help for xlink(Roger Newson)

Extra link functions for use with glm

glm [ varlist ] [if] [in] [weight] [, link(link_function_name) glm_options ]

where link_function_name is the name of a link function
and glm_options is a list of options other than link() used by glm.

Description

xlink is a library of extra link functions for use with glm.
A user-defined link function for glm is implemented as an ado file,
with the same name as the link function,
taking 4 arguments containing, respectively, a to-do indicator,
the name of the variable containing the link functions of the predicted means,
the name of the variable containing the predicted means,
and the name of the variable containing the first or second derivatives
of the means with respect to the link functions.
The to-do indicator is an integer argument, with values from -1 to 3,
indicating whether the ado-file is being asked to set global macros,
link functions, predicted means, first derivatives of predicted means,
and second derivatives of predicted means,
respectively.

Link functions

These are defined using twice-differential monotonic transformations,
defining the predicted mean mu as a function of the predicted link function eta
or vice versa. The link function is the quantity equal to the xb variable generated by predict
after glm.

robit1, robit2, robit3, robit4,
robit5, robit6, robit7, robit8, robit9, and robit10
indicates the robit link with 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 degrees of freedom,
respectively.
These link functions are defined by the formulas

mu = t(eta,k)

and

eta=invt(mu,k)

where k is the number of degrees of freedom.

The robit4 link function was recommended by
Kang and Shaffer (2007).
The robit7 link function was recommended by
Liu (2004)
as being similar to the logit link function,
but less influenced by outlying outcome values.
The robit9 link function was mentioned by
Mudholkar and George (1978)
as having a similar kurtosis to the logit link function.
In general, robit link functions with fewer degrees of freedom
are influenced less by outliers than robit link functions with more degrees of freedom.
In the limit, as k tends to infinity,
the robit link function with k degrees of freedom
tends to the probit link function.

Users are hereby encouraged by the author to suggest additional link functions
to be added to xlink.

Examples

. sysuse auto, clear

. glm foreign weight mpg, family(bernoulli) link(robit7) vce(robust) eform

References

Kang, J. D. Y. and Schafer, J. L. 2007.
Demystifying double robustness:
A comparison of alternative strategies forestimating a population mean from incomplete data.
Statistical Science 22: 523-539.

Liu, C. H.
2004.
Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression.
Chapter 21 of:
Gelman, A. and Meng, X-L.
2004.
Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives:
An Essential Journey with Donald Rubin's Statistical Family.
Chichester, UK: John Wiley & Sons Ltd.
Download from the Wiley Online website.

Mudholkar, G. S. and George, E. O.
1978.
A remark on the shape of the logistic distribution.
Biometrika 65: 667-668.

Author

Roger Newson, King's College London, UK.

Email: roger.newson@kcl.ac.uk

Also see

Manual: [R] glm

On-line: help for glm