Initial Parameter Estimates
By checking the "Provide initial parameter estimates" CheckBox on the Run Window screen, you can specify starting values of the beta parameters for parameter estimation. A dialog window listing all the beta parameters is presented, with edit boxes to enter the initial values for each parameter. Note that these are initial values for the betas, i.e., the transformed parameter prior to implementing the link function. Unless you have used the identity link function, you must provide estimates from the beta parameters, not the real parameters.
Initializing parameter estimates is useful when the parameter estimation optimization is not converging, or when you want to start the new estimation optimization closer to the final estimates to speed up the optimization process. You can use the Retrieve push button to retrieve the estimates of the betas from a similar model to the one being estimated. Note that the link function should be the same for the model where estimates were retrieved and for the model being estimated. The Retrieve push button tries to match columns of the design matrix of the retrieved model with the model for which estimates are desired, so that initial values of parameters are close to the correct starting values for the new model.
Another way to initial the parameter values is to use the Paste push button to paste values from the clipboard into the parameter entry boxes. You can fill the clipboard with parameter estimates from the model highlighted in the Results Browser Window by the Output | Specific Model Output | Copy Estimates to Clipboard | Beta Estimates | Copy only beta estimates to clipboard menu choices. See Copy Estimates Clipboard for more details.
By default, MARK starts the optimization of all parameter estimates at 0.01 for the sin, logit, log-log, and complementary log-log, which results in a real parameter value of just greater than 0.5 for an identity design matrix. For most of the data types in MARK, the 0.5 initial value is a "safe" value, providing a valid set of parameter estimates that allow the numerical optimization procedure to find the optimum. However, one data type in particular, the multi-strata model, has additional constraints on the parameters that are not implemented with initial values of 0.5. The psi parameters for transition from a particular strata must sum to less than 1, i.e., the probability of leaving the strata is the sum of the psi values for the strata, and the probability of remaining in the strata is 1 - sum of psi values. If there are 3 strata, and the probability of going from A to B is 0.5 and the probability of going from A to C is 0.5, then there is no probability of remaining in strata A. The result is that the optimization routine may never find the optimum set of parameter estimates. To remedy this problem, the user should specify smaller initial estimates for the psi values. If the sin link is being used, specifying 0 for initial values of the S and p parameters is reasonable (resulting in initial values of 0.5), and -1 for the psi values (resulting in initial values of about 0.08). These same values also work pretty well for the logit link function.
When a set of parameter values are invalid, in the sense that the probability of observing a particular encounter history is >1 or <0, a penalty if assessed to the likelihood function in an attempt to force the parameter estimates into a valid region.
Often when you are specifying intial parameter estimates, you can retrieve estimates from another model that is nested within the model you are currently building. One of the "tricks" of the initial estimates window is that you can double click on a parameter box, and all the parameter estimates in this box and below will be shifted down by one box. This trick allows you to shift the initial parameter estimates into the correct box after they have been retrieved from a previous model.