The Response report in the Repeated Measures Degradation platform contains three sections: the Formula Picture, Specifications for Bayesian Estimation, and MCMC Controls. A new Response report is created each time you click the Go to Bayesian Estimation button for a new path definition and transformation combination.
The Formula Picture section contains the equation for the selected model. Use this equation as a reference when specifying the priors in the Specifications for Bayesian Estimation section.
The Specifications for Bayesian Estimation section enables you to specify the prior distributions for the parameters in the path definition model. The table is populated with default values that provide starting points based on the initial model fit. The table for specifying prior distributions contains the following columns:
Parameter
A column that contains the parameters in the path definition model.
Parameter Distribution
A column of lists that enable you to specify the distribution for the random parameters in the path definition model. This column is not applicable for fixed parameters.
Prior
A column that contains the prior specification for each parameter.
Prior Distribution
A column of lists that enable you to specify the prior distribution for each parameter. Distributions can be specified using percentiles or parameters. A distribution name that contains angled brackets in this list implies that the prior distribution is defined using percentiles of the distribution. Otherwise, the prior distributions are defined by parameters.
Value columns
Each value column contains entry fields that enable you to define the prior distributions for the parameters in the path definition model. Distributions can be specified using percentiles or traditional parameters.
Tip: You can specify the parameters for prior distributions using percentiles or parameters. If you select a distribution name that contains angled brackets in the Prior Distribution list, you must define the distribution using percentiles of the distribution. If you select a distribution name that does not have angled brackets in the Prior Distribution list, you must define the distribution using parameters of the distribution.
Below the table for specifying prior distributions, there are the following additional options:
Number of Monte Carlo Iterations
Specifies the sample size that will be drawn from the posterior distribution after a burn-in procedure. This number must be greater than or equal to 2,000.
Random Seed
Specifies a random seed so that MCMC results can be reproduced.
Fit Model
Performs the MCMC procedure based on prior distributions that JMP fits using the specified values. Adds a report entitled Bayesian Estimates <N>, where N is an integer that consecutively numbers the Bayesian Estimates reports within each Response report. See Repeated Measures Degradation Bayesian Estimates Report.
The MCMC Controls section contains the following options for the Markov chain Monte Carlo (MCMC) procedure:
Warmup Laps
Specifies the number of iterations that are used to tune the candidate distribution at the beginning of the MCMC procedure. If the posterior distribution does not appear to have converged or shows a sign of high autocorrelation, consider increasing the number of warm-up laps. You should also increase the number of warm-up laps if the value of the N Chains option is greater than 1.
Auto Thinning
Specifies if the suggested thinning period is used or not. If this option is not selected, the thinning period is specified by the Thinning option. Thinning the samples from the posterior distribution reduces autocorrelation in the results. You should turn off the Auto Thinning option only if increasing the number of warm-up laps did not help reduce autocorrelation.
Thinning
(Applicable only if the Auto Thinning option is not selected.) Specifies the thinning value. The supplied thinning value should be larger than the Applied Thinning value that appears in the MCMC Controls report when the Auto Thinning option is used.
N Chains
Specifies the number of chains in the MCMC procedure. The default value is 1, which is recommended for exploratory analysis. When the N Chains option is 1, the procedure uses the values from the initial model to start, which usually leads to fast convergence. However, it is possible that the posterior values get trapped at a local optimum. When the N Chains option is greater than 1, the procedure uses random values for the rest of the chains. This can lead to slower convergence, but provides a chance to increase the confidence that the final results have converged. You might need to increase the value of the Warmup Laps option at the same time to address the slow convergence due to random starts.
Tip: You should increase this value only if you cannot get satisfactory results using the other MCMC Controls settings. Increase the N Chains value to investigate situations that cannot be identified with a single chain.
The Response red triangle menu contains the following option:
Remove
Removes the current Response report from the Repeated Measures Degradation with Random Parameters report window.