Generating an Orthogonal Design

The first step in a conjoint analysis is to create the combinations of factor levels that are presented as product profiles to the subjects. Since even a small number of factors and a few levels for each factor will lead to an unmanageable number of potential product profiles, you need to generate a representative subset known as an orthogonal array.

The Generate Orthogonal Design procedure creates an orthogonal array—also referred to as an orthogonal design—and stores the information in a data file. Unlike most procedures, an active dataset is not required before running the Generate Orthogonal Design procedure. If you do not have an active dataset, you have the option of creating one, generating variable names, variable labels, and value labels from the options that you select in the dialog boxes. If you already have an active dataset, you can either replace it or save the orthogonal design as a separate data file.

To create an orthogonal design:

  1. From the menus choose:

    Data > Orthogonal Design > Generate...

    Figure 1. Generate Orthogonal Design dialog box
    Generate Orthogonal Design dialog box
  2. Enter package in the Factor Name text box, and enter package design in the Factor Label text box.
  3. Click Add.

    This creates an item labeled package 'package design' (?). Select this item.

  4. Click Define Values.
    Figure 2. Generate Design Define Values dialog box
    Generate Design Define Values dialog box
  5. In the Define Values dialog, enter the values 1, 2, and 3 to represent the package designs A*, B*, and C*. Enter the labels A*, B*, and C* as well.
  6. Click Continue.

    You'll now want to repeat this process for the remaining factors, brand, price, seal, and money. Use the values and labels from the following table, which includes the values you've already entered for package.

    Table 1. Factor specifications
    Factor name Factor label Values Labels
    package package design 1, 2, 3 A*, B*, C*
    brand brand name 1, 2, 3 K2R, Glory, Bissell
    price price 1.19, 1.39, 1.59 $1.19, $1.39, $1.59
    seal Good Housekeeping seal 1, 2 no, yes
    money money-back guarantee 1, 2 no, yes

    Once you have completed the factor specifications:

  7. In the Data File group, in the Generate Orthogonal Design dialog, leave the default of Create a new dataset and enter a dataset name. The generated design will be saved to a new dataset, in the current session, with the specified name.
  8. Select Reset random number seed to and enter the value 2000000.

    Generating an orthogonal design requires a set of random numbers. If you want to duplicate a design—in this case, the design used for the present case study—you need to set the seed value before you generate the design and reset it to the same value each subsequent time you generate the design. The design used for this case study was generated with a seed value of 2000000.

  9. Click Options.
    Figure 3. Generate Orthogonal Design Options dialog box
    Generate Orthogonal Design Options dialog box
  10. In the Minimum number of cases to generate text box, in the Options dialog, type 18.

    By default, the minimum number of cases necessary for an orthogonal array is generated. The procedure determines the number of cases that need to be administered to allow estimation of the utilities. You can also specify a minimum number of cases to generate, as you've done here. You might want to do this because the default number of minimum cases is too small to be useful or because you have experimental design considerations that require a certain minimum number of cases.

  11. Select Number of holdout cases and type 4.

    Holdout cases are judged by the subjects but are not used by the conjoint analysis to estimate utilities. They are used as a check on the validity of the estimated utilities. The holdout cases are generated from another random plan, not the experimental orthogonal plan.

  12. Click Continue in the Generate Orthogonal Design Options dialog box.
  13. Click OK in the Generate Orthogonal Design dialog box.
Figure 4. Orthogonal design for the carpet-cleaner example
Data editor displaying orthogonal design for the carpet-cleaner example

The orthogonal design is displayed in the Data Editor and is best viewed by displaying value labels rather than the actual data values. This is accomplished by choosing Value Labels from the View menu.

The variables in the data file are the factors used to specify the design. Each case represents one product profile in the design. Notice that two additional variables, CARD_ and STATUS_, appear in the data file. CARD_ assigns a sequential number to each profile that is used to identify the profile. STATUS_ indicates whether a profile is part of the experimental design (the first 18 cases), a holdout case (the last 4 cases), or a simulation case (to be discussed in a later topic in this case study).

The orthogonal design is a required input to the analysis of the data. Therefore, you will want to save your design to a data file. For convenience, the current design has been saved in carpet_plan.sav (orthogonal designs are also referred to as plans).

Next