# RE: st: loglikelihood and loglikelihood ratio

 From "Lachenbruch, Peter" To Subject RE: st: loglikelihood and loglikelihood ratio Date Wed, 18 Mar 2009 08:33:23 -0700

```I don't know the answer to your problem.  As I said, I'm unfamiliar with
what you are doing.  Since the df are too small, is it possible that one
of your groups either has no observations or all observations are the
same?

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
jjc.li@utoronto.ca
Sent: Tuesday, March 17, 2009 4:11 PM
To: statalist@hsphsun2.harvard.edu
Subject: RE: st: loglikelihood and loglikelihood ratio

Hi Peter,

I am not sure if I understood you, but I will try to explain my
estimation.

First, sl, sm, sk and se equations are derived by logarithmic
differentiation fo the equation lnc. That means all the parameters in
sl, sm, sk and se are also appeared in lnc. Thus, the parameters in
the first model is 40, not 64.

Second, in loglikelihood ratio test, the degrees of freedom (the No.
in LR chis()) equal to the difference in the number of parameters for
the two models. So in my 3 regions case, the lrtest degree of freedom
is  32-29=3. You can see "3" in LR chi2().

What make me being confused now is:

1. In my 4 regions case, why the degree of freedom is 2, not 3?
Because according to the definition, it shoule be 40-37=3

2. In my 3 regions case, the LR chi(3) value is negative. It's not
normal.

Jingjing

Quoting "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>:

> I don't pretend to understand all you have done.  However, should the
> degrees of freedom be approaching or exceeding the number of
> observations?
> In your first model you have 72 observations and estimate 40+24=64
> parameters (getting close to saturation).
> In your second model you have 72 observations and 58 parameters
> estimated.
> Third model 54 observations and 53 parameters
> Fourth model 54 observations and 47 parameters estimated.
> Are you saturating the model?  Are there some linear dependencies that
> are causing the ills?
>
> Tony
>
> Peter A. Lachenbruch
> Department of Public Health
> Oregon State University
> Corvallis, OR 97330
> Phone: 541-737-3832
> FAX: 541-737-4001
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> jjc.li@utoronto.ca
> Sent: Tuesday, March 17, 2009 11:11 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: RE: st: loglikelihood and loglikelihood ratio
>
> 1. First, My euqation system is one translog cost function (lnc), with
> 4 cost share equatios(sl sk sm se). To use -sureg-, I just need to
> estimate the translog cost function with 3 cost share equations
> (choose any 3 of the 4)
>
> My total dataset contains 7 regions. The estimation results for the 7
> regions are fine. All R square are positive, all LR chi() are
> positive, and all degree of freedom are right.
>
>
>
> 2. I choose the last 4 regions of the total 7regions and create a new
> data set(changed the dummy variables).
>
> Here, all the R square are positive, all LR chi() are positive. But
> the degree of freedom are strange.
>
> 4 regions Unrestricted
> ----------------------------------------------------------------------
> Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
> ----------------------------------------------------------------------
> lnc                72     40    .0987079    0.9693   7.62e+07   0.0000
> sl                 72      8    .0230819    0.3033     417.70   0.0000
> se                 72      8    .0023162    0.9399    1246.72   0.0000
> sm                 72      8    .0292372    0.5744    1094.54   0.0000
> ----------------------------------------------------------------------
>   _cons in equation lnc are dropped, no other variable droped
>
>
> 4 regions Restricted
>
> ----------------------------------------------------------------------
> Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
> ----------------------------------------------------------------------
> lnc                72     37    .0930231    0.9727   1.47e+07   0.0000
> sl                 72      7    .0195899    0.4982     347.11   0.0000
> se                 72      7    .0022661    0.9425    1275.65   0.0000
> sm                 72      7    .0270912    0.6346    1003.91   0.0000
> ----------------------------------------------------------------------
> No _cons dropped, no variable dropped
>
> Likelihood-ratio test                                  LR chi2(2)  =
> 6.71
> (Assumption: B nested in A)                            Prob > chi2 =
> 0.0350
>
> I am thinking if the degree of freedom changed from 3 to 2 because of
> _cons in unrestricted model is dropped, but kept in restricted model?
>
>
> 3. I chose the first 3 regions and created them as a new dataset
> (changed the dummy variables). When I estimated equations lnc, sl, sm,
> se, there are two negative R square values. So I changed them to ln,
> sl, sk, se and got one negative R-sq this time. LR chi() here are
> negative.
>
> 3 regions unrestriced
> ----------------------------------------------------------------------
> Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
> ----------------------------------------------------------------------
> lnc                54     32    .0711293    0.9520   1.53e+08   0.0000
> sl                 54      7    .0517401   -0.9964    1022.17   0.0000
> sk                 54      7    .0089583    0.5192    1238.82   0.0000
> sm                 54      7    .0345315    0.5581     701.24   0.0000
> ----------------------------------------------------------------------
> lnq, _cons are dropped in equation lnc
>
>
> 3 regions restricted
> ----------------------------------------------------------------------
> Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
> ----------------------------------------------------------------------
> lnc                54     29     .061907    0.9637   1.27e+08   0.0000
> sl                 54      6    .0239187    0.5733     366.81   0.0000
> sk                 54      6    .0085489    0.5621     431.86   0.0000
> sm                 54      6    .0259183    0.7511     405.20   0.0000
> ----------------------------------------------------------------------
> _cons in equation lnc is dropped, no other variables dropped.
>
>
> Likelihood-ratio test                                  LR chi2(3)  =
> -5.07
> (Assumption: E nested in A)                            Prob > chi2 =
> 1.0000
>
>
>
>
> Jingjing
>
>
>
> Quoting "Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>:
>
>> I haven't been following this in detail, but one issue that might
>> simplify matters would be for Jingjing to copy the commands from the
>> results window and the error messages received.  Only copy the
> relevant
>> parts of the output - I don't want to see 15 pages of garbage.
> Maarten
>> has been very noble in this.
>>
>> Tony
>>
>> Peter A. Lachenbruch
>> Department of Public Health
>> Oregon State University
>> Corvallis, OR 97330
>> Phone: 541-737-3832
>> FAX: 541-737-4001
>>
>>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu
>> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
>> jjc.li@utoronto.ca
>> Sent: Tuesday, March 17, 2009 9:45 AM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: loglikelihood and loglikelihood ratio
>>
>> 1. I just checked the commands for the 3 regions case and found they
>> are right. But in the estimation of the unrestricted model, R square
>> of one of the three equations are negative, R square of the other
>> three euqations are positive. Does it cause the negative LR chi2
> value?
>>
>> 2. In my 7 regions case, LR chi are positive. However, there's some
>> strange thing about the degree of freedom. In unrestricted case, the
>> parameters for equation 1, 2, 3 are 40, 8, 8, respectively. In
>> restricted case, are 37, 7, 7. I though the degree of freedom should
>> be 40-37=3. But the result of lrtest given by stata is LR chi(2).
>> What's the problem?
>>
>> Thanks.
>>
>> Jingjing
>>
>>
>>
>> Quoting Maarten buis <maartenbuis@yahoo.co.uk>:
>>
>>>
>>> You definately should not use the -force- option. I was expecting
>>> that you were not telling us everything you did.
>>>
>>> -- Maarten
>>>
>>> -----------------------------------------
>>> Maarten L. Buis
>>> Institut fuer Soziologie
>>> Universitaet Tuebingen
>>> Wilhelmstrasse 36
>>> 72074 Tuebingen
>>> Germany
>>>
>>> http://home.fsw.vu.nl/m.buis/
>>> -----------------------------------------
>>>
>>>
>>> --- On Tue, 17/3/09, jjc.li@utoronto.ca <jjc.li@utoronto.ca> wrote:
>>>
>>>> From: jjc.li@utoronto.ca <jjc.li@utoronto.ca>
>>>> Subject: Re: st: loglikelihood and loglikelihood ratio
>>>> To: statalist@hsphsun2.harvard.edu
>>>> Date: Tuesday, 17 March, 2009, 2:59 PM
>>>> I am quite sure it's the same 3 regions. Because I just
>>>> input the 3
>>>> regions dataest. I will try to use-force-, then run it
>>>> again.
>>>>
>>>> Thank you.
>>>>
>>>> Quoting Maarten buis <maartenbuis@yahoo.co.uk>:
>>>>
>>>> >
>>>> > --- On Tue, 17/3/09, jjc.li@utoronto.ca  wrote:
>>>> >> The previous results is from the estimation of a
>>>> "7
>>>> >> regions dataset".
>>>> >>
>>>> >> Then I use almost the same command to do the
>>>> estimation of
>>>> >> a "3  regions dataset". The only thing I
>>>> change is that I
>>>> >> choose first 3 regions of the total 7 regions and
>>>> also
>>>> >> modify the command that related to the dummy
>>>> varible. This
>>>> >> time, it gives a negative value.
>>>> >
>>>> > Are you sure both models A and E refer to the same 3
>>>> regions?
>>>> >
>>>> > Did you specify the -force- option in -lrtest-?
>>>> >
>>>> > --Maarten
>>>> >
>>>> > -----------------------------------------
>>>> > Maarten L. Buis
>>>> > Institut fuer Soziologie
>>>> > Universitaet Tuebingen
>>>> > Wilhelmstrasse 36
>>>> > 72074 Tuebingen
>>>> > Germany
>>>> >
>>>> > http://home.fsw.vu.nl/m.buis/
>>>> > -----------------------------------------
>>>> >
>>>> >
>>>> >
>>>> >
>>>> >
>>>> >
>>>> >
>>>> > *
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>>>> >
>>>>
>>>>
>>>>
>>>>
>>>> *
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>>>
>>>
>>>
>>>
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>>
>>
>>
>>
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>
>
>
>
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```