# Método conjoint

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Analysis of Traditional Conjoint TM Using Microsoft Excel : An Introductory Example
Bryan K. Orme, Sawtooth Software, Inc., 2002

© Copyright 2002, Sawtooth Software, Inc. 530 W. Fir St. Sequim, WA 98382 (360) 681-2300 www.sawtoothsoftware.com

Analysis of Traditional Conjoint Using ExcelTM: An Introductory Example

In this example, we assume the reader has a basic understanding of multiple regression analysis. A traditional conjoint analysis is really just a multiple regression problem. The respondent’s ratings for the product concepts form the dependent variable. The characteristics of the product (the attribute levels) are the independent (predictor) variables. The estimated betas associated with theindependent variables are the utilities (preference scores) for the levels. The R-Square for the regression characterizes the internal consistency of the respondent. Consider a conjoint analysis problem with three attributes, each with levels as follows: Brand A B C Color Red Blue Price \$50 \$100 \$150 For simplicity, let’s consider a full-factorial experimental design. A full-factorial designincludes all possible combinations of the attributes. There are (3)·(2)·(3) = 18 possible product concepts (commonly called cards) that can be created from these three attributes. Further assume that respondents rate each of the 18 product concepts on a score from 0 to 10, where 10 represents the highest degree of preference.

1

Assume the data for one respondent are as follows (as if in an Excelspreadsheet): A B Card# Brand 1 1 2 1 3 1 4 1 5 1 6 1 7 2 8 2 9 2 10 2 11 2 12 2 13 3 14 3 15 3 16 3 17 3 18 3 C Color 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 D Price 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 E Preference 5 5 0 8 5 2 7 5 3 9 6 5 10 7 5 9 7 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

The first card is made up of level 1 of each of the attributes, or (Brand A, Red, \$50). Therespondent rated that card a “5” on the preference scale. After collecting the respondent data, the next step is to code the data in an appropriate manner for estimating utilities using multiple regression. We use a procedure called dummy coding for the independent variables (the product characteristics). In its simplest form, dummy coding uses a “1” to reflect the presence of a feature, and a “0” torepresent its absence. For example, we can code the Brand attribute as three separate columns. Brand A 1 0 0 Brand B 0 1 0 Brand C 0 0 1

If Brand is “A”, then dummy codes = If Brand is “B”, then dummy codes = If Brand is “C”, then dummy codes =

2

Applying dummy-coding for all attributes results in an array of columns as follows: A Card # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 B A 11 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 C B 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 D C 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 E Red 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 F Blue 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 G \$50 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 H \$100 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 0 I J \$150 Preference 0 5 0 5 1 0 0 8 0 5 1 2 0 7 0 5 1 3 0 9 0 6 1 5 0 10 0 7 1 5 0 9 0 7 1 6

1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 19

Again, we see that card 1 is defined as (Brand A, Red, \$50), but we have expanded the layout to reflect dummy coding. To this point, the coding has been very straightforward. But, there is one complication that must be resolved. In multiple regression analysis, no independent variable may be perfectly predictable based on the state of any other independent variableor combination of independent variables. If so, the regression procedure could not separate the effects of the confounded variables. We have that problem with the data above, since, for example, we can perfectly predict the state of brand A based on the states for brands B and C. This situation is termed linear dependency.

3

To resolve this linear dependency, we omit one column from each...