝ⧕đ⦹ʑ᭥⦽ႊჶᮝಽᯕᩑǍᨱᕽ۵Ǎe᮹ᯕḩᖒᮥ

Łಅ⦹ᩡᮝ໑, ࠥ⇽ࡽ༉⩶᮹đŝ۵እƱෝ᭥⧕ʑ᳕ᨱᔍᬊࡹᨩ

޹ᯝၹᱢᯙᮭᯕ⧎ŝ⧉̹ᱽ᜽ࡹᨩ݅. ༉⩶᮹ᖅ໦ಆᮡʑ᳕᮹

ᮭᯕ⧎༉⩶ᨱእ⧕׳ᮡäᮝಽӹ┡ԍ݅. ⅾ16}᮹Ʊ☖ప, Ǎe

šಉࡽᄡᙹॅᯕᔍᬊࡹᨩ݅. ᯕᵲ, 8}᮹ᄡᙹabǍeษ݅

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݅ෙ✚ᖒᮥӹ┡ԕ۵ᯕḩᖒᮥaḡ۵äᮝಽӹ┡ԍᮝ໑, ӹນḡ

8}᮹ᄡᙹ۵bǍeᨱšĥᨧᯕ࠺ᯝ⦽✚ᖒᮥӹ┡ӹ۵ᄡᙹಽ

ӹ┡ԍ݅. Ǎe᮹ʙᯕ, Ʊ☖ప, ₉ᖁᙹ(3, 4₉ᖁ), ᫝἞ʙᨕˉ⡎

(3-4, 10ftᯕᔢ - 90~120, 300cmᯕᔢ), ᪅ෙ἞ ʙᨕˉ⡎(5-9ft - 150~270cm), Ǎeԕ᳦݉łᖁ᮹↽ݡǍ႑aᯕḩᖒᮥaḡ۵

ᄡᙹಽࠥ⇽ࡹᨩ݅. ₉ᖁᙹ᮹Ğᬑ, 4₉ᖁᨱᕽ5₉ᖁᯕᔢᮝಽᄡ⦹

۵ Ğᬑ, ᔍŁqᗭᨱ ၙ⊹۵ ᩢ⨆ᯕ ᔢݡᱢᮝಽ ᵥᨕऽ۵ äᮥ

᦭ ᙹ ᯩᨩ۵ߑ, ᯕ۵ ₉ᖁᙹ᮹ ᷾aᨱ ঑ෙ እᬊŝ ⧉̹ əᨱ

঑ෙᔍŁእᬊ⊂໕ᨱᕽᅕ݅ᯱᖙ⦽ᩑǍa⦥᫵⧁äᮝಽᔍഭࡽ

݅. ᯕ్⦽✚ᖒᮡʙᨕˉ⡎ᨱᕽࠥӹ┡ԍ۵ߑ, ₉ᖁᙹ᪡ษ₍aḡ ಽ እᬊ-ᯕᯖ⊂໕ᨱᕽ᮹ ᩑǍa ⦥᫵⧁ äᯕ݅. ੱ⦽, ࠥಽÕᖅ

⪚ᮡʑ⦹Ǎ᳑᮹ᄡĞ᜽, ᯱᩑ⪹Ğ᮹ᱽ᧞॒ᮝಽᯙ⧕ʑᵡᨱ

ၙ⊹ḡ༜⦹۵ʑ⦹Ǎ᳑aÕᖅࡹᨕ᧝⧁Ğᬑ, ↽ݡ⦽᮹ᦩᱥᖒᮥ

Łಅ⧁ ᙹ ᯩ۵ ʑ⦹Ǎ᳑᮹ ḡ⋉ᯕ ࢁ ᙹ ᯩᮥ äᯕ݅.

ᯕᩑǍ۵ᦩᱥᇥ᧝ᨱᕽᮁ᮹⦽đŝaࠥ⇽ࡽ݅Ł❱݉ࡹ۵

5֥࠺ᦩ᮹ᔍŁᯱഭᅕ݅⭉ᦍ᪅௽ʑe࠺ᦩ᮹ᔍŁᯱഭaᯕᬊࡹ

ᨕ༉⩶᮹ᖅ໦ಆᯕ ׳ᦥᲭᮭᨱࠥᇩǍ⦹Łࠦพᄡᙹಽᔍᬊࡽ

ʑ⦹Ǎ᳑᮹Ğᬑ, əᄡ⪵ෝๅ֥⇵ᱢ⦹ʑᨱ۵ᯱഭ᮹ᙹḲ॒ᨱ

ၰ ᬕᱥᯱ✚ᖒ(ᖒᄥ, ӹᯕ, ᮭᵝ ॒)ᨱ šಉࡽ ᯱഭa ᱢᬊࡹḡ

༜⦹ᩡ݅. ᯕ༉ुᯱഭaᙹḲࡹʑᨱ۵ᅕ݅ฯᮡእᬊŝ᜽eᯕ

ᗭ᫵ࡹāḡอ, ĥᗮᱢᯙיಆᯕ᫵Ǎࡹ໑, ᯕ్⦽ᯱഭaᯕᬊa܆

⦹݅໕, Ʊ☖ᔍŁᐱอᦥܩ௝, እᬊ-⬉ŝᱢ⊂໕ᨱᕽ᮹ʑ⦹Ǎ᳑

ḡ⋉ᨱݡ⦽ᅕ݅ᯱᖙ⦹Łᖙၡ⦽ᩑǍᨱฯᮡࠥᬡᯕࢁäᯕ݅.

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