HB Advanced Settings (Applies to Both CBC and ACBC)
Covariance Matrix
Prior degrees of freedom
This value is the additional degrees of freedom for the prior covariance matrix (not including the number of parameters to be estimated), and can be set from 2 to 100000. The higher the value, the greater the influence of the prior variance and more data are needed to change that prior. The scaling for degrees of freedom is relative to the sample size. If you use 50 and you only have 100 subjects, then the prior will have a big impact on the results. If you have 1000 subjects, you will get about the same result if you use a prior of 5 or 50. As an example of an extreme case, with 100 respondents and a prior variance of 0.1 with prior degrees of freedom set to the number of parameters estimated plus 50, each respondent's resulting part worths will vary relatively little from the population means. We urge users to be careful when setting the prior degrees of freedom, as large values (relative to sample size) can make the prior exert considerable influence on the results.
Prior variance
The default is 1 for the prior variance for CBC/HB and ACBC/HB for each parameter, but users can modify this value. You can specify any value from 0.1 to 999. Increasing the prior variance tends to place more weight on fitting each individual's data, and places less emphasis on "borrowing" information from the population parameters. The resulting posterior estimates are relatively insensitive to the prior variance, except 1) when there is very little information available within the unit of analysis relative to the number of estimated parameters, and 2) the prior degrees of freedom for the covariance matrix (described above) is relatively large.
Use custom prior covariance matrix
HB uses a prior covariance matrix that works well for standard CBC and ACBC studies. Some advanced users may wish to specify their own prior covariance matrix. Check this box and click the Expand icon to make the prior covariance matrix visible. The number of parameters can be adjusted by using the up and down arrows on the Parameters field, or you may type a number in the field. The number of parameters needs to be the same as the number of parameters to be estimated. Values for the matrix may be typed in or pasted from another application such as Excel. The user-specified prior covariance matrix overrides the default prior covariance matrix as well as the prior variance setting.
Alpha Matrix
Most users will not change the default alpha matrix. Advanced users may specify new values for alpha using this dialog.
Covariates are a new feature with our latest versions of HB. More detail on the usefulness of covariates in HB is provided in the white paper, "Application of Covariates within Sawtooth Software's CBC/HB Program: Theory and Practical Example" available for downloading from our Technical Papers library at www.sawtoothsoftware.com
Use default prior alpha
Selecting this option will use a default alpha matrix with prior means of zero and prior variances of 100. No demographic variables will be used as covariates.
Use a custom prior alpha
Users can specify their own prior means and variances to be used in the alpha matrix. The means and variances are expanded by clicking the Expand icon.
The number of parameters for the means and variances can be adjusted by using the up and down arrows of the Parameters field, or you may type a number in the field. The number of parameters needs to be the same as the number of parameters to be estimated (k-1 levels per attribute, prior to utility expansion). Values for the matrix may be typed or pasted from another application such as Excel.
Use Covariates
HB allows demographic variables to be used as covariates during estimation. The available covariates can be expanded by clicking the Expand icon. If you have just merged the variable to be used as a covariate and it doesn't appear on the list, click the Refresh list link.
Individual variables can be selected for use by clicking the 'Include' checkbox. The labels provided are for the benefit of the user and not used in estimation. Each covariate can be either Categorical or Continuous.
Categorical covariates such as gender or region are denoted by distinct values (1, 2, etc.) in the demographic file. If a covariate is categorical, the number of categories is requested (i.e. the number of genders would be two: for male and female). The number of categories is necessary since they are expanded using dummy coding for estimation.
Continuous covariates are not expanded and used as-is during estimation. We recommend zero-centering continuous covariates for ease of interpreting the output.
You may wish to open the ExerciseName_hb_alpha.csv file to interpret the estimated alpha parameters associated with the covariates. For each utility parameter, an intercept as well as effects for the covariates is reported, per iteration (see the labels in this file to help intepret the data). You should ignore the initial iterations prior to convergence (typically the first 20,000) and focus your analysis on the draws of alpha after convergence.
