# [Gretl-users] Constant in log-likelihood and graph of two densities together (Allin Cottrell)

Tue Jul 9 12:52:32 EDT 2013

```GRAPH OF TWO DENSITIES TOGETHER: Thanks for providing the older link.
Although the code there is to plot two densities /consecutively /from
left to right, while what I need to do is to /superimpose/ them - and
this I realize now has the problem of having two different abscissaes
series. Still, I learned something new about handling plots in Gretl.

CONSTANT IN LOG-LIKELIHOOD
The basic code *without the constant in the log-l *is (omitting the
initial part where OLS executes to obtain initial values)

<<
matrix Depv = {LWAGE}
matrix Regrs = {const,  EXP,   EXP2, WKS,  OCC,  IND,  SOUTH, SMSA,
MS,  FEM,  UNION,   ED, BLK}
matrix cVec = {c0,c1,c2,c3,c4,c5,c6,c7,c8,c9,c10,c11,c12}'
scalar v0 = 1
scalar v1 = 1
scalar v2 = 1

mle logl = check ?   -ln(v) - 0.5*(e2hn/v)^2 + ln(cdf(D,l1/sqrt(1+l1^2),
e2hn/omega1, 0) - cdf(D,-l2/sqrt(1+l2^2), e2hn/omega2, 0)):NA
series e2hn = Depv - Regrs*cVec
scalar v = sqrt(v0^2 + v1^2 + v2^2)
scalar l1 = (v2/v1)*(v/v0)
scalar l2 = (v1/v2)*(v/v0)
scalar omega1 = (v*v0/v1)*sqrt(1+ (v2/v0)^2)
scalar omega2 = (v*v0/v2)*sqrt(1+ (v1/v0)^2)
scalar check = (v0>0) && (v1>0) && (v2>0)
params cVec  v0 v1 v2
end mle  --verbose
>>

and  gives final results
<<
--- FINAL VALUES:
loglikelihood = -447.517658694 (steplength = 8.38861e-017)
Parameters:       5.6103    0.029306 -0.00048463   0.0036368 -0.16393
0.083254
-0.058693     0.16568    0.093867    -0.32751 0.10612
0.056644
-0.18925     0.21983     0.26368     0.28759
Gradients:   7.1632e-005 -0.00019598   0.0051691 -0.00055942 5.6355e-005
2.3537e-006
4.7828e-005-7.9492e-006 2.2249e-005-2.2649e-006
2.5091e-005 -0.00029823
5.1958e-006 7.7593e-005 5.9452e-006-2.5091e-005 (norm
5.45e-003)

Tolerance = 1.81899e-012

Function evaluations: 397

Model 3: ML, using observations 1-595
logl = check ? -ln(v) - 0.5*(e2hn/v)^2 + ln(cdf(D,l1/sqrt(1+l1^2),
e2hn/omega1, 0) - cdf(D,-l2/sqrt(1+l2^2), e2hn/omega2, 0)):NA
Standard errors based on Outer Products matrix

estimate     std. error      z       p-value
----------------------------------------------------------
cVec[1]     5.61026       0.189973      29.53    1.12e-191 ***
cVec[2]     0.0293063     0.00650305     4.507   6.59e-06  ***
cVec[3]    -0.000484630   0.000127917   -3.789   0.0002    ***
cVec[4]     0.00363680    0.00253677     1.434   0.1517
cVec[5]    -0.163931      0.0372662     -4.399   1.09e-05  ***
cVec[6]     0.0832535     0.0305658      2.724   0.0065    ***
cVec[7]    -0.0586933     0.0300906     -1.951   0.0511    *
cVec[8]     0.165683      0.0296335      5.591   2.26e-08  ***
cVec[9]     0.0938665     0.0469460      1.999   0.0456    **
cVec[10]   -0.327510      0.0678567     -4.826   1.39e-06  ***
cVec[11]    0.106121      0.0335694      3.161   0.0016    ***
cVec[12]    0.0566442     0.00623447     9.086   1.03e-019 ***
cVec[13]   -0.189253      0.0551030     -3.435   0.0006    ***
v0          0.219829      0.0951096      2.311   0.0208    **
v1          0.263683      0.111617       2.362   0.0182    **
v2          0.287589      0.103953       2.767   0.0057    ***

Log-likelihood      -447.5177   Akaike criterion     927.0353
Schwarz criterion    997.2523   Hannan-Quinn         954.3796
>>

----------------------------------------------------------

If  I specify
mle logl = check ? *ln(4/sqrt(2/\$pi))* - ln(v)  etc
I get
<<
--- FINAL VALUES:
loglikelihood = 511.673340992 (steplength = 1.6384e-010)
Parameters:       5.6103    0.029306 -0.00048463   0.0036368 -0.16393
0.083254
-0.058694     0.16568    0.093868    -0.32751 0.10612
0.056644
-0.18925     0.21983     0.26368     0.28759
Gradients:   -0.00013035   0.0013600    0.052876  -0.0098550 6.4448e-005
-0.00051251
0.00057035-8.1379e-006 -0.00036188 -0.00042025
0.00034582  -0.0013756
0.00053909  -0.0013437  0.00054025 -0.00083513 (norm
1.11e-002)

Tolerance = 1.81899e-012

Function evaluations: 493

Model 3: ML, using observations 1-595
logl = check ? ln(4/sqrt(2/\$pi)) -ln(v) - 0.5*(e2hn/v)^2 +
ln(cdf(D,l1/sqrt(1+l1^2), e2hn/omega1, 0) - cdf(D,-l2/sqrt(1+l2^2),
e2hn/omega2, 0)):NA
Standard errors based on Outer Products matrix

estimate     std. error      z       p-value
----------------------------------------------------------
cVec[1]     5.61027       0.189973      29.53    1.12e-191 ***
cVec[2]     0.0293063     0.00650305     4.507   6.59e-06  ***
cVec[3]    -0.000484629   0.000127917   -3.789   0.0002    ***
cVec[4]     0.00363683    0.00253677     1.434   0.1517
cVec[5]    -0.163931      0.0372663     -4.399   1.09e-05  ***
cVec[6]     0.0832537     0.0305658      2.724   0.0065    ***
cVec[7]    -0.0586936     0.0300906     -1.951   0.0511    *
cVec[8]     0.165683      0.0296335      5.591   2.26e-08  ***
cVec[9]     0.0938678     0.0469461      1.999   0.0456    **
cVec[10]   -0.327508      0.0678569     -4.826   1.39e-06  ***
cVec[11]    0.106121      0.0335695      3.161   0.0016    ***
cVec[12]    0.0566442     0.00623448     9.086   1.03e-019 ***
cVec[13]   -0.189254      0.0551031     -3.435   0.0006    ***
v0          0.219833      0.0951107      2.311   0.0208    **
v1          0.263678      0.111623       2.362   0.0182    **
v2          0.287587      0.103956       2.766   0.0057    ***

Log-likelihood       511.6733   Akaike criterion    -991.3467
Schwarz criterion   -921.1297   Hannan-Quinn        -964.0024
>>

*COMMENT: **all parameter estimates are very close but the value of the
log-likelihood is positive.*

---------------------------------------------
If I specify  mle logl = check ? *0.467355827915218* - ln(v)  etc I get
<<
--- FINAL VALUES:
loglikelihood = -172.877055337 (steplength = 5.36871e-021)
Parameters:       5.7197    0.029288 -0.00048358   0.0037060 -0.17731
0.065087
-0.062683     0.16589    0.096647    -0.34367
0.098338    0.054146
-0.18382 2.2828e-008     0.33034     0.42766
-0.42174     0.31255
-0.078953     0.32094   -0.099944   -0.028678
1.6085      23.937
0.80591 6.6747e-005    0.045333   0.0018853 (norm
7.16e-001)

Tolerance = 1.81899e-012

Function evaluations: 502

Model 5: ML, using observations 1-595
logl = check ? 0.467355827915218 -ln(v) - 0.5*(e2hn/v)^2 +
ln(cdf(D,l1/sqrt(1+l1^2), e2hn/omega1, 0) - cdf(D,-l2/sqrt(1+l2^2),
e2hn/omega2, 0)):NA
Standard errors based on Outer Products matrix

estimate        std. error         z       p-value
----------------------------------------------------------------
cVec[1]     5.71974            0.179086      31.94     7.79e-224 ***
cVec[2]     0.0292883          0.00593066     4.938    7.87e-07 ***
cVec[3]    -0.000483577        0.000116778   -4.141    3.46e-05 ***
cVec[4]     0.00370595         0.00245961     1.507    0.1319
cVec[5]    -0.177311           0.0358279     -4.949    7.46e-07 ***
cVec[6]     0.0650868          0.0284437      2.288    0.0221 **
cVec[7]    -0.0626826          0.0289442     -2.166    0.0303 **
cVec[8]     0.165888           0.0279917      5.926    3.10e-09 ***
cVec[9]     0.0966475          0.0452880      2.134    0.0328 **
cVec[10]   -0.343670           0.0618104     -5.560    2.70e-08 ***
cVec[11]    0.0983375          0.0315998      3.112    0.0019 ***
cVec[12]    0.0541457          0.00606580     8.926    4.40e-019 ***
cVec[13]   -0.183823           0.0524279     -3.506    0.0005 ***
v0          2.28282e-08   405491              0.0000   1.0000
v1          0.330336           0.0328825     10.05     9.57e-024 ***
v2          0.427663           0.0335927     12.73     3.98e-037 ***

Log-likelihood      -172.8771   Akaike criterion     377.7541
Schwarz criterion    447.9711   Hannan-Quinn         405.0984
>>

*COMMENT: **slope coefficients are again comparable and the value of the
likelihood is close to what it should have been if its constant term was
added afterwards. But the estimates of the three variance terms v0 v1 v2
are totally different, the one reaching the specified boundary of the
parameter space (zero). *

Athens University of Economics and Business, Greece
Department of Economics
cell:+30-6945-378680
fax: +30-210-8259763

On 9/7/2013 16:00, gretl-users-request at lists.wfu.edu wrote:
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> than "Re: Contents of Gretl-users digest..."
>
>
> Today's Topics:
>
>     1. retrieving F-stat and p-value from a VAR system (cociuba mihai)
>     2. Re: Constant in log-likelihood and graph of two densities
>        together (Allin Cottrell)
>     3. Re: retrieving F-stat and p-value from a VAR system
>        (Allin Cottrell)
>     4. Re: retrieving F-stat and p-value from a VAR system
>        (Allin Cottrell)
>     5. Implement new criterion for var lag selection
>        (Gian Lorenzo Spisso)
>     6. Re: Implement new criterion for var lag selection
>        (Riccardo (Jack) Lucchetti)
>     7. Re: Implement new criterion for var lag selection
>        (Gian Lorenzo Spisso)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Tue, 9 Jul 2013 01:44:11 +0300
> From: cociuba mihai <cociuba at gmail.com>
> Subject: [Gretl-users] retrieving F-stat and p-value from a VAR system
> To: gretl-users at lists.wfu.edu
> Message-ID:
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear GRETL users,
> I'm testing Granger causality between inflation and inflation uncertainty
> for 15 countries and I would like to retrieve the result of the Wald test
> in a matrix, the script that I try to run gets stuck at the last step. Any
> suggestion are welcome.
>
> ###hansl###
> open Table_17.3.gdt
> var 10 M1 R --lagselect
> a=2
> b=3
> c=6
> d=8
> #number of rows 4, but the number of F statistics reported in the VAR
> output for #every equations is 3 so maybe I need more?
> scalar T = 4
> #generate the matrix with 4 rows and 2 colums
> matrix F_stat = zeros(T,2)
> #rename the colums
> # is it possible to have also the name of the F test?
> colnames(F_stat, "t-stat p-value")
>      loop foreach i a b c d
> var \$i M1 R --nc
> F_stat[\$i,] = \$test ~ \$pvalue
> endloop
> print F_stat
> ###end###
>
> Thanks, Mihai
> -------------- next part --------------
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> ------------------------------
>
> Message: 2
> Date: Mon, 8 Jul 2013 21:31:05 -0400 (EDT)
> From: Allin Cottrell <cottrell at wfu.edu>
> Subject: Re: [Gretl-users] Constant in log-likelihood and graph of two
> 	densities together
> To: Gretl list <gretl-users at lists.wfu.edu>
> Message-ID: <alpine.LFD.2.10.1307082117570.23324 at myrtle>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> On Mon, 8 Jul 2013, Alecos Papadopoulos wrote:
>
>> Good evening everybody. I am rather new to Gretl and my questions
>> are probably kindergarten-level, but I could not figure out the
>> answers myself or using Help. So here they are
>>
>> 1) I run maximum likelihood from the script window. I am trying
>> two different and non-nested stochastic specifications. I have to
>> compare and evaluate them by using the value of the maximized
>> log-likelihood. But since they are non-nested, their
>> log-likelihood functions are totally different. So, suddenly, the
>> constants of each log-likelihood, although they play no role in
>> the estimation of the parameters, influence the value of the
>> maximized logl - and they are different constants.
>>
>> If I don't include them in the logl function, then the values of
>> the maximized logl (and the AIC and BIC and HQ criteria) will be
>> misleading for comparison purposes of the two competing stochastic
>> specifications, and currently I am doing the corrections by hand
>> (which I can live with). But it would be nice not to have output
>> that needs such corrections. I tried to include them in the
>> specification of the logl after the "mle logl = " command. But
>> when I tried to include them as, say, "ln(4/sqrt(2/pi))" or
>> "ln(4/sqrt(2/%pi)) I get "syntax error on the command line".
> The recommended way of accessing pi = 3.14... in current gretl
> (version 1.9.12) is "\$pi", though plain "pi" (deprecated since May
> 2012) will still work; "%pi" will definitely not work. The
> expression
>
> ln(4/sqrt(2/\$pi))
>
> is correctly evaluated as 1.612... in current gretl.
>
>> When I calculate them explicitly, say 0.45678 and enter this
>> constant instead, Gretl runs, but the estimation goes astray, and
>> produces different results than when the constant is not included.
>> I suspect that this may have something to do with the fact that I
>> do not specify analytical derivatives, but I really don't know.
>> What am I doing wrong?
> The issue of analytical versus numerical derivatives wouldn't seem
> to be relevant to the inclusion or non-inclusion of a constant term
> (which obviously doesn't have a derivative) in the log-likelihood.
> I suppose something else must be wrong here. I think you'll have to
> show us your full script to get useful help.
>
>> 2) Again for comparison purposes, I would want to have in one graph the
>> estimated densities of two series. But when I select two series the
>> "Variable" menu becomes disabled, while in the "View" menu there are
>> various graph options, but not the option to graph the estimated
>> densities of the two series together. Is there a way around this?
> This question has come up before. Please see
> http://lists.wfu.edu/pipermail/gretl-users/2013-April/008745.html
>
> Allin Cottrell
>
>
> ------------------------------
>
> Message: 3
> Date: Mon, 8 Jul 2013 21:59:16 -0400 (EDT)
> From: Allin Cottrell <cottrell at wfu.edu>
> Subject: Re: [Gretl-users] retrieving F-stat and p-value from a VAR
> 	system
> To: Gretl list <gretl-users at lists.wfu.edu>
> Message-ID: <alpine.LFD.2.10.1307082142420.23324 at myrtle>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> On Tue, 9 Jul 2013, cociuba mihai wrote:
>
>> I'm testing Granger causality between inflation and inflation
>> uncertainty for 15 countries and I would like to retrieve the
>> result of the Wald test...
> What Wald test? (That is, for what null hypothesis?)
>
>> in a matrix, the script that I try to run gets stuck at the last
>> step. Any suggestion are welcome.
> [last step]
>> loop foreach i a b c d
>>    var \$i M1 R --nc
>>    F_stat[\$i,] = \$test ~ \$pvalue
>> endloop
> The "var" command in gretl does not supply a \$test accessor. In fact
> no model estimation command in gretl does that: the label "test" is
> much too general, given that many sorts of tests might be
> contemplated after estimating a given model (either single-equation
> or multi-equation).
>
> Since a VAR is just a collection of equations related in a certain
> way (identical right-hand sides, specific relation between left-hand
> side variables and right-hand sides), estimated in practice via OLS,
> you can get whatever Wald statistics you want by estimating the
> equations singly via the "ols" command, and using either "omit" or
> "restrict" (which do produce \$test and \$pvalue).
>
> (I suppose we could generalize the current scalar \$Fstat accessor
> for single equation models to a matrix for VARs, but that would
> require some decisions on which F-stats to include and in what
> configuration.)
>
> Allin Cottrell
>
>
> ------------------------------
>
> Message: 4
> Date: Mon, 8 Jul 2013 22:15:21 -0400 (EDT)
> From: Allin Cottrell <cottrell at wfu.edu>
> Subject: Re: [Gretl-users] retrieving F-stat and p-value from a VAR
> 	system
> To: Gretl list <gretl-users at lists.wfu.edu>
> Message-ID: <alpine.LFD.2.10.1307082212280.23324 at myrtle>
> Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed
>
> On Mon, 8 Jul 2013, Allin Cottrell wrote:
>
>> On Tue, 9 Jul 2013, cociuba mihai wrote:
>>
>>> I'm testing Granger causality between inflation and inflation uncertainty
>>> for 15 countries and I would like to retrieve the result of the Wald
>>> test...
>> What Wald test? (That is, for what null hypothesis?)
> OK, in fact clear enough from context. Trivial example of what I
> described in my previous posting:
>
> <hansl>
> open data9-7
> scalar p = 4
> var p PRIME UNEMP
> list RHS = const PRIME(-1 to -p) UNEMP(-1 to -p)
> # first equation: does UNEMP Granger-cause PRIME?
> ols PRIME RHS --quiet
> omit UNEMP(-1 to -p) --quiet --test-only
> eval \$test
> eval \$pvalue
> # second equation: does PRIME Granger-cause UNEMP?
> ols UNEMP RHS --quiet
> omit PRIME(-1 to -p) --quiet --test-only
> eval \$test
> eval \$pvalue
> </hansl>
>
> Allin Cottrell
>
>
> ------------------------------
>
> Message: 5
> Date: Tue, 9 Jul 2013 13:15:43 +0200
> From: Gian Lorenzo Spisso <glspisso at gmail.com>
> Subject: [Gretl-users] Implement new criterion for var lag selection
> To: gretl-users at lists.wfu.edu
> Message-ID:
> 	<CAJ_wB9=gLShM2DdET7uk_f0CDBTBRgdcsqj_G_mvhkHE4jcE_w at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Hi all,
> I would like to implement in GRETL the procedure for lag selection of a VAR
> as specified here:
> http://www.tandfonline.com/doi/pdf/10.1080/1350485022000041050 which
> essentialy replace BIC and HQC with a weighted average of the two.
>
> Is there any easy to install package that I could use?
> Otherwise could it be possible to simply reprogram AIC column to show this
> criterion instead? In case can anybody provide a little guidance for the
> process? I am not familiar with gretl programming.
>
> Thank you,
> -------------- next part --------------
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> ------------------------------
>
> Message: 6
> Date: Tue, 9 Jul 2013 14:45:28 +0200 (CEST)
> From: "Riccardo (Jack) Lucchetti" <r.lucchetti at univpm.it>
> Subject: Re: [Gretl-users] Implement new criterion for var lag
> 	selection
> To: Gretl list <gretl-users at lists.wfu.edu>
> Message-ID: <alpine.DEB.2.10.1307091444170.13798 at ec-4.econ.univpm.it>
> Content-Type: text/plain; charset="iso-8859-1"
>
> On Tue, 9 Jul 2013, Gian Lorenzo Spisso wrote:
>
>> Hi all,
>> I would like to implement in GRETL the procedure for lag selection of a VAR
>> as specified here:
>> http://www.tandfonline.com/doi/pdf/10.1080/1350485022000041050 which
>> essentialy replace BIC and HQC with a weighted average of the two.
>>
>> Is there any easy to install package that I could use?
>> Otherwise could it be possible to simply reprogram AIC column to show this
>> criterion instead? In case can anybody provide a little guidance for the
>> process? I am not familiar with gretl programming.
> I don't have a subscription to "Applied Economics Journal". Could you
> describe me the proposed method?
>
> -------------------------------------------------------
>     Riccardo (Jack) Lucchetti
>     Dipartimento di Scienze Economiche e Sociali (DiSES)
>
>     Universit? Politecnica delle Marche
>     (formerly known as Universit? di Ancona)
>
>     r.lucchetti at univpm.it
>     http://www2.econ.univpm.it/servizi/hpp/lucchetti
> -------------------------------------------------------
>
> ------------------------------
>
> Message: 7
> Date: Tue, 9 Jul 2013 14:58:42 +0200
> From: Gian Lorenzo Spisso <glspisso at gmail.com>
> Subject: Re: [Gretl-users] Implement new criterion for var lag
> 	selection
> To: r.lucchetti at univpm.it, Gretl list <gretl-users at lists.wfu.edu>
> Message-ID:
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear Riccardo,
> I attach a screenshot of the relevant part.
> You can see the formulas for the two criterion, and the new criterion
> proposed by Hatemi which simply averages the two. He then goes on and uses
> a Montecarlo simulation to show that this mixed criterion as higher
> probability in picking the right lag.
>
>
> On Tue, Jul 9, 2013 at 2:45 PM, Riccardo (Jack) Lucchetti <
> r.lucchetti at univpm.it> wrote:
>
>> On Tue, 9 Jul 2013, Gian Lorenzo Spisso wrote:
>>
>>   Hi all,
>>> I would like to implement in GRETL the procedure for lag selection of a
>>> VAR
>>> as specified here:
>>> http://www.tandfonline.com/**doi/pdf/10.1080/**1350485022000041050<http://www.tandfonline.com/doi/pdf/10.1080/1350485022000041050>which
>>> essentialy replace BIC and HQC with a weighted average of the two.
>>>
>>> Is there any easy to install package that I could use?
>>> Otherwise could it be possible to simply reprogram AIC column to show this
>>> criterion instead? In case can anybody provide a little guidance for the
>>> process? I am not familiar with gretl programming.
>>>
>> I don't have a subscription to "Applied Economics Journal". Could you
>> describe me the proposed method?
>>
>> ------------------------------**-------------------------
>>    Riccardo (Jack) Lucchetti
>>    Dipartimento di Scienze Economiche e Sociali (DiSES)
>>
>>    Universit? Politecnica delle Marche
>>    (formerly known as Universit? di Ancona)
>>
>>    r.lucchetti at univpm.it
>>    http://www2.econ.univpm.it/**servizi/hpp/lucchetti<http://www2.econ.univpm.it/servizi/hpp/lucchetti>
>> ------------------------------**-------------------------
>> _______________________________________________
>> Gretl-users mailing list
>> Gretl-users at lists.wfu.edu
>> http://lists.wfu.edu/mailman/listinfo/gretl-users
>>
>
>

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