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 The TRANSREG Procedure

## Example 65.2: Nonmetric Conjoint Analysis of Tire Data

This example uses PROC TRANSREG to perform a nonmetric conjoint analysis of tire preference data. Conjoint analysis decomposes rank ordered evaluation judgments of products or services into components based on qualitative product attributes. For each level of each attribute of interest, a numerical "part-worth utility" value is computed. The sum of the part-worth utilities for each product is an estimate of the utility for that product. The goal is to compute part-worth utilities such that the product utilities are as similar as possible to the original rank ordering. (This example is a greatly simplified introductory example.)

The stimuli for the experiment are 18 hypothetical tires. The stimuli represent different brands (Goodstone, Pirogi, Machismo)*, prices (\$69.99, \$74.99, \$79.99), expected tread life (50,000, 60,000, 70,000), and road hazard insurance plans (Yes, No). There are 3 ×3 ×3 ×2 = 54 possible combinations. From these, 18 combinations are selected that form an efficient experimental design for a main effects model. The combinations are then ranked from 1 (most preferred) to 18 (least preferred). In this simple example, there is one set of rankings. A real conjoint study would have many more.

First, the FORMAT procedure is used to specify the meanings of the factor levels, which are entered as numbers in the data step along with the ranks. PROC TRANSREG is used to perform the conjoint analysis. A maximum of 50 iterations is requested. The specification Monotone(Rank / Reflect) in the MODEL statement requests that the dependent variable Rank should be monotonically transformed and reflected so that positive utilities mean high preference. The variables Brand, Price, Life, and Hazard are designated as CLASS variables, and the part-worth utilities are constrained by ZERO=SUM to sum to zero within each factor. The UTILITIES a-option displays the conjoint analysis results.

The Importance column of the Utilities Table shows that price is the most important attribute in determining preference (57%), followed by expected tread life (18%), brand (15%), and road hazard insurance (10%). Looking at the Utilities Table for the maximum part-worth utility within each attribute, you see from the results that the most preferred combination is Pirogi brand tires, at \$69.99, with a 70,000 mile expected tread life, and road hazard insurance. This product is not actually in the data set. The sum of the part-worth utilities for this combination is

20.64 = 9.50 + 1.90 + 5.87 + 2.41 + 0.96

The following statements produce Output 65.2.1:

```   title 'Nonmetric Conjoint Analysis of Ranks';

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 ';
run;

data Tires;
input Brand Price Life Hazard Rank;
format Brand BrandF9. Price PriceF9. Life LifeF6. Hazard HazardF3.;
datalines;
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
;

proc transreg maxiter=50 utilities short;
ods select ConvergenceStatus FitStatistics Utilities;
model monotone(Rank / reflect) =
class(Brand Price Life Hazard / zero=sum);
output ireplace predicted;
run;

proc print label;
var Rank TRank PRank Brand Price Life Hazard;
label PRank = 'Predicted Ranks';
run;
```

Output 65.2.1: Simple Conjoint Analysis

 Nonmetric Conjoint Analysis of Ranks

 The TRANSREG Procedure

 Monotone(Rank) Algorithm converged.

 The TRANSREG Procedure Hypothesis Tests for Monotone(Rank)

 Root MSE 0.49759 R-Square 0.9949 Dependent Mean 9.5 Adj R-Sq 0.9913 Coeff Var 5.23783

 Utilities Table Based on the Usual Degrees of Freedom Label Utility Standard Error Importance(% UtilityRange) Variable Intercept 9.5000 0.11728 Intercept Brand Goodstone -1.1718 0.16586 15.463 Class.BrandGoodstone Brand Pirogi 1.8980 0.16586 Class.BrandPirogi Brand Machismo -0.7262 0.16586 Class.BrandMachismo Price \$69.99 5.8732 0.16586 56.517 Class.Price_69_99 Price \$74.99 -0.5261 0.16586 Class.Price_74_99 Price \$79.99 -5.3471 0.16586 Class.Price_79_99 Life 50,000 -1.2350 0.16586 18.361 Class.Life50_000 Life 60,000 -1.1751 0.16586 Class.Life60_000 Life 70,000 2.4101 0.16586 Class.Life70_000 Hazard Yes 0.9588 0.11728 9.659 Class.HazardYes Hazard No -0.9588 0.11728 Class.HazardNo The standard errors are not adjusted for the fact that the dependent variable was transformedand so are generally liberal (too small).

 Nonmetric Conjoint Analysis of Ranks

 Obs Rank Rank Transformation Predicted Ranks Brand Price Life Hazard 1 3 14.4462 13.9851 Goodstone \$69.99 60,000 Yes 2 2 15.6844 15.6527 Goodstone \$69.99 70,000 No 3 14 5.7229 5.6083 Goodstone \$74.99 50,000 No 4 10 5.7229 5.6682 Goodstone \$74.99 60,000 No 5 17 2.6699 2.7049 Goodstone \$79.99 50,000 Yes 6 12 5.7229 6.3500 Goodstone \$79.99 70,000 Yes 7 7 14.4462 15.0774 Pirogi \$69.99 50,000 No 8 1 18.7699 18.7225 Pirogi \$69.99 70,000 No 9 8 11.1143 10.5957 Pirogi \$74.99 50,000 Yes 10 5 14.4462 14.2408 Pirogi \$74.99 70,000 Yes 11 13 5.7229 5.8346 Pirogi \$79.99 60,000 Yes 12 16 3.8884 3.9170 Pirogi \$79.99 60,000 No 13 6 14.4462 14.3708 Machismo \$69.99 50,000 Yes 14 4 14.4462 14.4307 Machismo \$69.99 60,000 Yes 15 15 5.7229 6.1139 Machismo \$74.99 60,000 No 16 9 11.1143 11.6166 Machismo \$74.99 70,000 Yes 17 18 1.1905 1.2330 Machismo \$79.99 50,000 No 18 11 5.7229 4.8780 Machismo \$79.99 70,000 No

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