[Limdep Nlogit List] Survival Exponential and Gamma Models

[Oczkowski, Eddie]

Dear All,

Apologies if this has been raised previously on the list.

Find below some output from Survival models using the exponential model
and the generalised gamma model fixing sigma = 1. The latter model has
been termed the two-parameter gamma model by some of the literature
cited in the LIMDEP manual, Lancaster (1990, p38).  However, the LIMDEP
manual does not refer to the two-parameter gamma model.

Note from the output the same slope coefficients are produced (for the
exponential and gamma models) and the same predictions of the underlying
't' dependent variable are gained if the gamma model predictions are
appropriately generated by t = exp(Xb)*gamma(theta).

Are these two models 'statistically equivalent'?  Any literature on this
would be appreciated.

Regards, Eddie




************************************************************************
****
--> survival;lhs=lnprice;rhs=X;model=exponential;alg=newton$
Normal exit from iterations. Exit status=0.

+---------------------------------------------+
| Loglinear survival model: EXPONENTIAL       |
| Maximum Likelihood Estimates                |
| Model estimated: Aug 29, 2007 at 10:23:55AM.|
| Dependent variable              LNPRICE     |
| Weighting variable                 None     |
| Number of observations             5447     |
| Iterations completed                  4     |
| Log likelihood function       -5730.953     |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------
+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] | Mean of
X|
+---------+--------------+----------------+--------+---------+----------
+
          RHS of hazard model
 Constant      -.59807836      .45374366    -1.318   .1875
 SCORE          .03560295      .00541052     6.580   .0000    89.2586745
 CEL            .03555314      .00542247     6.557   .0000    8.85918854
 VIN            .10228866      .01229852     8.317   .0000    2.14393244
          Ancillary parameters for survival
 Sigma         1.00000000   ......(Fixed Parameter).......

 --> matrix;bb=-b$
--> calc;k=col(x)$
-->
survival;lhs=lnprice;rhs=x;model=gamma;alg=newton;start=bb,1,1;rst=k_b,1
,...
Normal exit from iterations. Exit status=0.

+---------------------------------------------+
| Loglinear survival model: GENRL.GAMMA       |
| Maximum Likelihood Estimates                |
| Model estimated: Aug 29, 2007 at 10:23:57AM.|
| Dependent variable              LNPRICE     |
| Weighting variable                 None     |
| Number of observations             5447     |
| Iterations completed                 21     |
| Log likelihood function       -1618.398     |
| Generalized GAMMA Model, Theta=   9.755     |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------
+
|Variable | Coefficient  | Standard Error |b/St.Er.|P[|Z|>z] | Mean of
X|
+---------+--------------+----------------+--------+---------+----------
+
          RHS of hazard model
 Constant     -2.87586724      .12961811   -22.187   .0000
 SCORE          .03560295      .00153425    23.205   .0000    89.2586745
 CEL            .03555314      .00121683    29.218   .0000    8.85918854
 VIN            .10228866      .00296144    34.540   .0000    2.14393244
          Ancillary parameters for survival
 Sigma         1.00000000   ......(Fixed Parameter).......
 THETA         9.75508694      .13483978    72.346   .0000