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

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: new package propcnsreg available on ssc |

Date |
Mon, 30 Jul 2007 18:12:05 +0100 (BST) |

Thanks to Kit Baum a new package -propcnsreg- is available on ssc. -propcnsreg- fits by maximum likelihood a linear regression with a proportionality constraint. Consider a model where the explained variable (y) depends on two explanatory variables (x1 and x2). Furthermore suppose that the effects of x1 and x2 differ for different values of a third variable (x3), i.e. the model contains interaction effects between x1 and x3 and between x2 and x3. The proportionality constraint imposes the constraint that the effects of x1 and x2 change by the same proportion as x3 changes. So if the effect of x1 doubles for a unit change in x3, than so does the effect of x2. One of the nice characteristics of this model is that the constrained variables can be interpreted as together measuring a latent variable, whereby their parameters measure how strong they load on that latent variable. It is an implementation of a so called MIMIC model (Hauser and Goldberger, 1971). The difficulty with this model is that the parameters are highly correlated, thus making it hard for the standard maximization algorithms to find the maximum of the likelihood function. To overcome this issue an EM algorithm is first used to find suitable starting values. The EM algorithm breaks the correlation by first treating the loadings of the constrained parameters as fixed and estimate the effect of the latent variable, and than treat the effect of the latent variable as fixed and estimate the loadings. This is iterated till convergence. Although this algorithm is likely to find the maximum in the end, it can end up taking a large number very small steps towards that maximum. To "lively this algorithm up" every fifth iteration will consist of two iterations from the standard -ml- algorithm for the entire likelihood. Once the EM algorithm has converged, the parameter estimates are fed into the standard -ml- algorithm to get the correct standard errors. I will give a presentation on this package at the UK Stata Users' Group Meeting on Monday, September 10. Maarten Hauser, Robert M. and Arthur S. Goldberger. 1971. "The Treatment of Unobservable Variables in Path Analysis." Sociological Methodology 3: 81-117. ----------------------------------------- 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/ ----------------------------------------- ___________________________________________________________ Yahoo! Answers - Got a question? Someone out there knows the answer. Try it now. http://uk.answers.yahoo.com/ * * 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/

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