[Limdep Nlogit List] random effects tobit vs random coefficient tobit
William Greene
wgreene at stern.nyu.edu
Mon Jan 18 02:59:19 EST 2010
Andreas. You are comparing a simulated log likelihood (the RPM) to one
that is just the likelihood computed with quadrature. What you should
do to carry out the test you are trying to carry out is as follows:
(This uses the same data and the same draws.)
skip $
tobit ; lhs=bet2lot4 ; rhs=x2 ; pds=10; rpm ; Halton ; Pts=200
fcn=one(n),treat_pr(n),treat_tr(n) ; marginal $
calc ; Logl10=logl $ $
tobit ; lhs=bet2lot4 ; rhs=x2 ; pds=10; rpm ; Halton ; Pts=200
fcn=one(n) ; marginal $
calc ; Logl4=logl$
calc ; list ; LRtest=-2*(Logl4-Logl10) ; DF=3; pvalue=1-Chi(LRtest,DF) $
/Bill Greene
----- Original Message -----
From: "Andreas Drichoutis" <adrihout at aua.gr>
To: limdep at limdep.itls.usyd.edu.au
Sent: Sunday, January 17, 2010 10:52:42 AM GMT -05:00 Colombia
Subject: [Limdep Nlogit List] random effects tobit vs random coefficient tobit
Dear all,
I'm using a LR test to choose between a random effects tobit model and a
random coefficient tobit model with panel structure. The commands I use are:
namelist ; x2=one,
gender,age,hsize,totfee,econpos1,econpos2,econpos3,econpos4,period,treat_pr,
treat_tr $
skip $
tobit ; lhs=bet2lot4 ; rhs=x2; random effects ; pds=10 $
calc ; Logl4=logl $
skip $
tobit ; lhs=bet2lot4 ; rhs=x2 ; pds=10; rpm ;
fcn=one(n),treat_pr(n),treat_tr(n) ; marginal $
calc ; Logl10=logl $
calc ; list ; LRtest=-2*(Logl4-Logl10) ; DF=3; pvalue=1-Chi(LRtest,DF) $
However, the log likelihood of the random coefficients tobit is smaller than
the log likelihood of the random effects tobit which of course produces the
below output:
--> calc ; list ; LRtest=-2*(Logl4-Logl10) ; DF=3; pvalue=1-Chi(LRtest,DF) $
+------------------------------------+
| Listed Calculator Results |
+------------------------------------+
LRTEST = -335.667941
DF = 3.000000
Error 471: Cannot compute CHI; parameter 1 is < = 0
Error 116: CALC - Unable to compute result. Check earlier message.
Calculator: Computed 2 scalar results
What am I doing wrong?? The full output is listed below:
--> skip $
--> tobit ; lhs=bet2lot4 ; rhs=x2; random effects ; pds=10 $
Normal exit from iterations. Exit status=0.
logl,k,n= -1416.333138 13 710
+---------------------------------------------+
| Limited Dependent Variable Model - CENSORED |
| Maximum Likelihood Estimates |
| Model estimated: Jan 17, 2010 at 02:55:30PM.|
| Dependent variable BET2LOT4 |
| Weighting variable None |
| Number of observations 710 |
| Iterations completed 4 |
| Log likelihood function -1416.333 |
| Number of parameters 13 |
| Info. Criterion: AIC = 4.02629 |
| Finite Sample: AIC = 4.02703 |
| Info. Criterion: BIC = 4.10988 |
| Info. Criterion:HQIC = 4.05858 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
| LM test [df] for tobit= 156.751[ 12] |
| Normality Test, LM = 60.348[ 2] |
| ANOVA based fit measure = .103095 |
| DECOMP based fit measure = .125142 |
+---------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
+--------+Primary Index Equation for Model |
|Constant| -15.3674*** 2.08069611 -7.386 .0000 |
|GENDER | 1.00451*** .17103259 5.873 .0000 .3943662|
|AGE | .31544*** .05005685 6.302 .0000 20.732394|
|HSIZE | -.02730 .07689967 -.355 .7225 4.3802817|
|TOTFEE | .46239*** .09951594 4.646 .0000 16.711268|
|ECONPOS1| 1.16291*** .40047154 2.904 .0037 .2676056|
|ECONPOS2| 1.61719*** .39306571 4.114 .0000 .2676056|
|ECONPOS3| 1.52737*** .37501870 4.073 .0000 .3239437|
|ECONPOS4| .95004** .45028925 2.110 .0349 .0845070|
|PERIOD | .18307*** .02701722 6.776 .0000 5.5000000|
|TREAT_PR| .21049 .16936398 1.243 .2139 .4929577|
|TREAT_TR| .72958*** .16449886 4.435 .0000 .5070423|
+--------+Disturbance standard deviation |
|Sigma | 2.03689*** .05871361 34.692 .0000 |
+--------+------------------------------------------------------------+
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
Normal exit from iterations. Exit status=0.
logl,k,n= -998.155408 14 710
+---------------------------------------------+
| Reestimated RANDOM EFFECTS Tobit Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 17, 2010 at 02:55:32PM.|
| Dependent variable BET2LOT4 |
| Weighting variable None |
| Number of observations 710 |
| Iterations completed 30 |
| Log likelihood function -998.1554 |
| Number of parameters 14 |
| Info. Criterion: AIC = 2.85114 |
| Finite Sample: AIC = 2.85199 |
| Info. Criterion: BIC = 2.94116 |
| Info. Criterion:HQIC = 2.88592 |
| Restricted log likelihood -1416.333 |
| McFadden Pseudo R-squared .2952538 |
| Chi squared 836.3555 |
| Degrees of freedom 1 |
| Prob[ChiSqd > value] = .0000000 |
| Sample is 10 pds and 71 individuals. |
+---------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|Constant| -14.6483*** 1.28389584 -11.409 .0000 |
|GENDER | 1.92285*** .11195057 17.176 .0000 .3943662|
|AGE | .28561*** .02628378 10.867 .0000 20.732394|
|HSIZE | -.06575 .05534556 -1.188 .2348 4.3802817|
|TOTFEE | .45537*** .06140064 7.417 .0000 16.711268|
|ECONPOS1| 1.24880*** .24493824 5.098 .0000 .2676056|
|ECONPOS2| 1.47099*** .24651507 5.967 .0000 .2676056|
|ECONPOS3| .99682*** .23244922 4.288 .0000 .3239437|
|ECONPOS4| .09404 .29304674 .321 .7483 .0845070|
|PERIOD | .15308*** .00854629 17.912 .0000 5.5000000|
|TREAT_PR| .18498* .10982735 1.684 .0921 .4929577|
|TREAT_TR| .84865*** .09862849 8.605 .0000 .5070423|
|Sigma(v)| 1.05254*** .01676555 62.780 .0000 |
|Sigma(u)| 1.85136*** .06332540 29.236 .0000 |
+--------+------------------------------------------------------------+
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
--> calc ; Logl4=logl $
--> skip $
--> tobit ; lhs=bet2lot4 ; rhs=x2 ; pds=10; rpm ; fcn=one(n),treat_pr(n),
treat_tr(n) ; marginal $
+----------------------------------------------------+
| OLS Starting values for random parameters model |
| Ordinary least squares regression |
| Model was estimated Jan 17, 2010 at 02:55:32PM |
| LHS=BET2LOT4 Mean = 2.118859 |
| Standard deviation = 2.065007 |
| WTS=none Number of observs. = 710 |
| Model size Parameters = 12 |
| Degrees of freedom = 698 |
| Residuals Sum of squares = 2448.101 |
| Standard error of e = 1.872781 |
| Fit R-squared = .1902701 |
| Adjusted R-squared = .1775093 |
| Model test F[ 11, 698] (prob) = 14.91 (.0000) |
| Diagnostic Log likelihood = -1446.866 |
| Restricted(b=0) = -1521.791 |
| Chi-sq [ 11] (prob) = 149.85 (.0000) |
| Info criter. LogAmemiya Prd. Crt. = 1.271609 |
| Akaike Info. Criter. = 1.271606 |
| Bayes Info. Criter. = 1.348765 |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|GENDER | .86421*** .15525106 5.567 .0000 .3943662|
|AGE | .28852*** .04511056 6.396 .0000 20.732394|
|HSIZE | -.01215 .06979876 -.174 .8617 4.3802817|
|TOTFEE | .36541*** .08981624 4.068 .0000 16.711268|
|ECONPOS1| 1.13420*** .35829935 3.166 .0015 .2676056|
|ECONPOS2| 1.36080*** .35263227 3.859 .0001 .2676056|
|ECONPOS3| 1.30121*** .33518827 3.882 .0001 .3239437|
|ECONPOS4| .76261* .40567359 1.880 .0601 .0845070|
|PERIOD | .18121*** .02446982 7.406 .0000 5.5000000|
|Constant| -12.8792*** 1.86921217 -6.890 .0000 |
|TREAT_PR| .27916* .15315829 1.823 .0683 .4929577|
|TREAT_TR| .65945*** .14911202 4.423 .0000 .5070423|
+--------+------------------------------------------------------------+
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
Normal exit from iterations. Exit status=0.
logl,k,n= -1165.989379 16 710
+---------------------------------------------+
| Random Coefficients Tobit Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 17, 2010 at 02:55:51PM.|
| Dependent variable BET2LOT4 |
| Weighting variable None |
| Number of observations 710 |
| Iterations completed 65 |
| Log likelihood function -1165.989 |
| Number of parameters 16 |
| Info. Criterion: AIC = 3.32955 |
| Finite Sample: AIC = 3.33065 |
| Info. Criterion: BIC = 3.43243 |
| Info. Criterion:HQIC = 3.36929 |
| Sample is 10 pds and 71 individuals. |
| TOBIT (censored) regression model |
| (Lower) censoring limit is .00 |
| Simulation based on 100 random draws |
+---------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
+--------+Nonrandom parameters |
|GENDER | .94807*** .10995143 8.623 .0000 .3943662|
|AGE | .32899*** .03286281 10.011 .0000 20.732394|
|HSIZE | -.06144 .05077379 -1.210 .2262 4.3802817|
|TOTFEE | .23699*** .06499989 3.646 .0003 16.711268|
|ECONPOS1| 1.25894*** .27894351 4.513 .0000 .2676056|
|ECONPOS2| 1.85986*** .27514168 6.760 .0000 .2676056|
|ECONPOS3| 2.08401*** .26263528 7.935 .0000 .3239437|
|ECONPOS4| 1.44497*** .30369499 4.758 .0000 .0845070|
|PERIOD | .18833*** .00888661 21.193 .0000 5.5000000|
+--------+Means for random parameters |
|Constant| -11.8760*** 1.36500586 -8.700 .0000 |
|TREAT_PR| -.46555*** .11270688 -4.131 .0000 .4929577|
|TREAT_TR| .75248*** .10430907 7.214 .0000 .5070423|
+--------+Scale parameters for dists. of random parameters |
|Constant| 1.29447*** .05431955 23.831 .0000 |
|TREAT_PR| 1.53339*** .08708320 17.608 .0000 |
|TREAT_TR| 1.11736*** .07967833 14.024 .0000 |
+--------+Variance parameter given is sigma |
|Std.Dev.| 1.22359*** .01405740 87.043 .0000 |
+--------+------------------------------------------------------------+
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
Implied standard deviations of random parameters
Matrix S.D_Beta has 3 rows and 1 columns.
1
+--------------
1| 1.29448
2| 1.53340
3| 1.11737
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Conditional Mean at Sample Point 1.8660 |
| Scale Factor for Marginal Effects .9326 |
+-------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|GENDER | .88416*** .10448649 8.462 .0000 .3943662|
|AGE | .30682*** .03125703 9.816 .0000 20.732394|
|HSIZE | -.05730 .04733977 -1.210 .2261 4.3802817|
|TOTFEE | .22101*** .06092928 3.627 .0003 16.711268|
|ECONPOS1| 1.17408*** .26015875 4.513 .0000 .2676056|
|ECONPOS2| 1.73449*** .25796974 6.724 .0000 .2676056|
|ECONPOS3| 1.94354*** .24804356 7.835 .0000 .3239437|
|ECONPOS4| 1.34757*** .28435880 4.739 .0000 .0845070|
|PERIOD | .17563*** .00995265 17.647 .0000 5.5000000|
|Constant| -11.0755*** 1.30217462 -8.505 .0000 |
|TREAT_PR| -.43417*** .10559238 -4.112 .0000 .4929577|
|TREAT_TR| .70176*** .10142687 6.919 .0000 .5070423|
+--------+------------------------------------------------------------+
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
--> calc ; Logl10=logl $
--> calc ; list ; LRtest=-2*(Logl4-Logl10) ; DF=3; pvalue=1-Chi(LRtest,DF) $
+------------------------------------+
| Listed Calculator Results |
+------------------------------------+
LRTEST = -335.667941
DF = 3.000000
Error 471: Cannot compute CHI; parameter 1 is < = 0
Error 116: CALC - Unable to compute result. Check earlier message.
Calculator: Computed 2 scalar results
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