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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   st: Interpreting coefficients for a gamma regression with log link (Stata 11)
Date   Sat, 17 Sep 2011 22:11:23 -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
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