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Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11)


From   Hitesh Chandwani <hchandwani.stata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11)
Date   Sun, 18 Sep 2011 15:12:13 -0500

> Dear Statalisters,
>
> I would really appreciate it if someone could help me with
> interpreting the coefficients of a gamma regression with log link. I
> am pasting my code as well as a part of the output. I am wondering if
> using the exponentiated coefficients would be a better idea than using
> the unexponentiated coefficients.
>
> I have gone through threads from previous years and have some clue
> about how to do this but the questions I have posted after the output
> are very specific and will make things very clear for me.
>
> char insurance[omit]3
> char disp_ed_recode[omit]1
> char zipinc_qrtl_num[omit]1
> char pl_nchs2006[omit]1
> char hosp_region[omit]1
> xi: svy: glm  totchg_num_2010 age_num female_num ndx i.pl_nchs2006
> i.zipinc_qrtl_num i.insurance hiv, f(gamma) link(log) eform
>
> Output (partial):
>
> i.pl_nchs2006     _Ipl_nchs20_0-6     (naturally coded; _Ipl_nchs20_1 omitted)
> i.zipinc_qrtl~m   _Izipinc_qr_0-4     (naturally coded; _Izipinc_qr_1 omitted)
> i.insurance       _Iinsurance_0-6     (naturally coded; _Iinsurance_3 omitted)
>
>
>          |             Linearized
> totchg_~2010 |     exp(b)   Std. Err.      t    P>|t|     [95% Conf. Interval]
>
>       age_num |   1.003005   .0005908     5.09   0.000     1.001846    1.004165
>  female_num |   1.015221   .0112376     1.36   0.173     .9934037    1.037518
>              ndx |   1.108942    .007053    16.26   0.000
> 1.095185    1.122871
>
> _Ipl_nchs2~2 |   .9884999   .0841089    -0.14   0.892     .8364708    1.168161
> _Ipl_nchs2~3 |   .9094983   .0829922    -1.04   0.299     .7603662     1.08788
> _Ipl_nchs2~4 |   .8639566   .0761008    -1.66   0.097     .7267948    1.027004
> _Ipl_nchs2~5 |   .7141041   .0553283    -4.35   0.000     .6133672    .8313855
> _Ipl_nchs2~6 |   .7161963   .0547321    -4.37   0.000      .616444    .8320904
>
> _Izipinc_q~2 |    .998728   .0403789    -0.03   0.975     .9225409    1.081207
> _Izipinc_q~3 |   .9324153   .0398631    -1.64   0.102     .8573704    1.014029
> _Izipinc_q~4 |   .9120168   .0431549    -1.95   0.052     .8311327    1.000772
>
> _Iinsuranc~1 |   .8908986   .0189602    -5.43   0.000     .8544528    .9288989
> _Iinsuranc~2 |   .8794975   .0242007    -4.67   0.000     .8332598     .928301
> _Iinsuranc~4 |   1.041744   .0265659     1.60   0.109     .9908879    1.095211
> _Iinsuranc~5 |   .7917427    .066762    -2.77   0.006     .6709806    .9342394
> _Iinsuranc~6 |   1.147096   .0572715     2.75   0.006     1.040023    1.265191
>
> _Idisp_ed_~2 |   1.854369   .0970536    11.80   0.000     1.673343    2.054978
> _Idisp_ed_~3 |    1.48299   .0618375     9.45   0.000     1.366458    1.609459
> _Idisp_ed_~4 |   2.268237   .3205057     5.80   0.000     1.718887    2.993157
> _Idisp_ed_~5 |   1.113794   .0440962     2.72   0.007     1.030526    1.203791
> _Idisp_ed_~6 |    6.78983   .2933466    44.33   0.000     6.237827    7.390682
> _Idisp_ed_~7 |   1.829764    .207162     5.34   0.000     1.465182    2.285064
> _Idisp_ed_~8 |   .5357227   .0705522    -4.74   0.000     .4137015     .693734
> _Ihosp_reg~2 |   .7159705   .0484584    -4.94   0.000     .6269098    .8176835
> _Ihosp_reg~3 |   .7451451   .0718139    -3.05   0.002     .6167274    .9003025
> _Ihosp_reg~4 |    1.22051   .1325471     1.83   0.067     .9862215    1.510457
>               hiv |   1.031383   .0569271     0.56   0.576
> .9254943    1.149388
>
>
> Since these are exponentiated coefficients, my specific questions are these:
>
> 1) For dummy coded variables like 'hiv' where 1=pt. is HIV+ and 0=pt.
> is HIV-, how would a coefficient of 1.031383 be interpreted? Would it
> be the arithmetic mean ratio in the dependent var between HIV+ and
> HIV- patients [specifically mean(hiv=1)/mean(hiv=0)]?
>
> 2) For dummy coded vars (e.g. insurance) created by the -xi- command,
> would the coefficient be interpreted as [mean(var)/mean(reference
> category of var)]? For e.g., in the case of insurance, 'insurance_3'
> is the reference category, so would the coeff for 'insurance_1' be
> interpreted as [mean(insurance_1)/mean(insurance_3)] or would it be
> interpreted as [mean(insurance_3)/mean(insurance_1)]?
>
> Any help would be greatly appreciated. I have no experience with gamma
> distributions hence am finding it hard to interpret this output.
>
> Thanks,
> --
> Hitesh S. Chandwani
> University of Texas at Austin
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>



-- 
Hitesh S. Chandwani
University of Texas at Austin

*
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