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st: Poisson -Multinomial Logit in gllamm


From   KONSTANTARAS KONSTANTINOS <[email protected]>
To   [email protected]
Subject   st: Poisson -Multinomial Logit in gllamm
Date   Sat, 10 Jan 2009 14:49:47 +0200 (EET)

Dear statalisters,

I am estimating using Stata 9.2 and gllamm a multinomial logit model with random unobserved heterogeneity for a dependent variable with three alternatives, trying to see whether typical binomial-family mlogit-link estimation (with expanded option) is the same with the one obtained through a Poisson estimation of the same model assuming log-link and the same choice variable for both cases. I get approximately the same coefficient significance, but not the same coefficients. I have tried to use, in the Poisson case, the dummy for third alternative (base case) with id the multiple of alternatives times the original id, but the results do not change.
According to published results, the two Log-likelihoods should be converging to the same parameters –their only difference in individual Likelihood contributions being exp(-Ti) multiplying the same integral- I wonder why do I get different estimates. Would anyone be able to explain me the difference in coefficient estimates?

The three equivalent models with results are:

MODEL 1: Typical Gllamm with mlogit link

gllamm alt a1X a2X a1K a2K a1 a2,l(mlogit) f(binom) expand(patt chose o) nocons i(id) nrf(2) eq(a1 a2)

number of level 1 units = 1092
number of level 2 units = 122
Condition Number = 8.5678076
gllamm model
log likelihood = -311.37363
			
alt	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
						
a1X	1.475683	.4331459	3.41	0.001	.6267325	2.324633
a2X	-.2295048	.2679697	-0.86	0.392	-.7547158	.2957063
a1K	1.272873	.4835972	2.63	0.008	.32504	2.220706
a2K	.3415553	.2757442	1.24	0.215	-.1988933	.882004
a1	-3.578403	.5921035	-6.04	0.000	-4.738904	-2.417901
a2	-1.169104	.2277309	-5.13	0.000	-1.615448	-.7227595
						
Variances and covariances of random effects
***level 2 (id)
var(1): 1.4726948 (1.0422332)
cov(2,1): -.15366121 (.36988808) cor(2,1):	-.9999997
var(2): .01603305 (.07603772)

MODEL 2. Gllamm Poisson estimation, dependent is the same as previous choice variable, same expanded dataset, units are identified by the same id as previously

gllamm chose a1X a2X a1K a2K a1 a2 ,l(log) f(poisson) nocons i(id) nrf(2) eqs(a1 a2)
number of level 1 units = 1092
number of level 2 units = 122
Condition Number = 5.8550015
gllamm model
log likelihood = -708.94394
						
chose	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
						
a1X	1.210423	.3545866	3.41	0.001	.5154462	1.9054
a2X	-.3455751	.233346	-1.48	0.139	-.8029248	.1117747
a1K	.6710833	.3394061	1.98	0.048	.0058597	1.336307
a2K	.1790438	.2369805	0.76	0.450	-.2854295	.643517
a1	-3.308728	.3937927	-8.40	0.000	-4.080547	-2.536908
a2	-1.487101	.2024753	-7.34	0.000	-1.883946	-1.090257
Variances and covariances of random effects
***level 2 (id)
var(1): .27401766 (.2084767)
cov(2,1): -.12775431 (.11310771) cor(2,1):	-1
var(2): .05956245 (.08636844)				

MODEL 3. Same as above, only difference is that I use the alternatives times the original id as identification and include the base case coefficients as covariates
gllamm chose a1X a2X a1K a2K a1 a2 ,l(log) f(poisson) nocons i(tsid) nrf(2) eqs(a1 a2)						
number of level 1 units = 1092
number of level 2 units = 314
Condition Number = 9.6440331
gllamm model
log likelihood = -679.18721

chose	Coef.	Std. Err.	z	P>z	[95% Conf.	Interval]
						
a1X	1.234599	.3511343	3.52	0.000	.5463883	1.922809
a2X	-.3593594	.2292559	-1.57	0.117	-.8086927	.0899738
a3X	-.1302092	.1353111	-0.96	0.336	-.3954139	.1349956
a1K	.6796322	.3412372	1.99	0.046	.0108195	1.348445
a2K	.1896021	.2343603	0.81	0.419	-.2697357	.6489399
a3K	-.1847696	.1355298	-1.36	0.173	-.4504032	.0808639
a1	-3.275452	.3952272	-8.29	0.000	-4.050083	-2.500821
a2	-1.454291	.1951595	-7.45	0.000	-1.836796	-1.071785
a3	-.2945889	.1092748	-2.70	0.007	-.5087637	-.0804142
						
Variances and covariances of random	effects
			
***level 2 (tsid)
var(1): .2058909 (.22887741)
cov(2,1): .01193146 (.10459653)	cor(2,1):	1
var(2): .00069143 (.01207873)

					

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