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From |
austin nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: RE: [Non Stata] Estimation strategy for a belief learning model. |

Date |
Mon, 8 Aug 2005 12:45:10 -0400 |

I'm not going to read Cheung and Friedman (1997) to figure out what the real model would be, I'm just going to assume you want to see the theoretical prediction "explains" each individual person's beliefs at each point in time, based on some initial starting point, using some test of whether the coefficients on the theoretical predictions are non-zero. It's not clear whether you are inferring beliefs from play, or just asking players to report beliefs. This distinction could have a huge impact on the error structure. Nevertheless, here is one way to go: Express beliefs as odds ratios: p(A)/p(not A) so the left-hand-side variable ranges from zero to infinity. Then take the logs of the odds ratios. Now the LHS variable ranges from negative infinity to positive infinity. Do the same for your theoretical predictions. If probabilities of zero or one are possible, you might have problems, both practically and theoretically, since this would be an absorbing state for any future updating of beliefs. Now you've got three real-valued LHS variables, call them A B C, in three equations, to regress on predictions from your model. They no longer sum to one, but the deviations are clearly correlated across the equations. Estimate each regression and then use -suest- to adjust for correlations of errors across all 3 simultaneously. You probably want to cluster by individual. I don't think you really want a learning curve model (aka latent growth curve model, see HLM software for these models), but you do want to allow for round-specific fixed effects, probably. Just -tab round, gen(rd)- and then include rd* as regressors in each model, like so... g C=ln(pc/(1-pc)) reg C theoreticalC rd* , score(sC) suest A B C, cluster(id) Maybe you want indiv fixed effects of some kind, too... If you want to see a graph of the log-odds-ratio versus probability, try: clear range p 0 1 100 g lor=ln(p/(1-p)) line lor p -----Original Message----- From: Antoine Terracol [mailto:Antoine.Terracol@univ-paris1.fr] To: statalist@hsphsun2.harvard.edu In the context of an economic experiment, I have data on the elicited beliefs of individuals on the probability that their opponent plays strategy A, B or C in the next round. I want to fit a learning model (Cheung and Friedman (1997) "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, 19, 46-76.) on the data to see wether it describes reasonably well the learning process of individuals. For a given strategy, say strategy A, I can estimate the parameters of Actual Belief = Theoretical Belief + epsilon where epsilon is a disturbance random variable However, because I only use the belief for a given strategy, I throw away valuable information (beliefs on strategy B) I obviously (??) can't simply multiply the likelihood contributions for both beliefs since they are almost mechanically negatively correlated; and I'm not sure whether using a bivariate distribution for the error terms would be appropriate. I'd appreciate any hint or advice on the subject... * * 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/

**Follow-Ups**:**Re: st: RE: [Non Stata] Estimation strategy for a belief learning model.***From:*austin nichols <austinnichols@gmail.com>

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