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help for glmcorr
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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