Conjoint Analysis Gp 1

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1 Klaus Goepel..00 The presentation explains the principle, using a simple example. It shows, how to calculate the part-worth utilities and how to derive the relative preferences from individual attributes from there. A full factorial and a fractional factorial design is used. An Excel template for this example is available from the author. Conjoint analysis or Stated preference analysis is a statistical technique that originated in mathematical psychology...00 Gp

2 Keywords conjoint analysis, stated preference analysis, linear regression, product management, marketing, part-worth, utilities, relative preference, statistics, analytic hierarchy process, AHP Today it is used in many of the social sciences and applied sciences including -Marketing, - Product management, - Operations research. Buying a smart phone, MP player a b Your Preference The preference for a combination of (conjoint) attributes will reveal the partworth of individual attributes. Attribute : Memory Attribute : Delivery Attribute : Memory Attribute : Delivery..00 Gp

3 Buying a smart phone, MP player a b The preference for a combination of (conjoint) attributes will reveal the partworth of individual attributes. Higher emphasis on short delivery time. Higher emphasis on large memory size Buying a smart phone, MP player Part-worth utilities of individual attributes are calculated based on the ranking of a defined set of combinations of attribute values...00 Gp

4 Buying a smart phone, MP player Attributes: Color green, red Models: Memory Delivery MB, MB day, week Levels: -; + Example Buying a smart phone Green, MB, week Red, MB, week Green, MB, day Red, MB, day Attribute values are coded with - and + Attribute : Color Green, MB, week Green, MB, day Attribute : Memory Attribute : Delivery Red, MB, week Red, MB, day Sequence Conjoint Attributes Color Memory Delivery Green, MB, week Red, MB, week Green, MB, week Example Buying a smart phone Red, MB, week - Green, MB, day Red, MB, day Green, MB, day Attribute values are coded with - and + Attribute : Color Attribute : Memory Attribute : Delivery Red, MB, day..00 Gp

5 Full factorial design Design Matrix k attributes: k combinations Design Matrix k attributes: k possible combinations Full factorial Design X X X delivery X X X memory color Representation of Combinations Full factorial Design X: Color = (+,-) X: Memory = (+,-) X: Delivery = (+,-)..00 Gp

6 Sequence Conjoint Attributes X X X Green, MB, week Red, MB, week Green, MB, week ing of combinations Red, MB, week - Green, MB, day Red, MB, day Green, MB, day X: Color = (+,-) X: Memory = (+,-) X: Delivery = (+,-) Red, MB, day Linear model function with part-worth utilities ing = part-worth of attribute * attribute level + part-worth of attribute * attribute level + part-worth of attribute * attribute level + baseline preference Y = β color *X + β memory *X + β delivery *X + µ Linear Model Function The system of linear equations can be solved with linear regression X: Color = (+,-) X: Memory = (+,-) X: Delivery = (+,-)..00 Gp

7 Part-worth utilities = - * β Color + - * β Memory + - * β Delivery + µ - - Linear Model Function The system of linear equations can be solved with linear regression X X X Representation of Combinations Gp

8 X X X Representation of Combinations - Calculating Part-worth Utilities X β Color = -0. Main effect X - β Col = ¼ [ - 0] = -0. X X X Representation of Combinations - Calculating Part-worth Utilities X Main effect X β Color = -0. β Memory = - β Mem = ¼ [0 - ] = Gp

9 X X X Representation of Combinations - Calculating Part-worth Utilities X Main effect X β Color = -0. β Memory = - β Delivery = - β Del = ¼ [ - ] = - Part-worth utilities β Color = -0. Representation of Combinations β Mem = - β Del = - Calculating Part-worth Utilities β Color = -0. β Memory = - β Delivery = Gp 9

10 Actual ranking and description with linear model function 9 Model ing and Model Function 0 week week week week day day day day MB MB MB MB MB MB MB MB green red green red green red green red β Color = -0. β Memory = - β Delivery = - Actual ranking and description with linear model function 9 Model ing and Model Function 0 week week week week day day day day MB MB MB MB MB MB MB MB green red green red green red green red β Color = -0. β Memory = - β Delivery = - Y =. -0. X color - X Memory - X Delivery..00 Gp 0

11 Variations for X i =± ± β Col = ±0. = Calculating relative preferences ± β Mem = ± = ± β Del = ± = Color = % Memory = % Delivery = 9% AHP Attributes Part-worth Utilities Levels ing Criteria, Sub-criteria - comparison Weights: Principal Eigenvector Ratio Scale, relative Scale Evaluation of Alternatives & Analytic Hierarchy Process AHP k Combinations k=: possible combinations k k Comparisons k=: pair-wise comparisons..00 Gp

12 X X X Fractional Design X X X Fractional Design - - Representation Gp

13 X X X - - Fractional Design - - Representation Fractional design - III ± = X X X Fractional Design - - Representation - Fractional design..00 Gp

14 Fractional factorial design k-p X X X Fractional Design - - Representation X Calculating Part-worth Utilities β Color = -0. Main effect X ½ [(+) (+)] = -0. Fractional factorial design k-p X X X Fractional Design - - Representation X Main effect X Calculating Part-worth Utilities β Color = -0. β Memory = - ½ [(+) (+)] = Gp

15 Fractional factorial design k-p X X X Fractional Design - - Representation X Main effect X Calculating Part-worth Utilities β Color = -0. β Memory = - β Delivery = - ½ [(+) (+)] = - Fractional Design Using a fractional factorial design the number of attribute combinations can be reduced...00 Gp

16 Simple conjoint analysis can be done with linear regression, but more sophisticated statistical models and solutions are available...00 Gp