# Max-Diff Case Study

## Contents |

## Setting up the data

In general, the most straightforward approach for setting up a max-diff experiment is using Marketing - Max-Diff - Max-Diff Setup from an Experimental Design from the Online Library. However, in this case study, you need to instead manually set the Question Type (see also Setting Up a Max-Diff Experiment):

- Download the example data file, which has been created in accordance with the Max-Diff Specifications.
- Import it into Q.
- Go to the Variables and Questions tab.
- Select the relevant rows (in this case, rows 6 to 65).
- Right-click and select Set Question.
- Enter a desired name (e.g.,
`Max-Diff`). - Set the Question Type to Ranking.
- Press OK.
- Double click on any one of the row numbers so that the question is in a SUMMARY tables on the Outputs Tab.

## Interpreting a Max-Diff SUMMARY table

The following table shows the default statistics for a max-diff SUMMARY table. A *rank-ordered logit model with ties* has been automatically estimated and the percentages shown are estimates of preference share. This example is from a max-diff study on technology brands and the interpretation of this table is that if respondents had been presented with all ten brands it is estimated that 10% would have selected Apple, 10% Microsoft, 5% IBM, etc.

By right-clicking on the table and selecting Statistics - Cells we can select additional statistics, including the computed Coefficients and t-Statistics. To obtain a more complete set of diagnostics, select all the cells on the table and press (Planned Tests Of Statistical Significance), which will obtain outputs like those below. Note that:

- These diagnostics are provided for statisticians; it is not essential that you understand these in order to intepret the max-diff study.
- The
`S.E.`is the Standard Error of the Probability % that is seen on the table displayed on the Outputs Tab, not`Coef`. Thus, the`p-Value`s and`t-Stat`s shown below are not computed by dividing the coefficient by the standard error. Instead, the tests show the differences relative to the average Probability %.

## Crosstabs of Max-Diff data

Create a crosstab by selecting `Q1_Gender` in the Brown Drop-down Menu. When a max-diff question is selected in the Blue Drop-down Menu and a Pick One (i.e., categorical) question is selected in the Brown Drop-down Menu Q automatically re-estimates the model for each of the categories of the question in the columns of the table and automatically tests for difference between the columns. Thus, looking at the example below, we can see the most preferred brand, Google, is equally preferred by the genders, whereas Apple is more preferred among women (11% versus 9% for men), while Intel and HP are stronger among the men.

Note that by re-estimating the model within each sub-group the resulting statistical tests have substantially more power than those that are conducted when testing using Individual-Level Parameters.^{[note 1]}

## Latent class models

Latent class analysis can be used to identify groups of consumers that exhibit similar preferences in a max-diff experiment. A latent class model is estimated as follows:

- Select
**Create > Segments**. In this example, ensure that`Max-Diff`is selected. - Ensure that the max-diff question is selected in
**Questions to analyze**and that**Form segments by**is set to**splitting by individuals (latent class analysis, cluster analysis, mixture models)**(in this case study, it will be set by default to**splitting by questions (tree)**due to gender being selected in the Brown Drop-down Menu. - If desired, specify the number of segments to be computed (by default, this is automatically selected using the
*Bayesian Information Criterion*). - Press OK.

### Latent class outputs

#### Tree

The first output generated by the latent class analysis is a technical report (described in the next section), but the main output is a 'tree', like the one shown below. The 'node' at the top of the screen shows the results for the total sample. Each of the nodes underneath show the results for the specific segments (10 in this example), with the sizes of the segments shown at the bottom.

#### Grow Settings and Analysis Report

Refer to Latent Class Analysis for a general discussion of these outputs. The discussion below concentrates upon the outputs most relevant for max-diff.

##### Class Sizes

The class sizes are estimates of the proportion of people in different segments. In this example we can see that ten segments (i.e., groups of people with different preferences) have been identified with estimated sizes from 6% to 17%. Note that these are estimates of the *population* and generally the proportion of respondents in a survey that are assigned to each of these clusters will differ somewhat from these estimated numbers (due to the inherent uncertainty about how people are allocated into segments). They may further differ from the sample size due to weighting.

##### Class Parameters

The **Probabilities** are the Probability %s discussed above. The **Parameters** are the Coefficients described above. Please note that the probabilities are the same as those shown on the 'tree', but will differ from any created from a crosstab of the latent class analysis with the `Max-Diff` question (this is because the segment membership variable is computed by allocating each person to one and only one class and thus it contains a degree of error, because generally there is insufficient information to know with certainty which class a respondent should be allocated to).

##### Individual-level parameter shrinkage

This outputs indicates the level of inaccuracy obtained if computing individual-level parameters (see Individual-Level Parameters). The output below reveals that if using the individual-level parameters the variation observed in the data will be about 90% of the true variation.

##### Parameters

This table shows the estimated coefficients of the model and associated statistics for inference.

### Segment membership variable

When you use latent class analysis a new Pick One question (i.e., variable) is automatically created called `Segments 8/05/2013 8:42:22 PM` (using the date and time that you created the analysis). This can then be crosstabulated with other variables in the study (however, the statistical tests used in such analysis have less power than if crosstabbing directly with the max-diff question).

### Individual-level parameters

Estimates of the max-diff coefficients can be computed for each respondent by:

- Right-clicking on the tree and selecting
**Save Individual-Level Parameters Means and Standard Deviations**(note that you need to specify**Case IDs**on the Data tab prior to selecting this option). - Selecting RAW DATA in the Brown Drop-down Menu.

These parameters are indexed against the first brand. See surveyanalysis.org for an explanation of how to compute Probability % from these coefficients and see Individual-Level Parameters for more information about these parameters.

## Hierarchical Bayes

Sawtooth Software markets a technique for analyzing max-diff that they refer to as 'hierarchical Bayes'. This model assumes a multivariate normal mixing distribution. The same theoretical model can be selected in Q by following the steps above for conducting a latent class analysis, but with the following changes:

- Press
**Advanced**. - Change the setting for
**Question-specific assumptions**and**Distribution**from**Finite**to**Multivariate Normal - Full Covariance**. - Press
**OK**. - Change the
**Number of segments per split**to**Manual**and set it to`1`. By specifying more than 1 segment more sophisticated models are created (however, the Sawtooth product uses one segment). - Press
**OK**. - Compute the individual-level parameters (see above).

The resulting model is estimated using an EM algorithm^{[1]}, whereas Sawtooth use *hierarchical Bayes* estimation. A second difference is that Sawtooth use a standard logit model which they tweak, whereas Q uses the the rank-ordered logit model with ties.

## See also

- Experiments
- Max-Diff
- Max-Diff Specifications
- Max-Diff at surveyanalysis.org for a detailed discussion of the the design and interpretation of max-diff experiments.
- Segments
- Completely Randomized Single Factor Experiment Case Study
- Brand Price Trade-Off Experiment
- Discrete Choice Experiment Case Study
- Conjoint Analysis Case Study

## Notes

- ↑ When individual-level parameters are estimated for each respondent there is always some shrinkage to the mean (Train, K. E. (2009). Discrete Choice Methods with Simulation. Cambridge, Cambridge University Press.)

## References

- ↑ EM Algorithms for Nonparametric Estimation of Mixing Distributions, Journal of Choice Modeling, Vol. 1, No. 1, pp. 40-69, 2008