help r2c
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Title

    Computes several goodness of fit measures for count data models

Syntax

    r2c [, NODp NOOffsetadj NOSummarize]

Description

    r2c generates r-squared fit statistics based on deviance, pearson
    deviance, squared correlation, and predicted value sums of squares.
    Cameron and Windmeijer (1996) recommend the use of the deviance-based R2
    (which produces identical results to the devr2 command for glm; findit
    devr2).  r2c also produces an adjusted deviance-based r-squared metric
    based on Heinzl and Mittlböck (2003).  The negative binomial adjustment
    is based on an overdispersed Poisson model.  The r2c command is specific
    to count data models but covers most built-in count data commands.  At
    current, r2c works only with the built-in commands poisson, tpoisson,
    zip, nbreg, tnbreg, gnbreg, zinb, and glm (with glm, r2c works only for
    count-based variance functions family(poisson) and family(nbinomial) and
    assumes the default link(log)).

    r2c adjusts fit statistics automatically for sample weights (see [R]
    weight) as well as offset and exposure variables (see estimation
    options).  r2c also does not currently accept the svy or mi prefixes.
    Probability weighted models must use the command depvar indepvars [pw=
    weight] syntax.

Options

    nodp suppresses the scaled deviance-based R2 measure comparing a the
        fitted negative binomial model with Poisson model specification.  The
        DP R2 is a ratio of the deviance of the full negative binomial model
        being fitted from a saturated Poisson model over the deviance of the
        constant-only Poisson from a saturated Poisson.  The DP R2 then
        allows for a direct comparison between negative binomial and Poisson
        models (see Cameron and Windmeijer, 1996; for details).  As Cameron
        and Windmeijer note, a large DP R2 would be expected in cases where
        there is a substantial alpha (NB2; dispersion(mean)) or delta (NB1;
        dispersion(constant)) value, as large alpha/delta values represent
        substantial overdispersion.  It is worth noting that the DP R2
        baseline poisson model is adjusted for truncation with tnbreg and
        zero-inflation with zinb.

    nooffsetadj overrides the default constant-only model adjustment for the
        inclusion of an offset or exposure variable.

    nosummarize overrides the default display of the summarize command with
        detail option for the dependent variable before r-squared results.

Saved results

    r2c saves the following results in r():

    Scalars   
      r(dev_r2)       Deviance-based R2
      r(dev_r2)       Bias-adjusted Deviance-based R2
      r(pear_r2)      Pearson deviance-based R2
      r(corr_r2)      Squared correlation between observed and predicted
                        values
      r(exp_r2)       Ratio of sums of squared differences between predicted
                        vs. mean observed values over observed vs. mean
                        observed values
      r(modeldev)     Deviance based on full model
      r(constdev)     Deviance based on constant only model
      r(modelpear)    Pearson deviance based on full model
      r(constpear)    Pearson deviance based on constant only model
      r(expvar)       Predicted value variance
      r(dp_r2)        Ratio of the deviance for a fitted negative binomial
                        model over the deviance for a constant-only Poisson
                        model
      r(modeldp)      DP deviance based on full model compared to saturated
                        Poisson
      r(constdp)      DP deviance based on constant only model compared to
                        saturated Poisson

Introductory examples

    To illustrate how r2c works click on colored text below:

    . webuse auto

    * r2c following traditional Poisson regression.

    . poisson price mpg rep78 headroom

    . r2c

    * r2c following negative binomial (NB1 or constant dispersion method)

    . nbreg price mpg rep78 headroom, dispersion(constant)

    . r2c, nosummarize

References

    Cameron, A. C. & Windmeijer, F. A. G. (1996). R-squared measures for
        count data regression models with applications to health-care
        utilization. Journal of Business & Economic Statistics, 14(2),
        209-220.
    Heinzl, H. & Mittlböck, M. (2003). Pseudo R-squared measures for Poisson
        regression models with over- or under-dispersion. Computational
        Statistics & Data Analysis, 44(1-2), 253-271.

Author

    Joseph N. Luchman
    Senior Research Associate
    Fors Marsh Group LLC
    Arlington, VA
    jluchman@forsmarshgroup.com

Also see

    [R] poisson, [R] zip, [R] tpoisson, [R] nbreg, [R] gnbreg, [R] tnbreg, 
             [R] zinb, [R] glm.