Example 90.5 Metric Conjoint Analysis of Tire Data

This example, which is more detailed than the previous one, uses PROC TRANSREG to perform a metric conjoint analysis of tire preference data. Conjoint analysis can be used to decompose preference ratings 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 ratings. Metric conjoint analysis, as shown in this example, fits an ordinary linear model directly to data assumed to be measured on an interval scale. Nonmetric conjoint analysis, as shown in Example 90.4, finds an optimal monotonic transformation of original data before fitting an ordinary linear model to the transformed data.

This example has three parts. In the first part, an experimental design is created. In the second part, a DATA step creates descriptions of the stimuli for the experiment. The third part of the example performs the conjoint analyses.

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).

For a conjoint study such as this, you need to create an experimental design with 3 three-level factors, 1 two-level factor, and 18 combinations or runs. The easiest way to get this design is with the %MktEx autocall macro. The %MktEx macro requires you to specify the number of levels of each of the four factors, followed by N=18, the number of runs. Specifying a random number seed, while not strictly necessary, helps ensure that the design is reproducible. The %MktLab macro assigns the actual factor names instead of the default names x1, x2, and so on, and it assigns formats to the factor levels. The %MktEval macro helps you evaluate the design. It shows how correlated or independent the factors are, how often each factor level appears in the design, how often each pair occurs for every factor pair, and how often each product profile or run occurs in the design. See http://support.sas.com/resources/papers/tnote/tnote_marketresearch.html (Kuhfeld; 2005) for more information about experimental design and conjoint analysis; look for the latest "Conjoint Analysis" report. The following statements create, evaluate, and display the design:

   title 'Tire Study, Experimental Design';
   
   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;
   
   %mktex(3 3 3 2, n=18, seed=448)
   
   %mktlab(vars=Brand Price Life Hazard, out=sasuser.TireDesign,
           statements=format Brand BrandF9. Price PriceF9.
                      Life LifeF6. Hazard HazardF3.)
   
   %mkteval;
   
   proc print data=sasuser.TireDesign;
   run;

The %MktEx macro (Kuhfeld; 2005) output displayed in Output 90.5.1 shows you that the design is 100% efficient, which means it is orthogonal and balanced. The %MktEval macro output displayed in Output 90.5.2 shows you that all of the factors are uncorrelated or orthogonal, the design is balanced (each level occurs once), and every pair of factor levels occurs equally often (again showing that the design is orthogonal). The n-way frequencies show that each product profile occurs once (there are no duplicates). The design is shown in Output 90.5.3. The design is automatically randomized (the profiles were sorted into a random order and the original levels are randomly reassigned). Orthogonality, balance, randomization, and other design concepts are discussed in detail in Kuhfeld (2005), in the "Experimental Design, Efficiency, Coding, and Choice Designs" report.

                                   Current          Best                        
           Design    Row,Col  D-Efficiency  D-Efficiency  Notes                 
           ----------------------------------------------------------           
                1      Start      100.0000      100.0000  Tab                   
                1        End      100.0000                                      
                                                                                

                              The OPTEX Procedure                               

                            Class Level Information                             

                             Class  Levels  Values                              

                             x1       3     1 2 3                               
                             x2       3     1 2 3                               
                             x3       3     1 2 3                               
                             x4       2     1 2