[Limdep Nlogit List] random effects tobit vs random coefficient tobit
Andreas Drichoutis
adrihout at aua.gr
Mon Jan 18 02:52:42 EST 2010
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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