# 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 analysis , MaxDiff hierarchical Bayes or MaxDiff 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

- Start typing the name of the QScript into the
**Search features and data**box in the top right of the Q window. - Click on the QScript when it appears in the
**QScripts and Rules**section of the search results.

*OR*

- Select
**Automate > Browse Online Library**. - Select this QScript from the list.

## Customizing the QScript

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

### Customizing QScripts in Q4.11 and more recent versions

- Start typing the name of the QScript into the
**Search features and data**box in the top right of the Q window. - Hover your mouse over the QScript when it appears in the
**QScripts and Rules**section of the search results. - Press
**Edit a Copy**(bottom-left corner of the preview). - Modify the JavaScript (see QScripts for more detail on this).
- Either:
- Run the QScript, by pressing the blue triangle button.
- Save the QScript and run it at a later time, using
**Automate > Run QScript (Macro) from File**.

### Customizing QScripts in older versions

## 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']);
```

## See also

- QScript for more general information about QScripts.
- QScript Examples Library for other examples.
- Online JavaScript Libraries for the libraries of functions that can be used when writing QScripts.
- QScript Reference for information about how QScript can manipulate the different elements of a project.
- JavaScript for information about the JavaScript programming language.
- Table JavaScript and Plot JavaScript for tools for using JavaScript to modify the appearance of tables and charts.

See MaxDiff Software or What is MaxDiff? for an overview of key MaxDiff concepts and resources.

Extensions

Q Technical Reference

Q Technical Reference

Q Technical Reference > Setting Up Data > Creating New Variables

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R Online Library

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