[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
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