Hierarchical Bayes

If there is heterogeneity among individuals, HB can significantly improve upon traditional aggregate models such as OLS regression or logit for conjoint/choice analysis.

What is Hierarchical Bayes?
The Hierarchical Bayes model is called "hierarchical" because it has two levels. At the higher level, we assume that individuals' parameters (betas or part worths) are described by a multivariate normal distribution. Such a distribution is characterized by a vector of means and a matrix of covariances. At the lower level we assume that, given an individual's betas, his/her probabilities of achieving some outcome (choosing products, or rating brands in a certain way) is governed by a particular model, such as multinomial logit or linear regression.

ACA/HB Estimation of ACA
Starting with v6 of SSI Web, users who have purchased the standalone ACA/HB software for hierarchical Bayes estimation of part-worth utilities may run HB estimation on ACA data from within the SSI Web interface.

HB estimation is considered the "gold standard" for ACA part-worth utility estimation, exceeding the quality of the default OLS estimation. The benefits of HB estimation for ACA include:

1. Greater precision of estimates for each individual,
2. It relaxes the assumption of equidistant part-worths in the Priors for a priori ordered attributes,
3. Improved accuracy of part-worths for predicting holdout concepts,
4. It provides a theoretically more defensible approach for combining self-explicated and conjoint data.

CBC/HB Estimation of CBC
Researchers and academics have argued that respondents are unique. The world does not consist of clean market segments, and aggregate models that neglect respondent differences cannot be optimal. The Latent Class Module takes an important step toward recognizing respondent heterogeneity, but stops short of achieving strong individual-level predictions.

The generally preferred method for analyzing CBC data is hierarchical Bayes (HB) estimation. Importantly, HB develops individual-level part worth from choice data. Having individual-level estimates improves the accuracy of market simulations, and leads to better understanding of market structure and attribute importances than aggregate logit modeling. The CBC/HB module leverages information from all respondents to estimate results for each individual. The individual-level part worths are estimated by a statistical simulation technique called Gibbs Sampling. HB uses each individual's choices along with information about the distribution of part worths for all respondents to estimate individual-level parameters. If the market is truly segmented, separating respondents first into groups using Latent Class analysis and then running HB within those groups might be a useful approach, though many attempts to do this have demonstrated that HB works very well, even if the population includes mixtures of relatively distinct segments.

The analysis of many data sets has confirmed that HB generally improves predictions for holdout concepts relative to aggregate logit and Latent Class. A long-standing complaint against aggregate logit has been its IIA assumption, often referred to as the red bus/blue bus problem. Very similar products tend to capture too much net share in competitive aggregate logit simulations. With individual-level modeling, this effect is less problematic. If you use the First Choice model, it is entirely resolved.

The CBC/HB Module features estimation of individual-level part worths or linear functions (main effects and/or first-order interactions) for standard CBC or allocation-based (constant-sum) CBC questionnaires. Typical run times for market research data sets are from 5 minutes to an hour if using a 2 GHz processor or better. CBC/HB reads and writes data to/from text-only files. You do not need to have used CBC to collect the data as long as you arrange the data in the CBC-compatible text-only format. The part worths from CBC/HB can be used within most versions of Sawtooth Software's market simulators.

The CBC/HB Module benefits from a fast computer. We recommend a PC running under Windows 2000 or later with at least a 2 GHz processor and 256 MB of RAM.

CBC/HB Quick Start Instructions:
1. Prepare the .CHO or .CHS file that contains choice data to be analyzed.
a. From CBC/Web (SSI Web System), select File | Export Data and choose the .CHO or .CHS options.
b. From CBC (SMRT), select File | Export and choose the .CHO option.
2. Start CBC/HB, by clicking Start | Programs | Sawtooth Software | Sawtooth Software CBC/HB.
3. Click File | Open | Open a data file in the .CHO or .CHS format, browse to the folder containing the file, and click Open/Finish. (Wait a few moments for CBC/HB to read the file and prepare to perform analysis.)
4. To perform a default HB estimation, click Estimate Parameters Now.... When complete, a file containing the individual-level part worths called studyname.CSV (easily opened with Excel) is saved to the same folder as your original data file. A text-only file named studyname.HBU is also created with the same information. If using the HB utilities in the market simulator (SMRT software), within SMRT click Analysis | Run Manager | Import and browse to the studyname.HBU.