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st: RE: random number generator for gamma

 From jhilbe@aol.com To statalist@hsphsun2.harvard.edu Subject st: RE: random number generator for gamma Date Thu, 30 Sep 2010 14:50:41 -0400

I get the Stata Digest, which comes a day later. Unfortunately I have been so busy lately that I rarely get to actually review the queries and responses. I did check this morning, however,
so have a chance to explain a bit about the rndgamx.

The pseudo-random number generator you are using is part of a suite of pseudo-random number generators that Walter Linde-Zwirble and I wrote about 15 years ago. These were used by many members of the Stata community until Stata provided its new (with version 11) group of pseudo-random number generators last year. Let's just call them random number generators for now. I suggest using Stata's official random number generators, unless you want a short way to create synthetic data sets for members of the generalized linear models family. That's what the random number generators that have a final x in the
name are designed to do -- such as rndgamx.

In short, the -rndgam- command is to generate gamma random numbers with a specficied mean and scale. -rndgamx- is for constructing synthetic GLM gamma models; eg canonical inverse link
or log linked gamma models.

Although I suggest using --rgamma-- instead of --rndgam--, from what I have observed the two generators yield similar results. Know that our random number generators are based on the rejection method; Stata's generators are not. If you don't have version 11, however,
I think you need to stick with rndgam.

Let me explain the point of rndgamx, and all of our generators that end in x. Again, they were designed to use for constructing synthetic models. The mean value is NOT a constant, as it is for -rndgam-, but rather a variable having a variety of values, based on predictor values.

Let's use randgamx to construct a synthetic log-gamma model with specified coefficients as: intercept=1, coefficient of x1=.5, and coefficient of x2 = -1.75. The variables x1 and x2
will be uniformally distributed.

The code:

. set obs 100000
obs was 0, now 100000

. gen x1 = runiform()
. gen x2 = runiform()
. gen xb = 2 + .5*x1 - 1.75*x2
. gen mu=exp(xb)
. rndgamx mu, s(1)    #  GLM gamma models have scale=1
( Generating . )
Variable xg created.

. glm xg x1 x2, fam(gam) link(log) nolog

Generalized linear models No. of obs = 100000 Optimization : ML Residual df = 99997 Scale parameter = .995001 Deviance = 114525.1513 (1/df) Deviance = 1.145286 Pearson = 99497.11697 (1/df) Pearson = .995001 <= point estimate of scale

Variance function: V(u) = u^2                      [Gamma]
Link function    : g(u) = ln(u)                    [Log]

AIC = 4.74273 Log likelihood = -237133.5085 BIC = -1036733

-------------------------------------------------------------------------
-----
|                 OIM
xg | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+-----------------------------------------------------------
-----
x1 | .5002173 .0109491 45.69 0.000 .4787575 .5216771 x2 | -1.758486 .0109075 -161.22 0.000 -1.779864 -1.737108 _cons | 2.000245 .0083384 239.88 0.000 1.983903 2.016588
-------------------------------------------------------------------------
-----

See how well the log-gamma response, given x1 and x2, can be fit using Stata's
glm command with a gamma family and log link.

I have not used or really thought of -- at least for 10 years -- using -rndgamx- in manner other than for construcing synthetic GLM models. It was not designed for any other purpose. I suggest using either -rndgam- or Stata's -rgamma- commands for
generating gamma data with specified mean and scale parameters. .

Joseph Hilbe

=========================================================================

Date: Wed, 29 Sep 2010 16:26:50 +0100
From: Nick Cox <n.j.cox@durham.ac.uk>
Subject: st: RE: random number generator for gamma

Joe Hilbe will no doubt answer this. Meanwhile official Stata has -rgamma()-.

Nick
n.j.cox@durham.ac.uk

Tomas Lind

I´ve been using the -rnd- ado-package from Hilbe/Linde-Zwirble (update from STB-28: sg44).

The following syntax produces sensible results (mean and sd) when I generate
20000 Gamma distributed random numbers with shape=11.11 and scale=0.18

clear *
rndgam 20000 11.11  0.18
summarize xg    // mean=2.0 sd=0.60

However, with -rndgamx- I don´t get the same values. I have probably missed
something fundamental. Someone know what goes on?

clear *
set obs 20000
gen m=2     // mean=2
rndgamx  m , s(11.11)
summarize xg    // mean=247 sd=74

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