Obsidian | Level 7

## Questions about convergence in Proc Model

1. What is the exact measure the iteration process is used to determine when to stop, is it R or Objective on PPC/ RPC/S? Most softwares I know, for example Matlab, have two, one for the change in objective function and one for the change in parameter. If it is the change in objective funciton, we usually should set a lower criterion, but it could be higher for the change of parameters.

2. Under what conditions, the convergence statistics can output a missing value? One of my programs gives a missing RPC value but everything else has a value. Does it mean there are missing values for some parameters in the previous step?

4 REPLIES 4
SAS Employee

## Re: Questions about convergence in Proc Model

You might be able to find the details you need in the PROC MODEL documentation: https://support.sas.com/documentation/cdl/en/etsug/68148/HTML/default/viewer.htm#etsug_model_toc.htm

Obsidian | Level 7

## Re: Questions about convergence in Proc Model

I actually went through the document, but to be honest, I did not find the answer I want.

My first question is: What is the convergence measure used by the iteration process to determine when to stop?

Here is what the document say:

"

There are a number of measures that could be used as convergence or stopping criteria. PROC MODEL computes five convergence measures labeled R, S, PPC, RPC, and OBJECT.

When an estimation technique that iterates estimates of is used (that is, IT3SLS), two convergence criteria are used. The termination values can be specified with the CONVERGE=(p,s) option in the FIT statement. If the second value, s, is not specified, it defaults to p. The criterion labeled S (described later in the section) controls the convergence of the S matrix. When S is less than s, the S matrix has converged. The criterion labeled R is compared to the p-value to test convergence of the parameters.

The R convergence measure cannot be computed accurately in the special case of singular residuals (when all the residuals are close to 0) or in the case of a 0 objective value. When either the trace of the S matrix computed from the current residuals (trace(S)) or the objective value is less than the value of the SINGULAR= option, convergence is assumed.  "

The first paragraph tells there are five measures. However, does all five measures are used? If so, how are the five measures used, should the minimum or the maximum among the five to satisfy the p value specified? If not, which one is used or there is a sequence or some combination of them are used?

The second paragraph went to the discuss the case when " an estimation technique that iterates estimates of is used (that is, IT3SLS),"  My guess Sigma here is the variance-covariance matrix of the residuals. In this case, SAS accept two values, p and s. That being said, which measure (R, RPC, PPC) will be gauged against p and which one (object or trace (S)) is s used for?

My second question is about under what situations some of the convergence measures can have a missing value. In my case, RPC gives a missing value and none of others. Based on the definition shown in the document, it looks a missing value could show if the estimation in the previous iteration is missing. Furthermore, the measure is the maximum relative change; therefore, does it suggest all paramter estimates in the previous step are missing or just one is missing?

Again, after reading the document, I did not get the answers to my questions. Am I reading the wrong sections? If so, would you help me to pin point the right section I should read or share some knowledge about those issues?

Thanks.

Community Manager

## Re: Questions about convergence in Proc Model

I have identified someone in R&D who should be able to help you. They are out of the office today, so you should hear from them in a day or two.

Thanks for using the communities!

Shelley

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SAS Employee

## Re: Questions about convergence in Proc Model

1) In general, the convergence criteria which you set with the CONVERGE= option used to stop the iteration process is R.  This is typically how PROC MODEL determines convergence; however, convergence can also be satisified if the objective function value falls below the value of the SINGULAR= option.

2) RPC will be missing when there is no previous iteration available to compute a value.  This could happen, for instance, when the initial parameter estimates meet the problem's convergence criteria.  If you're seeing a missing RPC in other cases I'd be intersted in seeing your program.

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