Marketing - MaxDiff - Save Variable(s) - Sawtooth-Style Preference Shares (K Alternatives)

Create new variables which contain the Sawtooth-style preference shares (formula below) for the alternatives in a MaxDiff latent class analysisMaxDiff latent class analysis, MaxDiff hierarchical BayesMaxDiff hierarchical Bayes or MaxDiff ensembleMaxDiff ensemble output. The shares are computed from the individual-level coefficients generated by the MaxDiff analysis. You should select the output before running this script.

Example

The script produces a SUMMARY table with the new variables:

Technical details

Each respondent's coefficients are first zero-centered by subtracting the average. The zero-centered utility score for alternative [math]\displaystyle{ j }[/math] is denoted [math]\displaystyle{ U_{j} }[/math]. The un-scaled Sawtooth-style preference parameter for alternative [math]\displaystyle{ j }[/math] is then:

[math]\displaystyle{ P_{j} = \frac{e^{U_{j}}}{e^{U_{j}} + K - 1} }[/math]

where [math]\displaystyle{ K }[/math] is the number of alternatives that were shown to the respondent in each task of the MaxDiff experiment.

The final Sawtooth-style preference share is obtained by scaling these parameters so that they add up to 1 (or 100%):

[math]\displaystyle{ S_{j} = \frac{P_{j}}{\sum_{j'}P_{j'}} }[/math]

How to apply this QScript

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Customizing the QScript

This QScript is written in JavaScript and can be customized by copying and modifying the JavaScript.

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JavaScript

includeWeb('QScript R Output Functions');

saveVariables('Sawtooth-style preference shares', 'MaxDiff',
              'input.maxdiff = ',
              '\ncoeffs = as.matrix(flipMaxDiff::RespondentParameters(input.maxdiff))\n' +
              'zero.centered = coeffs - rowMeans(coeffs)\n' +
              'numerator = exp(zero.centered)\n' +
              'denominator = numerator + input.maxdiff$n.alternatives.per.task - 1\n' +
              'P = numerator/denominator\n' +
              'sawtooth.shares = prop.table(P, 1)', null, null, 'sawth.pref.shr', ['FitMaxDiff', 'MaxDiffEnsemble']);