This example uses PROC TRANSREG to perform a nonmetric conjoint analysis of tire preference data. Conjoint analysis decomposes rankordered evaluation judgments of products or services into components based on qualitative product attributes. For each level of each attribute of interest, a numerical “partworth utility” value is computed. The sum of the partworth utilities for each product is an estimate of the utility for that product. The goal is to compute partworth 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),^{[1]} prices ($69.99, $74.99, $79.99), expected tread life (50,000, 60,000, 70,000 miles), and road hazard insurance plans (Yes, No). There are possible combinations. From these, 18 combinations are selected that form an efficient experimental design for a maineffects 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 partworth utilities are constrained by ZERO=SUM to sum to zero within each factor. The UTILITIES aoption 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 partworth utility within each attribute, you see from the results that the most preferred combination is Pirogi brand tires, at $69.99, with a 70,000mile expected tread life and road hazard insurance. This product is not actually in the data set. The sum of the partworth utilities for this combination is as follows:

The following statements produce Output 97.4.1.
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 TestsNote 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 97.4.1: Simple Conjoint Analysis
Nonmetric Conjoint Analysis of Ranks 
Monotone(Rank) 

Algorithm converged. 
Root MSE  0.49759  RSquare  0.9949 

Dependent Mean  9.50000  Adj RSq  0.9913 
Coeff Var  5.23783 
Utilities Table Based on the Usual Degrees of Freedom  

Label  Utility  Standard Error  Importance (% Utility Range) 
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 transformed and 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 