topic Re: Equation from Gamma on log link in Statistical Procedures

Equation from Gamma on log link

Miracle — Mon, 23 May 2016 05:01:29 GMT

Dear Sir or Madam,

How are you?

Can I please ask your help on how can I write the equation out from the model below and how the Least Squares Means are calculated given the ML Parameter Estimates?

Your help is greatly appreciated.

proc genmod data=temp plots=all;
 class raps help inv ob;
 model occ=raps help inv ob / dist=gamma link=log type3;
 contrast 'linear' raps -2 -1 0 1 2;
 lsmeans raps help inv ob / pdiff ilink;
run; 

                     Analysis Of Maximum Likelihood Parameter Estimates

                                           Standard       Wald 95%             Wald
Parameter                    DF  Estimate     Error   Confidence Limits  Chi-Square  Pr > ChiSq

Intercept                     1    4.9922    0.2273    4.5466    5.4377      482.19      <.0001
raps          0               1   -0.8423    0.2053   -1.2447   -0.4399       16.83      <.0001
raps          1               1   -0.2972    0.2080   -0.7049    0.1104        2.04      0.1529
raps          2               1   -0.1911    0.2112   -0.6050    0.2229        0.82      0.3657
raps          3               1    0.1381    0.2247   -0.3023    0.5786        0.38      0.5388
raps          4               0    0.0000    0.0000    0.0000    0.0000         .         .
Help          No              1   -0.3832    0.1302   -0.6384   -0.1280        8.66      0.0032
Help          yes             0    0.0000    0.0000    0.0000    0.0000         .         .
INV           At least once   1    0.3124    0.0822    0.1513    0.4735       14.44      0.0001
INV           Zero            0    0.0000    0.0000    0.0000    0.0000         .         .
OB            At least once   1    0.1512    0.0316    0.0892    0.2132       22.85      <.0001
OB            Zero            0    0.0000    0.0000    0.0000    0.0000         .         .
Scale                         1    2.2357    0.0661    2.1099    2.3690


                         raps Least Squares Means

                                                                   Standard
                    Standard                                       Error of
raps    Estimate       Error    z Value    Pr > |z|        Mean        Mean

0         4.1900     0.07543      55.55      <.0001     66.0259      4.9803
1         4.7351     0.08240      57.46      <.0001      113.87      9.3837
2         4.8413     0.08641      56.02      <.0001      126.63     10.9427
3         5.1704      0.1148      45.04      <.0001      175.99     20.2018
4         5.0323      0.2064      24.39      <.0001      153.29     31.6330


          Differences of raps Least Squares Means

                             Standard
raps    _raps    Estimate       Error    z Value    Pr > |z|

0       1         -0.5450     0.04245     -12.84      <.0001
0       2         -0.6512     0.06169     -10.56      <.0001
0       3         -0.9804     0.09989      -9.81      <.0001
0       4         -0.8423      0.2053      -4.10      <.0001
...

Re: Equation from Gamma on log link

Rick_SAS — Mon, 23 May 2016 19:49:21 GMT

The easiest way to see the model is to use the CODE statement to create DATA step statements that evaluate (or "score") the model. Then look at the file that is created.

Based on your parameter estimates, the model will look something like this:

eta = 4.9922 +
(raps=0)*( -0.8423) +
(raps=1)*( -0.2972) +
(raps=2)*( -0.1911) +
(raps=3)*( 0.1381) +
(Help="No")*( -0.3832) +
(INV="At least once")*(0.3124) +
(OBS="At least once")*(0.1512);
Pred_occ = exp(eta);

If the Help and INV and OBS variables have formats on them, then use the unformatted (raw) values instead of the formatted values.

The LSMEANS are linear combinations of the parameter estimates. Because you used the ILINK option, those estimates are then transformed to the data scale. For details see the GLM documentation. You might also want to read "CONTRAST and ESTIMATE Statements Made Easy: The LSMESTIMATE Statement"

Re: Equation from Gamma on log link

Miracle — Tue, 24 May 2016 10:59:15 GMT

Hi @Rick_SAS.

Thank you for your reply and all the links.

I'm still trying to understand them.