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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Multinomial logit-type probability in log likelihood for ML model |

Date |
Sun, 2 Sep 2007 20:15:26 +0100 (BST) |

I posted a -ml- program that does a multinomial logit on statalist some time ago: http://www.stata.com/statalist/archive/2007-05/msg00449.html Hope this helps, Maarten --- Bob Hammond <robert.g.hammond@vanderbilt.edu> wrote: > All, > > I am having trouble coding an ML program for my log likelihood > function. I'll simplify several aspects of the log likelihood that > seem > unrelated to my question. Define `lnf' for an individual observation > as > follows: > > replace `lnf' = (Binomial(n,j,q) - Binomial(n,j+1,q)) * f(x) if > $ML_y1 == 1 > > In words, the probability that Y is 1 is the probability of observing > > exactly j successes out of n (where q is the probability of a success > on > an individual trial) times some function f(x). The probability q > takes > a multinomial logit form: > > q_i = exp(X_i * `theta') / (1 + sum(exp(X_h * `theta'))) > > where the sum goes from h=1, ..., J, so it sums the product of the > covariate vector X times the parameter vector `theta' for all > observations in the data set. > > It seems that I need some way to construct the summation in the > denominator of q first, but my confusion is that this denominator > contains the `theta' parameter vector. Basically, for every > observation > in the data set, I need to construct a scalar that multiplies the 1 x > k > covariate vector X by the k x 1 parameter vector `theta' that needs > to > be estimated. Then I need to sum these J scalars up (call this a, > which > is a function of `theta'). If I could do that, then, after > constructing > a, I would write: > > replace `lnf' = (Binomial(n,j, exp(`theta') / (1 + a) - Binomial(n,j, > > exp(`theta') / (1 + a)) * f(x) > if $ML_y1 == 1 > > I don't know how to construct "a" because it contains the parameter > vector `theta'. I've tried taking a look at the ado file for mlogit, > > but didn't find the answer. Thanks in advance, > > Bob > -- > ------------------------------------------------------------------------ > Bob Hammond > Department of Economics > Vanderbilt University > http://people.vanderbilt.edu/~robert.g.hammond/ > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- ___________________________________________________________ Want ideas for reducing your carbon footprint? Visit Yahoo! For Good http://uk.promotions.yahoo.com/forgood/environment.html * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Multinomial logit-type probability in log likelihood for ML model***From:*Bob Hammond <robert.g.hammond@vanderbilt.edu>

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