[R] how to get likelihood function and negative hessian matrix
Hjellvik, Vidar
Vidar.Hjellvik at fhi.no
Mon Nov 3 11:02:17 CET 2014
I would like to implement in R a method that was proposed in a paper recently published in Am J Epidemiol: Adjustment for Missing Confounders in Studies Based on Observational Databases: 2-Stage Calibration Combining Propensity Scores From Primary and Validation Data. Am J Epidemiol. 2014;180(3):308-317. http://aje.oxfordjournals.org/content/180/3/308
My question is: Is it possible to obtain the U_i's in the lines below (from the web-appendix - somewhat modified) in R if the model G is a cox or poisson regression model?
Let gamma be a parameter estimate obtained from a model G based on data for subjects {i=1,...,N}. E.g. the effect of an exposure on an outcome.
Let < \sum{i=1}^N Q_i > be the likelihood function and < I > the negative hessian (information) matrix of the likelihood for the model .
Let < U_i > be the efficient score of gamma for the i'th subject, defined by the subset of components in the vector < I^{-1}Q_i > that corresponds to the parameter gamma.
Then < {U_i, i=1,...,N} > are variables with identical and independent distributions and < gamma = \sum_{i=1}^N U_i > asymptotically.
Best regards,
Vidar Hjellvik
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