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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 * * 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/

**Follow-Ups**:**Re: st: Interpreting coefficients for a gamma regression with log link (Stata 11)***From:*Hitesh Chandwani <hchandwani.stata@gmail.com>

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