```-------------------------------------------------------------------------------
help for glmcorr
-------------------------------------------------------------------------------

Correlation measure of predictive power and RMS error for GLMs

glmcorr [ , jackknife ]

Description

glmcorr calculates the correlation between the response and the fitted or
predicted response, its square, and the root mean square error after glm.

Remarks

Zheng and Agresti (2000) discuss the correlation between the response and
the fitted or predicted response as a general measure of predictive power
for GLMs. This measure has the advantages of referring to the original
scale of measurement, of being applicable to all types of GLM and of
being familiar to many users of statistics. Preferably, it should be used
as a comparative measure for different models applied to the same data
set, given that restrictions on values of the response may imply
limitations on its value (see e.g. Cox and Wermuth, 1992).

For an arbitrary GLM, this correlation is invariant under a
location-scale transformation and it is the positive square root of the
average proportion of variance explained by the predictors. However,
again for an arbitrary GLM, it need not equal the positive square root of
other definitions of R-square (e.g. Hardin and Hilbe, 2001); and it need
not be monotone increasing in the complexity of the predictors, although
in practice that is common. The correlation is necessarily sensitive to
outliers.

As the predicted is a function of the observed, the correlation
calculated from a sample may be expected to be biased upwards.  A
jackknifed correlation is provided as one alternative.  Zheng and Agresti
provide more discussion of this point, including other estimators and a
bootstrap approach to providing confidence intervals for the correlation
and to estimating the degree of overfitting.

The root mean square error is calculated as the square root of the sum of
squares of (observed - fitted) divided by the residual degrees of
freedom.

Options

jackknife specifies that a jackknifed estimate of the correlation be
provided.

Examples

. glm whatever
. glmcorr

Author

Nicholas J. Cox, University of Durham, U.K.
n.j.cox@durham.ac.uk

References

Cox, D.R. and N. Wermuth. 1992. A comment on the coefficient of
determination for binary responses. American Statistician 46: 1-4.

Hardin, J. and J. Hilbe. 2001.  Generalized linear models and extensions.
College Station, TX: Stata Press.

Zheng, B. and A. Agresti. 2000. Summarizing the predictive power of a
generalized linear model. Statistics in Medicine 19: 1771-1781.

Saved results

r(rho)         correlation between observed and predicted
r(rsq)         square of correlation between observed and predicted
r(jrho)        jackknifed correlation between observed and predicted (if
requested)
r(rmse)        root mean square error

Also see

Manual:  [R] glm, [R] jknife
On-line:  help for glm, jknife

```