# [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

[[alternative HTML version deleted]]