MAKING MAXDIFF MORE INFORMATIVE: STATISTICAL DATA FUSION BY WAY OF LATENT VARIABLE MODELING LYND BACON !"#$"%&'"()*+,-)./0)!120 PETER LENK 3,+'4+!0-"3305#3)!+330314""(06,0,4+0#!)%+-3),!0"70*)14)$6!00 KATYA SERYAKOVA 8!"9(+:$+0!+,9"-83/0)!120 ELLEN VECCIA 8!"9(+:$+0!+,9"-83/0)!120 0

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Correlation True vs RIMEX True vs MaxDiff True vs LR Skew RIMEX vs MaxDiff RIMEX vs LR Skew MaxDiff vs LR Skew RMSE True vs RIMEX True vs MaxDiff True vs LR Skew RIMEX vs MaxDiff RIMEX vs LR Skew MaxDiff vs LR Skew

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D75'5";R"w"s"w";V"$'5"*75"18*B&)+*0>"?+"*75"(&2)*"#&45(@"O")0"*75"18#8($*)C5"4)0*')98*)&+" ,8+1*)&+",&'"*75"')27*60E5D54@"5.*'5#5"C$(85"4)0*')98*)&+")+",&&*+&*5"c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d" 2 " ? = ! ?@A !?@A % D?@A

" ? % Gz P ? = F ?

"

D75'5" R> k)%E")0"089%51*")A0"($*5+*"8*)()*3",&'"B'&,)(5"E")+"17&)15"*$0E"%" I> .)%E"")0"*75"450)2+"C51*&'",&'"B'&,)(5"E>" [> !)%E")0"*75"'$+4&#"*5'#"5)*75'",'&#"$"')27*60E5D54@"5.*'5#5"C$(85"4)0*')98*)&+":(&2)*" #&45(="&'"#8(*)C$')$*5"+&'#$("4)0*')98*)&+":B'&9)*"#&45(=>" c> _)")0"$"089%51*6(5C5("1&C$')$*5W"G")0"$"#$*')."&,"'52'500)&+"1&5,,)1)5+*0@"$+4"F)")0"$" #8(*)C$')$*5"+&'#$("5''&'"*5'#"D)*7"#5$+"J"$+4"1&C$')$+15"H>"" G5"805"0*$+4$'4"B')&'0",&'"*75"B$'$#5*5'0":L55"Q5+E"$+4"""F75"#&45("1&8(4"95"5$0)(3"#&4),)54",&'"*75"&')2)+$("-$./),,",&'#8($*)&+"&'"*75" ;&75+N^'#5"$BB'&$17>" F75"E53"*&"'51&C5')+2"*75"1&##&+"&')2)+")0"#&C)+2"*75"0*$+4$'4")45+*),)1$*)&+" 1&+0*'$)+*0",'&#"*75"17&)15"*$0E"*&"*75"'$*)+20"#&45(>""G5"4&"+&*"1&+0*'$)+"*75"B$'*D&'*70" m")n@"$+4"D5"4&"+&*"$008#5"*7$*"*75"01$(5"B$'$#5*5'":(&2)*="&'"$"C$')$+15":B'&9)*=",&'"*75" '$+4&#"*5'#"m!)%En")0"&+5>""?+0*5$4@"D5"$008#5"*7$*"&+5"&,"*75"mA#n")0"_5'&@"$+4"&+5"&,"*75" 4)$2&+$("5(5#5+*0"&,"C")0"&+5>"""

338

"

4. APPLICATIONS Q5+E"$+4"""V5'5@"D5"B'505+*"*D&" $BB()1$*)&+0"*7$*")((80*'$*5"*75"B'$1*)1$("95+5,)*0"'5*$)+)+2"$"1&##&+"&')2)+",&'"089%51*0A" 8*)()*3"01$(50")+"&'45'"*&"1&#B$'5"089%51*0"&+"*75)'"B'5,5'5+15"0*'81*8'50>"" 4.1 Educational Goals

!"0*843"&+"*75")#B&'*$+15"&,"5)27*"5481$*)&+$("2&$(0"7$4"RcKJ"089%51*0"9&*7"'$*5"*75" )#B&'*$+15",&'"5$17"2&$(@"$+4"*75+"B5',&'#"$"950*ND&'0*"*$0E"1&+0)0*)+2"&,"e"17&)15"05*0"D)*7" *7'55"2&$(0"B5'"17&)15"05*>""G)*7&8*"'$*)+20"4$*$@"D5")45+*),3"*75"#&45("93"$008#)+2"*7$*"*75" 8*)()*3",&'"f&$("e")0"_5'&>"G5",)**54"*75"#&45("D)*7"%80*"*75"950*ND&'0*"4$*$"$+4"D)*7"9&*7"*75" 950*ND&'0*"$+4"'$*)+20"4$*$>""!(0&@"D5",)**54"9&*7"(&2)*"$+4"B'&9)*"#&45(0@"D7)17"2$C5"0)#)($'" '508(*0>""G5"D)(("'5B&'*"*75"'508(*0",&'"*75"B'&9)*"#&45(>"""G5"D)(("+&*"'5B&'*"$(("&,"*75" 50*)#$*50"&,"*75"B$'$#5*5'")+"L51*)&+"c@"$+4"D5"D)(("&+(3",&180"&+"*75"50*)#$*54"B$'*D&'*70>" O)28'5"c"B(&*0"*75"50*)#$*54"B$'*D&'*70",&'"*75"*D&"#&45(0d"*75".6$.)0")0",&'"*75"0*$+4$'4" -$./),,"#&45("D)*7&8*"'$*)+20"$+4"*75"36$.)0")0"&8'"B'&B&054"#&45(>"""F75"2'$B7"07&D0"*7$*" D)*7"$"1&##&+"&')2)+@"089%51*0"$'5"4)0*)+28)0754"93"*75"$90&(8*5"8*)()*3"5C$(8$*)&+0>"""G5" 5#B7$0)_5"*7)0"B&)+*"93"052#5+*)+2"*75"089%51*0")+*&"*7'55"*)5'0>""F75"*&B"*)5'"1&+0)0*0"&," 089%51*0"D)*7"*7'55"&'"#&'5"B$'*D&'*70"*7$*"$'5"2'5$*5'"*7$+"u@"$+4"*75"9&**&#"*)5'"1&+0)0*0"&," 089%51*0"D)*7"*7'55"&'"#&'5"B$'*D&'*70"(500"*7$+"R>Z>""F75'5"$'5"$BB'&.)#$*5(3"IJ{"&,"*75" 089%51*0")+"5$17"&,"*75"*&B"$+4"9&**&#"*)5'0>""F75"*&B"*)5'"'5B'505+*0"089%51*0"D7&"$'5"7)27(3" 1&+15'+54"D)*7"5481$*)&+@"D7)(5"*75"9&**&#"*)5'")0"+&*>""O)28'5"Z"B'505+*0"9&.B(&*0"&,"*75" B$'*D&'*70",&'"*75"*7'55"*)5'0"D)*7"'$*)+20"$+4"D)*7&8*"'$*)+20>""F75"9&.B(&*0"07&D"*75" B$'*D&'*70")+1'5$0)+2"*7'&827"*75"*)5'0"D75+"*753"$'5"50*)#$*50"D)*7"*75"'$*)+20@"98*"*753"$'5" ,($*"D75+"50*)#$*54"D)*7&8*"'$*)+20>"" O)28'5"c>" ]0*)#$*54"B$'*D&'*70",&'"5481$*)&+$("2&$(0"D)*7"$+4"D)*7&8*"'$*)+20>"" 8

6

QUESTION 4

Q8

Partworths with Ratings

Q7 2

Q6 Q5

0 Q4 Q3

-2

Q2 Q1

-4 -4

-3

-2

-1

0

Partworths w/o Ratings: Q8 = 0

1

2

3

" 339

"

" O)28'5"Z" ""F75" B$'*)1)B$+*0"D5'5"IRJ"-""F7505"089%51*0"'$*54"IJ"B'&,)(50" &+"$"J"*&"RJ"Q)E5'*"01$(5",&'"*75"()E5()7&&4"&,"B8'17$05@"$+4",&'"5$17"B'&,)(5@"*753"$(0&" )+4)1$*54""""G5"805"$"*7'507&(4" #&45(",&'"*75"4)01'5*5"17&)15"*$0E"D75'5"089%51*")"05(51*0"`a"" O&'"5.$#B(5@"),"*75"089%51*"$('5$43"&D+0"$"g;@"*75+"")F"1$+"95")+*5'B'5*54"$0"*75"8*)()*3",&'" *7$*"g;>""?+"0*$+4$'4"9)+$'3"17&)15"#&45(0"D)*7&8*"'$*)+20@"*75"8*)()*3"&,"*75"&8*0)45"2&&4")0" $008#54"*&"95"J>""?+"&8'",80)&+"#&45(@"D5"$'5"$9(5"*&"05B$'$*5(3"50*)#$*5"9&*7"*75"8*)()*3"&," *75"&8*0)45"2&&4"$+4"*75")+*5'15B*@"D7)17")0"*75"8*)()*3"&,"*75"`$C5'$25a"g;")+"*75"0*843"0)+15" D5"805"5,,51*0"1&4)+2",&'"*75"9)+$'3"$**')98*50>""" O)28'5"u"4)0B($30"9&.B(&*0"&,"*75"B$'*D&'*7"75*5'&25+5)*3",&'"*75"#&45(0"D)*7"$+4" D)*7&8*"*75")#B&'*$+15"'$*)+2"4$*$>""G)*7")#B&'*$+15"'$*)+2":')27*67$+4"B$+5(=@"*75"B$'*D&'*7" ,&'"*75"&8*0)45"2&&4":*75"*7'507&(4="$+4"*75"`$C5'$25"g;a":*75")+*5'15B*="$'5"05B$'$*5(3" 50*)#$*54@"D7)(5"*753"$'5"1&+,&8+454",&'"*75"#&45("D)*7&8*"'$*)+20>""O)28'5"K"0&'*0"089%51*0" $11&'4)+2"*&"*75)'"8*)()*3"&,"*75"&8*0)45"2&&4"$+4"08B5')#B&054"*75"B')15"B$'*D&'*7>""F75" 1&''5($*)&+"95*D55+"*75"B$'*D&'*70",&'"B')15"$+4"*75"&8*0)45"2&&4")0"TJ>[Ku>""F75"B(&*"07&D0" *7$*"*75"089%51*0"D)*7"0#$((5'"8*)()*)50"&,"&8*0)45"2&&40"$(0&"*5+4"*&"95"(500"B')15"05+0)*)C5@" $+4"1&+C5'05(3>""F7)0")#B()50"*7$*"089%51*0"D7&"&D+"$",$)'(3"2&&4"g;"'5U8)'5"$+"&8*0*$+4)+2" 45$("*&"983"$"+5D"g;@"D7)(5"089%51*0"D)*7"(&D"8*)()*3",&'"*75"&8*0)45"2&&4"$'5"D)(()+2"*&"B$3" #&'5>"

340

"

O)28'5"u>" g;"450)2+"0*843d"9&.B(&*0"&,"*75"75*5'&25+5)*3")+"*75"50*)#$*54"B$'*D&'*70">" F75"50*)#$*50"D)*7&8*"'$*)+20")0"*75"(5,*67$+4"B$+5(@"$+4"*75"#&45("D)*7"" '$*)+20")0"*75"')27*67$+4"B$+5(>" 3

4

2

3

1

2

0

1

-1

0 -2

-1

Software

Guarantee

Warrantee

Color

Channel

CD

Cache

CPU

Hard Disk Size

RAM

Screen Size

Price

-4 Threshold

Software

-3

Guarantee

Warrantee

Color

Channel

CD

Cache

CPU

Hard Disk Size

RAM

Screen Size

Price

Hot Line

Intercept

-6

Hot Line

-5

-2

Intercept

Part-worths

-4

Threshold

Part-worths

-3

"

"

O)28'5"K>" g;"450)2+"0*843d""089%51*0"$'5"0&'*54"93"*75)'"8*)()*)50",&'"*75"&8*0)45"2&&4>" " Threshold

Price

4

Part-worth

2 0 -2 -4 -6

201

191

181

171

161

151

141

131

121

111

101

91

81

71

61

51

41

31

21

1

11

-8 Subject Sorted by Threshold

"

5. CONCLUSION F75"B8'B&05"&,"*7)0"B$B5'")0"*D&,&(4d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

341

"

"

B0317&(&2)1$("9)$050")+75'5+*")+"'$*)+20@"$0"1&#B$'54"*&"17&)150@"$+4"01$(5"80$25"9)$050",&'" '$*)+20>""?+"*D&"4$*$05*0"D5"45#&+0*'$*5"*7$*"'51&C5')+2"$"1&##&+"&')2)+")+1'5$050"*75"8*)()*3" &,"17&)1569$054"5.B5')#5+*0>""

REFERENCES !(95'*"H"V"$+4";7)9"L":RSS[=>"`" !)*17)0&+"H"$+4"L)(C5'3"L/":RSZK=>"`F75"25+5'$()_$*)&+"&,"B'&9)*"$+$(30)0"*&"*75"1$05"&," #8(*)B(5"'50B&+050@a"5?NLGBO?A;@"cc@"H8+5@"R[R6RZJ>" "`!00500)+2"*75"B&*5+*)$("45#$+4",&'"5(51*')1" 1$'0@a"QN>OR;F0NH0+SNRNLGBO?S=@"RK@"(6IJ>" "`;&#B$'$*)C5"%842#5+*0"$0"$+"$(*5'+$*)C5"*&"'$*)+20d?45+*),3)+2"*75" 01$(5"&')2)+@a"'=TSMNFNU?S;F0*GBMNK=@"S":c=@"cZ[6cuZ>" ;7$B#$+@"X"f"$+4"L*$5()+"X":RSeI=>"`].B(&)*)+2"'$+E"&'45'54"17&)15"05*"4$*$"D)*7)+"*75" 0*&17$0*)1"8*)()*3"#&45(@a"QN>OR;F0NH0*;OAGB?RU0-G=G;OSM@"RS":[=@"!82@"Iee6[JR>" ;&75+@"L*5C5":IJJ[=>"`-$.)#8#"/),,5'5+15"L1$()+2d"?#B'&C54"-5$08'50"&,"?#B&'*$+15"$+4" g'5,5'5+15",&'"L52#5+*$*)&+@a"VWWX03;JBNNBM03NHBJ;OG01NRHGOGRSG0'ONSGGK?RU=@"L5U8)#@" G!>"" ;&75+@"L>"P"^'#5@"":IJJc=>"`G7$*A0"3&8'"B'5,5'5+15|a"*;OAGB?RU0-G=G;OSM0*;U;P?RG/" L8##5'@"[I6[K>" ;&75+@"L>"P"\5)'$@"Q>":IJJ[=>"`-5$08')+2"B'5,5'5+15",&'"B'&481*"95+5,)*0"$1'&00"&8+*')50d" ^C5'1&#)+2"01$(5"80$25"9)$0"D)*7"#$.)#8#"4),,5'5+15"01$()+2>a""g$B5'"B'505+*54"$*"*75" Q$*)+"!#5')1$+"1&+,5'5+15"&,"*75"]8'&B5$+"0&1)5*3",&'"&B)+)&+"$+4"#$'E5*)+2"'505$'17@" g8+*$"45("]0*5@"Y'828$3":BB>"RTII=>"X5B')+*54")+"+DSGFFGRSG0?R0)RBGOR;B?NR;F0-G=G;OSMd" IJJc>"]L^-!X@"!#0*5'4$#@"\5*75'($+40@"IJJc>" O)++"!"$+4"Q&8C)5'5"H"H":RSSI=>"`/5*5'#)+)+2"*75"$BB'&B')$*5"'50B&+05"*&"5C)45+15"&,"B89()1" 1&+15'+d"F75"1$05"&,",&&4"0$,5*3@a"QN>OR;F0NH0'>"$+4"g(&**@";>"":RSKS=>"`]1&+&#)1"*75&'3"&,"17&)15"$+4"*75"B'5,5'5+15"'5C5'0$(" B75++$@a"6LGO?S;R0+SNRNL?S0-GC?GJ@"uS@"uI[6u[e>" Q5+E@"g"$+4""`]0*)#$*)+2";&##&+"Y*)()*3"^')2)+0"$+4"L1$(50")+"/)01'5*56 ;7&)15";&+%&)+*"D)*7"!8.)()$'3"/$*$@a"D&'E)+2"B$B5'@"F75"Y+)C5'0)*3"&,"-)17)2$+>"" Q5+E@"g>@"/5L$'9&@"G>@"f'55+@"g>@"$+4"k&8+2@"->":RSSu=>"`V)5'$'17)1$("OR;F0NH0+DZGO?LGRB;F0'=TSMNFNUT@"eS@"cu6ZZ>" Q&8C)5'5"H"$+4"G&&4D&'*7"f":RSSJ=>"`":IJJZ=>"`L"B'&9$9)()0*)1"#&45(0"&,"950*@"D&'0*@"$+4" 950*6D&'0*"17&)150@a"QN>OR;F0NH0*;BMGL;B?S;F0'=TSMNFNUT@"cS@"cuc6ceJ>" -1;8((&17@"X"$+4"X&00)"g"]":RSSc=>"`!+"5.$1*"()E5()7&&4"$+$(30)0"&,"*75"#8(*)+&#)$("B'&9)*" #&45(@a"QN>OR;F0NH0+SNRNLGBO?S=@"uc":R6I=@"L5B*6^1*@"IJK6IcJ>" -1O$445+"/":RSKc=>"`;&+4)*)&+$("(&2)*"$+$(30)0"&,"U8$+*)*$*)C5"17&)15"957$C)&'@a"O'&+*)5'0" )+"]1&+*')10@"54"93"g"i$'5#9E$@"!1$45#)1"g'500@"\5D"k&'E@"RJZ6RcI>" \&D()0@"L>"->"$+4"L)#&+0&+@"?>":RSSK=>"`!**')98*56*$0E"1&#B$*)9)()*3"$0"$"45*5'#)+$+*"&," 1&+08#5'"B'5,5'5+15"'5C5'0$(0@a"QN>OR;F0NH0*;OAGB?RU0-G=G;OSM@"[c":I=@"-$3@"IJZ6IRe>" X&00)@"g>"]>@"f)(8($@"i>@"$+4"!((5+93@"f>"->":IJJR=>"`^C5'1&#)+2"01$(5"80$25"75*5'&25+5)*3d"!" "`F75";&+0*'81*)&+"&,"g'5,5'5+15@a"!#5')1$+"g0317&(&2)0*@"ZJ":Z=@"-$3@" [uc6[KR>" L$D*&&*7"L&,*D$'5":IJJZ=>0,MG0*;D:?HH&9G" y')5+0@"->@"^BB5D$(@"V>@"$+4"G545(@"->":RSSe=>"`X$*)+20"9$054"C5'080"17&)1569$054"($*5+*" 1($00"1&+%&)+*"#&45(0"6"!+"5#B)')1$("1&#B$')0&+@a"QN>OR;F0NH0BMG0*;OAGB0-G=G;OSM0 3NS?GBT@"cJ":[=@"H8(3@"I[K6Ice>" "

"

343