[Limdep Nlogit List] LM, LR and Wald tests in heteroscedastic selection model
Jadwiga Kostrzewska
dwakotki at wp.pl
Thu May 28 02:15:42 EST 2009
Dear Professor,
>The LM test is probably not best because the starting
> values actually used are not the constrained MLEs for your model.
> The starting values for the probit model are not the MLEs subject
> to the restriction you are testing - they are also computed assuming
> RHO=0.
That means that I can not also use the LM test to verify the hypothesis
about the statistically significance of the subset of explanatory
variables in the regression equation in the selection model
(homoscedastic). Am I right? (I have used it incorrectly, I think).
Does another starting values for the probit equation change anything? I
try with:
PROBIT;LHS=SEL;RHS=W;HOLD$
SELECT;LHS=ZAL;RHS=XW;MLE$
CALC;KW=COL(W)$
MATRIX;STARTPRO=B(1:KW)$
PROBIT;LHS=SEL;RHS=W;HOLD$
SELECT;LHS=ZAL;RHS=XW;HFN=XHBA;MLE$
CALC;LOGL0=LOGL;ODCH=S;RORO=RHO$
CALC;J3=COL(XW)+COL(XHBA);J5=COL(AXH);STSW=COL(AXH)$
MATRIX;START1=B(1:J3)$
PROBIT;LHS=SEL;RHS=W;START=STARTPRO;RST=KW_();HOLD$
SELECT;LHS=ZAL;RHS=XW;HFN=XHHIP;MLE;START=START1,J5_0,ODCH,RORO;MAXIT=0$
and the results are identical.
> I can't say for sure the Wald test is right either - there is
> some code missing.
I was wondering what may be missing, so I have checked the results of my
procedure for the selection model with heterosced. and the results of
the Wald test via command:
PROBIT; Lhs=SEL; Rhs=W; Hold$
SELECT; Lhs=ZAL; Rhs=XW; Hfn=XH; MLE;
test: b(....)=0,...$
The results are exactly the same. By the way, how many restriction can I
put in LimDep in 'test: ...' command? (I have a lot of variables so I
had to write my own procedure.)
When I am testing less variables then
Regards,
Jadwiga Kostrzewska
Dnia 24-05-2009 o godz. 18:10 William Greene napisał(a):
> Jadwiga. I do not see enough to know for sure that you have set up
> the procedures correctly. But, I would say that your best bet is the
> LR test. The LM test is probably not best because the starting
> values actually used are not the constrained MLEs for your model.
> The starting values for the probit model are not the MLEs subject
> to the restriction you are testing - they are also computed assuming
> RHO=0. I can't say for sure the Wald test is right either - there is
> some code missing. But, based on what I see, as noted, I would say
> the LR test is the safe one.
> Regards,
> Bill Greene
>
>
> ----- Original Message -----
> From: "Jadwiga Kostrzewska" <dwakotki at wp.pl>
> Cc: "Limdep and Nlogit Mailing List" <limdep at limdep.itls.usyd.edu.au>
> Sent: Saturday, May 23, 2009 11:11:43 AM GMT -05:00 US/Canada Eastern
> Subject: [Limdep Nlogit List] LM, LR and Wald tests in heteroscedastic
> selection model
>
> 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$
> 1| 19.47718 .03460 - LM
> 2| 48.14571 .5837791D-06 - LR
> 3| 1.83534 .99745 - Wald
> another example:
> 1| 20.36425 .06050 - LM
> 2| 49.46820 .1731958D-05 - LR
> 3| 6.79378 .87093 - Wald
> another example:
> 1| 23.59600 .09871 - LM
> 2| 54.31762 .4601083D-05 - LR
> 3| 13.65864 .62413 - Wald
>
> The sample is not small, n=6987 observations:
> |SEL | Total | 0 1 |
> +--------+--------+----------------+
> | 0| 1132 | 1132 0 |
> | 1| 5855 | 0 5855 |
> +--------+--------+----------------+
> | Total| 6987 | 1132 5 |
> +--------+--------+----------------+
>
> (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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