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Conjoint Model

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Conjoint Model


Conjoint analysis indicates consumer preferences for products with multiple characteristics, wherein these characteristics vary among several categories. For example, the researcher might want to learn consumer preferences for a coffee maker with three characteristics: price (with three levels), number of cups brewed (with three levels), and timed start (yes or no). The task is to determine which of the 3x3x2 = 12 combinations of characteristics is most preferred by consumers.

The Conjoint Model

Conjoint analysis is based on a main effects analysis-of-variance model. Data are collected by asking subjects about their preferences for hypothetical products defined by attribute combinations. Conjoint analysis decomposes the judgment data into components, based on qualitative attributes of the products. A numerical utility or part-worth utility value is computed for each level of each attribute. Large utilities are assigned to the most preferred levels, and small utilities are assigned to the least preferred levels. The attributes with the largest utility range are considered the most important in predicting preference. Conjoint analysis is a statistical model with an error term and a loss function. Metric conjoint analysis models the judgments directly. When all of the attributes are nominal, the metric conjoint analysis is a simple main-effects ANOVA with some specialized
output. The attributes are the independent variables, the judgments comprise the dependent variable, and the utilities are the parameter estimates from the ANOVA model. The following is a metric conjoint analysis model for three factors.
Conjoin3
This model could be used, for example, to investigate preferences for cars that differ on three attributes: mileage, expected reliability, and price. Yijk is one subject’s stated preference for a car with the ith level of mileage, the jth level of expected reliability, and the k th level of price. The grand mean is , and the error is ijk. Nonmetric conjoint analysis finds a monotonic transformation of the preference judgments.
The model, which follows directly from conjoint measurement, iteratively fits the ANOVA model until the transformation stabilizes. The R2 increases during every iteration until convergence, when the change in R2 is essentially zero. The following is a metric conjoint analysis model for three factors. 

Conjoin
Conjoin1
The R2 for a nonmetric conjoint analysis model will always be greater than or equal to the R2 from a metric analysis of the same data. The smaller R2 in metric conjoint analysis is not necessarily a disadvantage, since results should be more stable and reproducible with the metric model. Metric conjoint analysis was derived from nonmetric conjoint analysis as a special case. Today, metric conjoint analysis is used more often than nonmetric conjoint analysis. In the SAS System, conjoint analysis is performed with the SAS/STAT procedure TRANSREG (transformation regression). Metric conjoint analysis models are fit using
ordinary least squares, and nonmetric conjoint analysis models are fit using an alternating least squares algorithm.

SAS Program Statements


OPTIONS PAGENO=1 PAGESIZE=56 NOLABEL;
*
* Define a data set named TIRES.
* The variable RANK typically would be the average across all subjects.
*;
DATA TIRES;
INPUT BRAND 1 PRICE 3 LIFE 5 HAZARD 7 RANK 9-10;
CARDS;
1 1 2 1 3
1 1 3 2 2
1 2 1 2 14
1 2 2 2 10
1 3 1 1 17
1 3 3 1 12
2 1 1 2 7
2 1 3 2 1
2 2 1 1 8
2 2 3 1 5
2 3 2 1 13
2 3 2 2 16
3 1 1 1 6
3 1 2 1 4
3 2 2 2 15
3 2 3 1 9
3 3 1 2 18
3 3 3 2 11
;
*
* Set up value labels.
*;
PROC FORMAT;
VALUE BRANDF
1 = ‘GOODSTONE’
2 = ‘PIROGI ‘
3 = ‘MACHISMO ‘;
VALUE PRICEF
1 = ‘$69.99’
2 = ‘$74.99’
3 = ‘$79.99’;
VALUE LIFEF
1 = ‘50,000’
2 = ‘60,000’
3 = ‘70,000’;
VALUE HAZARDF
1 = ‘YES’
2 = ‘NO ‘;
PROC FREQ NOPRINT;
FORMAT BRAND BRANDF. PRICE PRICEF. LIFE LIFEF. HAZARD HAZARDF.;
*
* Conduct nonmetric (i.e., simple) conjoint analysis.
*;
PROC TRANSREG MAXITER=50 UTILITIES SHORT;
ODS SELECT TESTSNOTE COVERGENCESTATUS FITSTATISTICS UTILITIES;
MODEL MONOTONE(RANK / REFLECT) = CLASS(BRAND PRICE LIFE HAZARD / ZERO=SUM);
OUTPUT IREPLACE PREDICTED;
*;
PROC PRINT LABEL;
VAR RANK TRANK PRANK BRAND PRICE LIFE HAZARD;
LABEL PRANK = ‘PREDICTED RANKS’;
*
* Conduct metric conjoint analysis using the %mktex SAS macro.
* The parentheses after the %MKTEX macro defines:
* The number of categories for each variable.
* The number of combinations being evaluated.
* Seed= [some number] is not strictly necessary, but helps ensure a
reproducible design.
*;
%MKTEX(3 3 3 2, N=18, SEED=448)
%MKTLAB(VARS = BRAND PRICE LIFE HAZARD, OUT=SASUSER.TIREDESIGN,
STATEMENTS = FORMAT BRAND BRANDF. PRICE PRICEF. LIFE LIFEF. HAZARD HAZARDF.)
%MKTEVAL;
PROC PRINT DATA=SASUSER.TIREDESIGN;
RUN;

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Conjoint Model


Conjoint analysis indicates consumer preferences for products with multiple characteristics, wherein these characteristics vary among several categories. For example, the researcher might want to learn consumer preferences for a coffee maker with three characteristics: price (with three levels), number of cups brewed (with three levels), and timed start (yes or no). The task is to determine which of the 3x3x2 = 12 combinations of characteristics is most preferred by consumers.

The Conjoint Model

Conjoint analysis is based on a main effects analysis-of-variance model. Data are collected by asking subjects about their preferences for hypothetical products defined by attribute combinations. Conjoint analysis decomposes the judgment data into components, based on qualitative attributes of the products. A numerical utility or part-worth utility value is computed for each level of each attribute. Large utilities are assigned to the most preferred levels, and small utilities are assigned to the least preferred levels. The attributes with the largest utility range are considered the most important in predicting preference. Conjoint analysis is a statistical model with an error term and a loss function. Metric conjoint analysis models the judgments directly. When all of the attributes are nominal, the metric conjoint analysis is a simple main-effects ANOVA with some specialized
output. The attributes are the independent variables, the judgments comprise the dependent variable, and the utilities are the parameter estimates from the ANOVA model. The following is a metric conjoint analysis model for three factors.
Conjoin3
This model could be used, for example, to investigate preferences for cars that differ on three attributes: mileage, expected reliability, and price. Yijk is one subject’s stated preference for a car with the ith level of mileage, the jth level of expected reliability, and the k th level of price. The grand mean is , and the error is ijk. Nonmetric conjoint analysis finds a monotonic transformation of the preference judgments.
The model, which follows directly from conjoint measurement, iteratively fits the ANOVA model until the transformation stabilizes. The R2 increases during every iteration until convergence, when the change in R2 is essentially zero. The following is a metric conjoint analysis model for three factors. 

Conjoin
Conjoin1
The R2 for a nonmetric conjoint analysis model will always be greater than or equal to the R2 from a metric analysis of the same data. The smaller R2 in metric conjoint analysis is not necessarily a disadvantage, since results should be more stable and reproducible with the metric model. Metric conjoint analysis was derived from nonmetric conjoint analysis as a special case. Today, metric conjoint analysis is used more often than nonmetric conjoint analysis. In the SAS System, conjoint analysis is performed with the SAS/STAT procedure TRANSREG (transformation regression). Metric conjoint analysis models are fit using
ordinary least squares, and nonmetric conjoint analysis models are fit using an alternating least squares algorithm.

SAS Program Statements


OPTIONS PAGENO=1 PAGESIZE=56 NOLABEL;
*
* Define a data set named TIRES.
* The variable RANK typically would be the average across all subjects.
*;
DATA TIRES;
INPUT BRAND 1 PRICE 3 LIFE 5 HAZARD 7 RANK 9-10;
CARDS;
1 1 2 1 3
1 1 3 2 2
1 2 1 2 14
1 2 2 2 10
1 3 1 1 17
1 3 3 1 12
2 1 1 2 7
2 1 3 2 1
2 2 1 1 8
2 2 3 1 5
2 3 2 1 13
2 3 2 2 16
3 1 1 1 6
3 1 2 1 4
3 2 2 2 15
3 2 3 1 9
3 3 1 2 18
3 3 3 2 11
;
*
* Set up value labels.
*;
PROC FORMAT;
VALUE BRANDF
1 = ‘GOODSTONE’
2 = ‘PIROGI ‘
3 = ‘MACHISMO ‘;
VALUE PRICEF
1 = ‘$69.99’
2 = ‘$74.99’
3 = ‘$79.99’;
VALUE LIFEF
1 = ‘50,000’
2 = ‘60,000’
3 = ‘70,000’;
VALUE HAZARDF
1 = ‘YES’
2 = ‘NO ‘;
PROC FREQ NOPRINT;
FORMAT BRAND BRANDF. PRICE PRICEF. LIFE LIFEF. HAZARD HAZARDF.;
*
* Conduct nonmetric (i.e., simple) conjoint analysis.
*;
PROC TRANSREG MAXITER=50 UTILITIES SHORT;
ODS SELECT TESTSNOTE COVERGENCESTATUS FITSTATISTICS UTILITIES;
MODEL MONOTONE(RANK / REFLECT) = CLASS(BRAND PRICE LIFE HAZARD / ZERO=SUM);
OUTPUT IREPLACE PREDICTED;
*;
PROC PRINT LABEL;
VAR RANK TRANK PRANK BRAND PRICE LIFE HAZARD;
LABEL PRANK = ‘PREDICTED RANKS’;
*
* Conduct metric conjoint analysis using the %mktex SAS macro.
* The parentheses after the %MKTEX macro defines:
* The number of categories for each variable.
* The number of combinations being evaluated.
* Seed= [some number] is not strictly necessary, but helps ensure a
reproducible design.
*;
%MKTEX(3 3 3 2, N=18, SEED=448)
%MKTLAB(VARS = BRAND PRICE LIFE HAZARD, OUT=SASUSER.TIREDESIGN,
STATEMENTS = FORMAT BRAND BRANDF. PRICE PRICEF. LIFE LIFEF. HAZARD HAZARDF.)
%MKTEVAL;
PROC PRINT DATA=SASUSER.TIREDESIGN;
RUN;

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