[Limdep Nlogit List] LM, LR and Wald tests in heteroscedastic selection model

Jadwiga Kostrzewska dwakotki at wp.pl
Sat May 23 21:31:35 EST 2009


Dear All,
I am estimating the selection model with heteroscedasticity. I have 
chosen some variables (the set XH) to heteroscedasticity equation, and I 
am going to test statistically significance of a subset of variables 
(say AXH). I have written some procedures for three tests LM, LR and 
Wald, but I have a problem, because the results are very divergent. The 
procedure is as follows. (First my symbols are introduced.)

XH - a set of variables is heteroscedasticity equation
AXH - a subset of the XH
XHbA=XH\AXH
XHhip={XHbA,AXH} - the same variables as in the XH, but in another order:
variables from XHbA are at the beginning, then variables from AXH.

H0: all variables in AXH are statistically insignificant
H1: not all of them

PROC=hetS_zbB$
   ? model H0 (restrictive):
	   PROBIT; Lhs=SEL; Rhs=W; Hold$
	   SELECT; Lhs=ZAL; Rhs=XW; Hfn=XHbA; MLE$
	   CALC; logL0=LOGL; odch=s; roro=rho$
	? t e s t  LM:
		CALC;	j3=Col(XW)+Col(XHbA);
			j5=Col(AXH); stsw=Col(AXH)$
		MATRIX; start1=b(1:j3)$
		PROBIT; Lhs=SEL; Rhs=W; Hold$
		SELECT; Lhs=ZAL; Rhs=XW; Hfn=XHhip; MLE
			; Start=start1,j5_0,odch,roro; Maxit=0$
		CALC; statLM=LMSTAT; pvLM=1-Chi(StatLM,stsw)$
	? t e s t  LR:
	   ? model H1 (unrestrictive):
	      PROBIT; Lhs=SEL; Rhs=W; Hold$
 	      SELECT; Lhs=ZAL; Rhs=XW; Hfn=XHhip; MLE$
	      CALC; logL1=LOGL; StatLR=2*(logL1-LogL0)$
	      CALC; pvLR=1-Chi(StatLR,stsw)$
	? t e s t  Walda:
		? bhp and vbhp - are the b and the varb for tested parameters
		? jp2, jk2 - the first and the last index for AXH;
			CALC; jp2=Col(XW)+Col(XHbA)+1;	                    
jk2=Col(XW)+Col(XHbA)+Col(AXH)$
			MATRIX; bhp=b(jp2:jk2)$
			MATRIX; vbhp=varb(jp2:jk2,jp2:jk2)$
			MATRIX; StatWald=bhp'<vbhp>bhp$
			CALC;   pvWALD=1-Chi(StatWald,stsw)$
	MATRIX; List; istLMLRW=[StatLM,pvLM/StatLR,pvLR/StatWald,pvWald]$
	CALC; Delete 
statLM,LMSTAT,statLR,pvLM,pvLR,pvWald,logL1,logL0,roro,odch,j3,j5,jp2,jk2,stsw$
	MATRIX; Delete bhp,vbhp,StatWald,start1$
ENDPROC$ ? ****** PROC=hetS_zbB$

The results are like below:
--> 	 MATRIX; List; istLMLRW$
LM test:	       1|   19.47718       .03460
LR test	       2|   48.14571    .5837791D-06
Wald	       3|    1.83534       .99745
another example:
LM       	1|   20.36425       .06050
LR       	2|   49.46820       .1731958D-05
Wald      3|    6.79378       .87093
another example:
LM         1|   23.59600       .09871
LR         2|   54.31762    .4601083D-05
Wald       3|   13.65864       .62413

The sample is not small,  n=6987 observations:
|SEL     | Total  |     0      1 |
+--------+--------+--------------+
|       0|  1132  |  1132      0 |
|       1|  5855  |     0   5855 |
+--------+--------+--------------+
|   Total|  6987  |  1132    855 |
+--------+--------+--------------+

(I have analogous procedures for the homoscedastic selection model, and 
the results of three tests are rather similar, not like in the 
heteroscedastic selection model.)

My question:
Is the situation caused by the “two-step” MLE for the heteroscedastic 
model or by reparametrisation in likelihood function?
What is wrong? Why the results of three tests are so distant one from 
each other?
Which test should I use?
Are there any mistakes in my procedure?
;-(

Any ideas are very welcome!

Best regards,
Jadwiga Kostrzewska

----------------------------------------------------
Śledzisz trendy? Nosisz w torebce aparat fotograficzny i robisz sobie
fajne fotki? Weź udział w konkursie! Czekamy na Twoje zdjęcie w stylu
"boho-chic"! http://klik.wp.pl/?adr=http%3A%2F%2Fkonkurs.streetmoda.pl%2F%3Fsrc01%3D85ae5&sid=737





More information about the Limdep mailing list