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## Why do I get slightly different results when running a ml procedure on Stata/SE and Stata/MP?

 Title Difference in calculations for Stata versions and processors Author Theresa Boswell, StataCorp

Users may encounter slightly different results among different versions or flavors of Stata. These slightly different results may occur when using an estimation command that calls the ml command or when different numbers of processors are used in Stata/MP when using the ml command directly.

These differences are very small and can be ignored because, statistically, the results do not differ. The possible reasons for the slight difference are explained below.

### Stata/SE vs. Stata/MP

Slight differences in results can arise on the same computer between different versions of an application, even if you run the same command in different versions. Depending on factors such as the operating system version, the processor in the computer, and the compiler used to produce the application, numerical calculations may use different mathematical libraries or may begin an algorithm at slightly different initial values. This may result in very small differences in results from the ml command.

### Stata/MP and number of processors

When more than one processor is used in Stata/MP, the computations for the likelihood are split into pieces (one piece for each processor) and then are added at the end of the calculation on each iteration. Because of round-off error, addition is not associative in computer science as it is in mathematics. This may cause a slight difference in results. For example, a1+a2+a3+a4 can produce different results from (a1+a2)+(a3+a4) in numerical computation. When changing the number of processors used in Stata, the order in which the results from each processor are combined in calculations may not be the same depending on which processor completes its calculations first.

To summarize, you should treat SE, MP with one processor, MP with two processors, etc., as different machines—even if they are on the same physical machine—when you want to reproduce results exactly.

When trying to reproduce results, you should use the same operating system, application version, and processor type. This is particularly true when using any estimation command that uses the ml command. If this is not possible, you can set the convergence tolerance of the maximization lower than the default value of 1e-5 by specifying the nrtolerance() option to aid in reproducibility.