CVA Ordinary Least Squares Settings

This dialog controls the settings used for estimating part-worths using OLS (Ordinary Least Squares) Regression. OLS is recommended for CVA questionnaires involving ratings data, where respondents rated individual conjoint cards or compared two concepts at a time using a sliding rating scale. Please see the section entitled How CVA Calculates Utilities for more information about OLS Regression.

Minimum Scale Value: If you chose either Logit or Zero-centered recoding methods, you must specify the minimum scale value. If you used a 0 to 100 purchase likelihood scale, the minimum is 0. If you used a 1 to 9 scale with a pairwise questionnaire and used 0 as the missing value, the Minimum Scale Value is 1.

Maximum Scale Value: If you chose either Logit or Zero-centered recoding, you must specify the maximum value.

Scale Direction: We assume that most users field ratings-based CVA questionnaires. For single-concept designs, we have made "Highest Number Best" the default, meaning that higher numbers indicate higher preference. However, for ranking tasks, lower numbers frequently imply higher utility. In that case, "Lowest Number Best" should be chosen. For pairwise comparison designs, "Highest Number on Right" should be chosen if the values run from lower numbers on the left to higher numbers on the right. If you specify this field incorrectly, the part-worths will appear opposite to how you expect them (i.e. higher prices will be preferred, etc.).

Recode Method:

Sometimes it is desirable or even necessary to recode the CVA responses. CVA provides three options: None, Logit (default) and Zero-centered. Each of these is described below. If you only plan to use the First Choice model in the CVA market simulator, whether you center or not does not impact your results. If you plan to use the Purchase Likelihood model, you must use single concept presentation and specify a Logit recoding to ensure meaningful results. If you plan to use the Share of Preference option or Randomized First Choice, it is probably helpful to specify a zero-centered or a logit rescaling. Scaling of part-worths can have a significant impact upon Share of Preference results. The scaling can be adjusted later in the Market Simulator using the Exponent setting.

None. This setting uses the responses in the data file as-is. If you only plan to use the First Choice model in the CVA market simulator, you may choose this option.

Logit. It is common in "single concept at a time" questionnaires for respondents to rate concepts on "Level of interest" or "likelihood of buying" scales. The scale could be three digit (from 0 to 100) or single digit (from 1 to 5). In those cases it is standard procedure to calculate part-worths using the actual ratings as dependent variables.

Consider a 0 to 10 purchase likelihood scale. If we calculate part-worths using the original scale values, we will be assuming that the difference between ratings of say, 5 and 6, is as meaningful as the difference between ratings of 9 and 10. Yet it would seem reasonable to believe that the difference between 9 and 10 is a larger subjective difference for the respondent than the difference between 5 and 6. When data are probabilities, this problem is often handled by transforming the data to a new scale that shrinks the differences in the center of the scale and stretches differences at the extremes of the scale. This is called the "logit" transformation, given by the formula:

Recoded value = ln[p/(1-p)]

where p is equal to the probability of purchase.

When using the Purchase Likelihood model, the Market Simulator requires that utilities be scaled so that antilogs of their sums are equal to expected likelihoods of purchase. Thus, the data should be recoded into logits. Here is an example of a logit transformation for a 0 to 10 scale:

     Scale  Interpreted      Logit
     Value  Probability      Value
         0       .0         -3.000
         1       .1         -2.197
         2       .2         -1.386
         3       .3         -0.847
         4       .4         -0.405
         5       .5          0.000
         6       .6          0.405
         7       .7          0.847
         8       .8          1.386
         9       .9          2.197
        10      1.0          3.000

Notice that in the middle of the scale the difference between adjacent logit values is only 0.405, but the difference between logit values for ratings of 8 and 9 is 0.811. Logit values are undefined for probabilities of 0 and 1, but approach plus and minus infinity. To keep things under control, we arbitrarily limit the logit values to the range of plus or minus 3.

The example above shows a simple way for converting numeric responses on a 1 to 9 scale first to probabilities, and then to logits. The method CVA actually employs for the logit recode is only slightly different. Because the logit transform is very sensitive at high and low probabilities, we first map numeric responses to probabilities using the following formula:

p = (y-min+1)/(max-min+2)

where: p=probability

y=answer

min=minimum scale value

max=maximum scale value

After calculating the probability p using the above formula, we again use the formula:

Recoded value = ln[p/(1-p)]

Researchers who wish to use other recoding schemes can do so by using the paper-and-pencil method of importing respondent answers and directly modifying the values in the respondent answer file.

Logit recodes can also be useful in "pairwise" questionnaires, where the rating scale may run from 1 to 9 with 5 meaning "no preference."

Zero-centered. Many researchers find that zero-centering the response scale yields more interpretable utilities than when the response scale features only positive values. Whether you adopt this option or use no recoding method has no impact in the reported average utilities from the simulator or the competitive simulation models. But, if you plan to export and use the raw utilities in another way, you may want the resulting utilities to be based on a zero-centered response scale

We suggest zero-centered or logit scaling for paired-comparison questionnaires. If we asked paired-comparison questions using CVA's default 1 to 9 point scale, the recode values would be: -4 -3 -2 -1 0 1 2 3 4.

Notice that these recoded values fall roughly in the same zero-centered range as the logit transformation for purchase likelihood models, but that the zero-centered rescaling assumes equal increments instead of "stretching" the scale at the ends.

Tasks to include:

This lets you specify which tasks (conjoint questions) should be included when estimating part-worths. By default, all tasks are included. Generally, you should include all conjoint tasks in estimation. However, if you have placed holdout tasks within the survey (by exporting the design, modifying it to include additional holdout tasks, and re-importing the design), you may decide to omit those holdouts from the part-worth estimation. Please see the section entitled Importing Designs into CVA for more information about including holdout cards in your CVA studies.

Constraints:

The Edit... button lets you specify that certain levels within certain attributes have known a priori preference order and that the part-worths should be constrained accordingly. All rank-order relationships you originally specified when entering your list of attributes and levels are carried forward to the Additional Utility Constraints dialog. But, you can modify those selections.