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From |
"David Roodman (DRoodman@cgdev.org)" <DRoodman@CGDEV.ORG> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: new ml evaluator type needed?/cmp upgrade |

Date |
Mon, 14 Jul 2008 12:17:39 -0400 |

I have just posted another upgrade to -cmp-. See http://stata.com/statalist/archive/2008-07/msg00231.html for more on the program. "ssc install cmp, replace" installs the progam. The new version is significantly faster in many situations. I no longer so readily recommend relying on tech(dfp) because -cmp- now often works quite well with -ml-'s default Newton-Raphson search method. Sometimes alternating between DFP and NR is the best, such as with tech(dfp nr). NR seems best where the likelihood is concave, and DFP when it isn't. The main internal change is that -cmp- is now by default a "pseudo-d2" evaluator. It computes scores analytically, like a d1 evaluator, and then it computes the Hessian numerically, based on those analytical scores. The advantage in this is that it can compute the Hessian faster than -ml- does when working with d1 evaluators, by taking advantage of the linear form of -cmp- models. This means it only needs to compute the likelihood twice for each *equation* (at +h and -h relative to the current solution, where h is a small number) rather than twice for each *parameter*. This leads to a larger question in my mind about -ml-: is there a missing evaluator type? With -ml-, d1-type evaluators save time compared to d0 by computing scores analytically. Meanwhile, -lf- evaluators save time compared to d0 by assuming the likelihood has linear form: in computing scores in lf mode, -ml- only needs to compute the likelihood once for each equation instead of once for each parameter (and ditto quadratically for the Hessian). So for linear-form likelihoods for which one can compute scores analytically, one faces a trade-off: lf and d1 save time in different ways, so sometimes one will be better and sometimes the other. It struck me that this trade-off may be theoretically unnecessary. Perhaps -ml- should have a "lfd1" evaluator type that accepts analytically computed scores *and* takes advantage of the linear form.

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