XBOX 實例

Discrete Choice Analysis-- Random Utility Theory

100 people were shown eight Price Scenarios fo r XBOX, PlayStation(PS), and Wii.

Each person was asked which product they would buy (or none) for the given prices.

Relative Importance of Brand and Price

Choice# XBOX PS WIIPick XBOX

Pick PS

Pick WII

Pick nothing

1 $221 $267 $275 28 11 14 472 $193 $295 $275 38 1 14 473 $278 $294 $176 10 2 43 454 $288 $191 $250 2 44 10 445 $162 $224 $221 30 16 17 376 $172 $249 $157 23 15 24 387 $167 $251 $169 24 12 25 398 $213 $255 $158 21 25 9 45

Value

Value Xbox = Xbox brand weight + (Xbox price) * (Xbox price sensitivity)

Value PS = PS brand weight + (PS price) * (Xbox price sensitivity)

Value Wii = Wii brand weight + (Wii price) * (Xbox price sensitivity)

Weight for nothing =0, Value of Nothing = 0

How to apply Discrete Choice Analysis to estimate brand weight and price sensitivity ?

Excel Impelmentation

Decision Variables(B4:E5):

Objective Function(S5):

Max(Sum of Utility )

Score

Value Xbox = Xbox brand weight + (Xbox price) * (Xbox price sensitivity)

Probability

EXP(Value Xbox)/

(EXP(Value Xbox)+ EXP(PS)+EXP(Wii)

Brand1.878

9 4.967 0.489price -0.012 -0.024 -0.01

sum-984.7550485

XBOX score

PS Score

WII Score

Nothing Score

-0.882 -1.5539 -1.2175 0-0.532 -2.2376 -1.2175 0

-1.594 -2.2132-

0.60319 0

-1.7190.3021

4-

1.06238 0

-0.145 -0.5038-

0.88243 0-0.27 -1.1143 -0.4853 0

-0.207 -1.1631-

0.55976 0-0.782 -1.2608 -0.4915 0

XBox prob PS prob

WII Prob

Nothing Prob

0.2155 0.11004 0.1540.52044

9

0.29520.05362

1 0.14870.50249

6

0.10920.05880

4 0.29420.53776

7

0.06230.47008

7 0.12010.34750

4

0.30010.20957

8 0.14350.34683

4

0.28210.12121

3 0.22740.36937

8

0.30140.11588

8 0.21190.37082

9

0.19450.12047

1 0.26 0.42505

Utility

#Xbox*LN(Prob of box)+#PS*LN(Prob of PS)+#Wii* (Prob of Wii)+#Nothing*(LN(Prob of Nothing)

Ln(Likelihood)-124.1354628-108.3181076-108.3357813-106.4650498-133.2964867-134.1584807-132.1271517

-137.918528

cost $180 $160 $155

Nothing

Brand1.878

9 4.967 0.489 0price -0.012 -0.024 -0.01