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Expt12.txt
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/*=================================================================
Example 20.12. Censoring in the Tobit and Poisson Regression Models
*/=================================================================
? (continued)
?
Dstat ; Rhs=*
Histogram;rhs=y$
?
Descriptive Statistics
All results based on nonmissing observations.
===============================================================================
Variable Mean Std.Dev. Minimum Maximum Cases
===============================================================================
Y 1.45590682 3.29875773 .000000000 12.0000000 601
Z1 .475873544 .499833583 .000000000 1.00000000 601
Z2 32.4875208 9.28876170 17.5000000 57.0000000 601
Z3 8.17769551 5.57130315 .125000000 15.0000000 601
Z4 .715474210 .451564115 .000000000 1.00000000 601
Z5 3.11647255 1.16750940 1.00000000 5.00000000 601
Z6 16.1663894 2.40255457 9.00000000 20.0000000 601
Z7 4.19467554 1.81944266 1.00000000 7.00000000 601
Z8 3.93178037 1.10317949 1.00000000 5.00000000 601
Histogram for Y NOBS= 601, Too low: 0, Too high: 0
Bin Lower limit Upper limit Frequency Cumulative Frequency
========================================================================
0 .000 1.000 451 ( .7504) 451( .7504)
1 1.000 2.000 34 ( .0566) 485( .8070)
2 2.000 3.000 17 ( .0283) 502( .8353)
3 3.000 4.000 19 ( .0316) 521( .8669)
4 4.000 5.000 0 ( .0000) 521( .8669)
5 5.000 6.000 0 ( .0000) 521( .8669)
6 6.000 7.000 0 ( .0000) 521( .8669)
7 7.000 8.000 42 ( .0699) 563( .9368)
8 8.000 9.000 0 ( .0000) 563( .9368)
9 9.000 10.000 0 ( .0000) 563( .9368)
10 10.000 11.000 0 ( .0000) 563( .9368)
11 11.000 12.000 0 ( .0000) 563( .9368)
12 12.000 13.000 38 ( .0632) 601(1.0000)
?
? Specification analysis for the tobit model
?
Create ;q=y>0$
Namelist ; X = one,z1,z2,z3,z4,z5,z6,z7,z8 $
Namelist ; Xr= one, z2,z3, z5, z7,z8 $
?
? Tobit specification tests for three variables
? Wald
?
Tobit ; Lhs = y ; Rhs = X ; Wald:b(2)=0,b(5)=0,b(7)=0$
Calc ; LogLU=Logl $
Tobit ; Lhs = y ; Rhs = XR$
?
? Likelihood Ratio
?
Calc ; List ; LogLR=Logl ; LRTest = -2*(LogLR - LogLu) $
?
? lagrange Multiplier
?
Tobit ; Lhs = y ; Rhs = X ; Maxit = 0
; Start=b(1),0,b(2),b(3),0,b(4),0,b(5),b(6),s$
+---------------------------------------------+
| Limited Dependent Variable Model - CENSORED |
| Log likelihood function -704.7311 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
| Wald test of 3 linear restrictions |
| Chi-squared = 1.66, Sig. level = .64546 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Primary Index Equation for Model
Constant 7.608487071 3.9059870 1.948 .0514
Z1 .9457873252 1.0628656 .890 .3735 .47587354
Z2 -.1926982765 .80968360E-01 -2.380 .0173 32.487521
Z3 .5331896065 .14660745 3.637 .0003 8.1776955
Z4 1.019181783 1.2795746 .797 .4257 .71547421
Z5 -1.698999723 .40548331 -4.190 .0000 3.1164725
Z6 .2536077921E-01 .22766679 .111 .9113 16.166389
Z7 .2129825522 .32115700 .663 .5072 4.1946755
Z8 -2.273284428 .41540687 -5.472 .0000 3.9317804
Disturbance standard deviation
Sigma 8.258432069 .55458061 14.891 .0000
+---------------------------------------------+
| Limited Dependent Variable Model - CENSORED |
| Log likelihood function -705.5762 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Primary Index Equation for Model
Constant 8.174197436 2.7414456 2.982 .0029
Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521
Z3 .5541418128 .13451794 4.119 .0000 8.1776955
Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725
Z7 .3260532488 .25442475 1.282 .2000 4.1946755
Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804
Disturbance standard deviation
Sigma 8.247080326 .55336401 14.904 .0000
LRTEST = .16903037971408140D+01
Maximum iterations reached. Exit iterations with status=1.
Maxit = 0. Computing LM statistic at starting values.
No iterations computed and no parameter update done.
+---------------------------------------------+
| Limited Dependent Variable Model - CENSORED |
| Iterations completed 1 |
| LM Stat. at start values 1.681409 |
| LM statistic kept as scalar LMSTAT |
| Log likelihood function -705.5762 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Primary Index Equation for Model
Constant 8.174197436 3.8998101 2.096 .0361
Z1 .0000000000 1.0537723 .000 1.0000 .47587354
Z2 -.1793325837 .80623305E-01 -2.224 .0261 32.487521
Z3 .5541418128 .14686554 3.773 .0002 8.1776955
Z4 .0000000000 1.2675769 .000 1.0000 .71547421
Z5 -1.686220493 .40440804 -4.170 .0000 3.1164725
Z6 .0000000000 .22719456 .000 1.0000 16.166389
Z7 .3260532488 .31951084 1.020 .3075 4.1946755
Z8 -2.284972720 .41462602 -5.511 .0000 3.9317804
Disturbance standard deviation
Sigma 8.247080326 .55345418 14.901 .0000
/*
? Get main results, and MLEs. OLS is part of output
?
Tobit ; Lhs = y ; Rhs = XR ; MarginalEffects ; Par ; OLS $
Calc ; List ; Ltobit=Logl $
?
? Scaled tobit estimates and standard errors
?
Wald ; Start=B ; Var=varb ; labels=b1,b2,b3,b4,b5,b6,sg
; fn1=b1/sg ; fn2=b2/sg ; fn3=b3/sg
; fn4=b4/sg ; fn5=b5/sg ; fn6=b6/sg$
?
? Cragg/Greene consistency test for probability
?
Create ; q = y>0 $
Probit ; Lhs=q ; Rhs=xr ; Marginals$
Calc ; Lprobit=Logl $
Trunc ; Lhs=y ; Rhs=Xr ; Marginals $
Calc ; LTrunc=Logl $
Calc ; List ; Cragg = -2*(Ltobit - Lprobit - Ltrunc) $
/*
+-----------------------------------------------------------------------+
| Limited Dependent Variable Model - CENSORED Regression |
| Ordinary least squares regression Weighting variable = none |
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 5.608160612 .79659947 7.040 .0000
Z2 -.5034734786E-01 .22105810E-01 -2.278 .0228 32.487521
Z3 .1618520786 .36896903E-01 4.387 .0000 8.1776955
Z5 -.4763238840 .11130785 -4.279 .0000 3.1164725
Z7 .1060059379 .71100666E-01 1.491 .1360 4.1946755
Z8 -.7122423539 .11828889 -6.021 .0000 3.9317804
+---------------------------------------------+
| Limited Dependent Variable Model - CENSORED |
| Log likelihood function -705.5762 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Primary Index Equation for Model
Constant 8.174197436 2.7414456 2.982 .0029
Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521
Z3 .5541418128 .13451794 4.119 .0000 8.1776955
Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725
Z7 .3260532488 .25442475 1.282 .2000 4.1946755
Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804
Disturbance standard deviation
Sigma 8.247080326 .55336401 14.904 .0000
+-------------------------------------------+
| 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 1.1263 |
| Scale Factor for Marginal Effects .2338 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.910805170 .65758415 2.906 .0037
Z2 -.4192088958E-01 .18444435E-01 -2.273 .0230 32.487521
Z3 .1295365141 .31167559E-01 4.156 .0000 8.1776955
Z5 -.3941718881 .93379144E-01 -4.221 .0000 3.1164725
Z7 .7621839800E-01 .59471640E-01 1.282 .2000 4.1946755
Z8 -.5341365586 .94896126E-01 -5.629 .0000 3.9317804
LTOBIT = -.70557621764203170D+03
+-----------------------------------------------+
| WALD procedure. Estimates and standard errors |
| for nonlinear functions |
+-----------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Fncn( 1) .9911625827 .33652215 2.945 .0032
Fncn( 2) -.2174497842E-01 .95484533E-02 -2.277 .0228
Fncn( 3) .6719248399E-01 .16136495E-01 4.164 .0000
Fncn( 4) -.2044627222 .48371582E-01 -4.227 .0000
Fncn( 5) .3953559755E-01 .30825623E-01 1.283 .1996
Fncn( 6) -.2770644434 .48258618E-01 -5.741 .0000
+---------------------------------------------+
| Binomial Probit Model |
| Log likelihood function -307.2955 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant .9766647244 .36104809 2.705 .0068
Z2 -.2202376072E-01 .10177371E-01 -2.164 .0305 32.487521
Z3 .5990084920E-01 .17086004E-01 3.506 .0005 8.1776955
Z5 -.1836462412 .51493239E-01 -3.566 .0004 3.1164725
Z7 .3751312008E-01 .32844576E-01 1.142 .2534 4.1946755
Z8 -.2729824396 .52473295E-01 -5.202 .0000 3.9317804
+-------------------------------------------+
| Partial derivatives of E[y] = F[*] with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant .2969094977 .11108860 2.673 .0075
Z2 -.6695300413E-02 .30909282E-02 -2.166 .0303 32.487521
Z3 .1821006800E-01 .51704684E-02 3.522 .0004 8.1776955
Z5 -.5582910069E-01 .15568275E-01 -3.586 .0003 3.1164725
Z7 .1140411992E-01 .99845393E-02 1.142 .2534 4.1946755
Z8 -.8298761795E-01 .15933104E-01 -5.209 .0000 3.9317804
+---------------------------------------------+
| Limited Dependent Variable Model - TRUNCATE |
| Log likelihood function -392.7103 |
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
| Observations after truncation 150 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 8.323045133 3.9597250 2.102 .0356
Z2 -.8414425459E-01 .11941653 -.705 .4810 33.410000
Z3 .5597703506 .21897633 2.556 .0106 9.5319467
Z5 -1.502400347 .61728675 -2.434 .0149 2.8533333
Z7 .1891403416 .37677181 .502 .6157 4.3133333
Z8 -1.349377201 .56454613 -2.390 .0168 3.4466667
Sigma 5.529829399 .65959601 8.384 .0000
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
| Conditional Mean at Sample Point 5.5614 |
| Scale Factor for Marginal Effects .4843 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 4.030447257 1.9175029 2.102 .0356
Z2 -.4074698319E-01 .57827634E-01 -.705 .4810 33.410000
Z3 .2710696431 .10603962 2.556 .0106 9.5319467
Z5 -.7275396519 .29892205 -2.434 .0149 2.8533333
Z7 .9159149792E-01 .18245232 .502 .6157 4.3133333
Z8 -.6534379609 .27338232 -2.390 .0168 3.4466667
CRAGG = .11140859667898440D+02
? Moment based tests for normality
Tobit ; Lhs = y ; Rhs = XR ; Par$
Matrix ; Beta=b(1:6)$
Create ; bx=beta'xr ; eps=y-bx ; lambda=n01(bx/s)/phi(-bx/s)
; bi= .5*q*(((eps/s)^2-1)/s^2)+.5*(1-q)*bx*lambda/s^3
; ei=(q*eps-(1-q)*s*lambda)/s^2
; a1=ei ;a2=ei*z2 ;a3=ei*z3 ;a4=ei*z5 ;a5=ei*z7
; a6=ei*z8 ;a7=bi ;a8=ei^3 ;a9=ei^4-3*ei^2 $
Namelist ; A=a1,a2,a3,a4,a5,a6,a7,a8,a9$
Matrix ; List ; Chesher=1'a*<a'a>*a'1$
Create ; m1=-(1-q)*(s^3*lambda*(bx/s+2)^2) + q*eps^3
; m2= (1-q)*(s^4*lambda*bx/s*((bx/s)^2+3))
+ q *(eps^4 - 3*s^4)$
Namelist ; G=a1,a2,a3,a4,a5,a6,a7 ; M=m1,m2$
Matrix ; Pagan=m'm-m'g*<g'g>*g'm
; List ; Pagan=1'm*<pagan>*m'1$
CHESHER +--------------
1| .5622181D+03
PAGAN +--------------
1| .2031353D+02
?
? Doubly censored (at 0 and 4) tobit model. Compared to standard case
?
Tobit ; Lhs = y ; Rhs = XR ; Mar $
Tobit ; Lhs = y ; Rhs = XR ; Mar ; Limits=0,4 $
?
+---------------------------------------------+
| Threshold values for the model: |
| Lower= .0000 Upper=+infinity |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 8.174197436 2.7414456 2.982 .0029
Z2 -.1793325837 .79093240E-01 -2.267 .0234 32.487521
Z3 .5541418128 .13451794 4.119 .0000 8.1776955
Z5 -1.686220493 .40375155 -4.176 .0000 3.1164725
Z7 .3260532488 .25442475 1.282 .2000 4.1946755
Z8 -2.284972720 .40782792 -5.603 .0000 3.9317804
Sigma 8.247080326 .55336401 14.904 .0000
+---------------------------------------------+
| Threshold values for the model: |
| Lower= .0000 Upper= 4.0000 |
+---------------------------------------------+
Constant 7.900980451 2.8038548 2.818 .0048
Z2 -.1775982087 .79906293E-01 -2.223 .0262 32.487521
Z3 .5323021100 .14116841 3.771 .0002 8.1776955
Z5 -1.616335655 .42439672 -3.809 .0001 3.1164725
Z7 .3241864581 .25387778 1.277 .2016 4.1946755
Z8 -2.207007447 .44983190 -4.906 .0000 3.9317804
Sigma 7.943219445 .87690019 9.058 .0000
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| Conditional Mean at Sample Point 1.1263 |
| Scale Factor for Marginal Effects .2338 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.910805170 .65758415 2.906 .0037
Z2 -.4192088958E-01 .18444435E-01 -2.273 .0230 32.487521
Z3 .1295365141 .31167559E-01 4.156 .0000 8.1776955
Z5 -.3941718881 .93379144E-01 -4.221 .0000 3.1164725
Z7 .7621839800E-01 .59471640E-01 1.282 .2000 4.1946755
Z8 -.5341365586 .94896126E-01 -5.629 .0000 3.9317804
+-------------------------------------------+
| Lower= .0000 Upper= 4.0000 |
| Conditional Mean at Sample Point .2257 |
| Scale Factor for Marginal Effects .1229 |
+-------------------------------------------+
Constant .9712865849 .34346628 2.828 .0047
Z2 -.2183257619E-01 .95804001E-02 -2.279 .0227 32.487521
Z3 .6543718236E-01 .16101450E-01 4.064 .0000 8.1776955
Z5 -.1987000409 .48288948E-01 -4.115 .0000 3.1164725
Z7 .3985302327E-01 .31004563E-01 1.285 .1987 4.1946755
Z8 -.2713127490 .48803373E-01 -5.559 .0000 3.9317804
? Poisson and Negative Binomial Regressions. Uncensored
?
Poisson ; Lhs=y ; rhs = Xr ; MarginalEffects $
Negbin ; Lhs=y ; rhs = Xr ; MarginalEffects $
?
? Censored Poisson and Negative Binomial Models, censored at 4
?
Create ; yc=y ; If(yc>=4)yc=4 $
Poisson ; Lhs=yc ; Rhs = Xr ; Limit=4 ; MarginalEffects$
?
? Create predictions from least restrictive model. Convert
? conditional means to integers, then censor.
?
Negbin ; Lhs=yc ; Rhs = Xr ; Limit=4 ; Margin ; keep=yfnb$
Create ; Iyfnb=int(yfnb) ; If(iyfnb>4)iyfnb=4$
+---------------------------------------------+
| Poisson Regression |
| Log likelihood function -1427.037 |
| Restricted log likelihood -1709.723 |
| Chi- squared = 4125.90994 RsqP= .0800 |
| G - squared = 2360.08448 RsqD= .1933 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 2.533905282 .19692367 12.867 .0000
Z2 -.3225529750E-01 .58514053E-02 -5.512 .0000 32.487521
Z3 .1156984318 .99084864E-02 11.677 .0000 8.1776955
Z5 -.3540371394 .30892099E-01 -11.460 .0000 3.1164725
Z7 .7982824190E-01 .19448856E-01 4.105 .0000 4.1946755
Z8 -.4094427239 .27381245E-01 -14.953 .0000 3.9317804
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| Conditional Mean at Sample Point 1.4559 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 3.689129986 .39117889 9.431 .0000
Z2 -.4696070767E-01 .11623520E-01 -4.040 .0001 32.487521
Z3 .1684461361 .19682706E-01 8.558 .0000 8.1776955
Z5 -.5154450866 .61365588E-01 -8.400 .0000 3.1164725
Z7 .1162224820 .38634166E-01 3.008 .0026 4.1946755
Z8 -.5961104549 .54391454E-01 -10.960 .0000 3.9317804
+---------------------------------------------+
| Log likelihood function -728.2441 |
| Restricted log likelihood -1427.037 |
| Chi-squared 1397.586 |
| Degrees of freedom 1 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 2.189665176 .85899305 2.549 .0108
Z2 -.2623881896E-02 .17955428E-01 -.146 .8838 32.487521
Z3 .8481865225E-01 .40012554E-01 2.120 .0340 8.1776955
Z5 -.4222270934 .17050728 -2.476 .0133 3.1164725
Z7 .6044301285E-01 .90859681E-01 .665 .5059 4.1946755
Z8 -.4313313504 .16739868 -2.577 .0100 3.9317804
Overdispersion parameter for negative binomial model
Alpha 7.014805680 .94459163 7.426 .0000
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| Conditional Mean at Sample Point 1.4984 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 3.280911000 1.8007047 1.822 .0685
Z2 -.3931524815E-02 .37639913E-01 -.104 .9168 32.487521
Z3 .1270890418 .83878204E-01 1.515 .1297 8.1776955
Z5 -.6326490143 .35743393 -1.770 .0767 3.1164725
Z7 .9056551106E-01 .19046889 .475 .6344 4.1946755
Z8 -.6462904866 .35091738 -1.842 .0655 3.9317804
+---------------------------------------------+
| Poisson Regression |
| Log likelihood function -747.7541 |
| RIGHT Censored Data: Threshold = 4. |
| Chi- squared = 1520.43723 RsqP= .0799 |
| G - squared = 1077.99336 RsqD= .1877 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.899932460 .28256837 6.724 .0000
Z2 -.3284957645E-01 .83771861E-02 -3.921 .0001 32.487521
Z3 .1053474148 .14041819E-01 7.502 .0000 8.1776955
Z5 -.3233479425 .43740859E-01 -7.392 .0000 3.1164725
Z7 .7984038573E-01 .27533200E-01 2.900 .0037 4.1946755
Z8 -.3896778919 .39122373E-01 -9.960 .0000 3.9317804
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| Conditional Mean at Sample Point .7663 |
| Scale Factor for Marginal Effects .7166 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.361437133 .28978016 4.698 .0000
Z2 -.2353906474E-01 .75918324E-02 -3.101 .0019 32.487521
Z3 .7548893733E-01 .14750440E-01 5.118 .0000 8.1776955
Z5 -.2317018658 .45888605E-01 -5.049 .0000 3.1164725
Z7 .5721133153E-01 .24384424E-01 2.346 .0190 4.1946755
Z8 -.2792320060 .45043450E-01 -6.199 .0000 3.9317804
+---------------------------------------------+
| Negative Binomial Regression |
| Log likelihood function -482.0505 |
| Restricted log likelihood -747.7541 |
| Chi-squared 531.4072 |
| Degrees of freedom 1 |
| RIGHT Censored Data: Threshold = 4. |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 4.792788283 1.1636038 4.119 .0000
Z2 -.1659616715E-01 .24963901E-01 -.665 .5062 32.487521
Z3 .1744625408 .56779368E-01 3.073 .0021 8.1776955
Z5 -.7229290289 .19807844 -3.650 .0003 3.1164725
Z7 .8998362814E-01 .11558144 .779 .4363 4.1946755
Z8 -.8544311272 .21634356 -3.949 .0001 3.9317804
Overdispersion parameter for negative binomial model
Alpha 9.395956878 1.3533645 6.943 .0000
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| Conditional Mean at Sample Point .7170 |
| Scale Factor for Marginal Effects .2577 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.235198281 .79158359 1.560 .1187
Z2 -.4277167262E-02 .71500734E-02 -.598 .5497 32.487521
Z3 .4496251822E-01 .30220047E-01 1.488 .1368 8.1776955
Z5 -.1863134028 .11685569 -1.594 .1108 3.1164725
Z7 .2319059725E-01 .33257461E-01 .697 .4856 4.1946755
Z8 -.2202041478 .13847023 -1.590 .1118 3.9317804
Histogram; Rhs=yc$ (Actual data)
Histogram; Rhs=iyfnb$(Predictions)
Histogram for YC NOBS= 601, Too low: 0, Too high: 0
Bin Lower limit Upper limit Frequency Cumulative Frequency
========================================================================
0 .000 1.000 451 ( .7504) 451( .7504)
1 1.000 2.000 34 ( .0566) 485( .8070)
2 2.000 3.000 17 ( .0283) 502( .8353)
3 3.000 4.000 19 ( .0316) 521( .8669)
4 4.000 5.000 80 ( .1331) 601(1.0000)
Histogram for IYFNB NOBS= 601, Too low: 0, Too high: 0
Bin Lower limit Upper limit Frequency Cumulative Frequency
========================================================================
0 .000 1.000 251 ( .4176) 251( .4176)
1 1.000 2.000 96 ( .1597) 347( .5774)
2 2.000 3.000 50 ( .0832) 397( .6606)
3 3.000 4.000 34 ( .0566) 431( .7171)
4 4.000 5.000 170 ( .2829) 601(1.0000)
? Zero inflated (split population) Poisson model+ Tobit(0,4)
?
Poisson ; Lhs=yc ; Rhs = XR
; ZIP; Rh2=Xr;par; keep=yfpz ; Mar $
Matrix ; Beta = B(1:6) ; Gamma = B(7:12)$
Create ; Lambda=exp(Beta'xr);qi=lgp(gamma'xr)
; Ey=(1-qi)*lambda ; Iey=int(ey)$
Histogram; Rhs=Iey$
Tobit ; Lhs=yc ; Rhs = XR ; Alg=BFGS ;Mar $
Tobit ; Lhs=yc ; Rhs = XR ; Limits = 0,4 ; Alg=BFGS ;Mar $
/*
Histogram for IEY NOBS= 601, Too low: 0, Too high: 0
Bin Lower limit Upper limit Frequency Cumulative Frequency
========================================================================
0 .000 1.000 448 ( .7454) 448( .7454)
1 1.000 2.000 134 ( .2230) 582( .9684)
2 2.000 3.000 17 ( .0283) 599( .9967)
3 3.000 4.000 2 ( .0033) 601(1.0000)
+----------------------------------------------------------------------+
| Zero Altered Poisson Regression Model |
| Logistic distribution used for splitting model. |
| ZAP term in probability is F[tau x Z(i) ] |
| Comparison of estimated models |
| Pr[0|means] Number of zeros Log-likelihood |
| Poisson .55783 Act.= 451 Prd.= 335.3 -771.44432 |
| Z.I.Poisson .77364 Act.= 451 Prd.= 465.0 -551.72760 |
| Note, the ZIP log-likelihood is not directly comparable. |
| ZIP model with nonzero Q does not encompass the others. |
| Vuong statistic for testing ZIP vs. unaltered model is 21.6436 |
| Distributed as standard normal. A value greater than |
| +1.96 favors the zero altered Z.I.Poisson model. |
| A value less than -1.96 rejects the ZIP model. |
+----------------------------------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Poisson/Negbin regression model
Constant 1.274187369 .43940971 2.900 .0037
Z2 -.4219823370E-02 .12229828E-01 -.345 .7301 32.487521
Z3 .3312258287E-01 .23127736E-01 1.432 .1521 8.1776955
Z5 -.9085096098E-01 .72054203E-01 -1.261 .2074 3.1164725
Z7 .2052418829E-01 .44126404E-01 .465 .6418 4.1946755
Z8 -.8166127920E-01 .66574722E-01 -1.227 .2200 3.9317804
Zero inflation model
Constant -1.848860263 .66436621 -2.783 .0054
Z2 .3970949740E-01 .19046738E-01 2.085 .0371 32.487521
Z3 -.9814600629E-01 .31795289E-01 -3.087 .0020 8.1776955
Z5 .3062225236 .95089852E-01 3.220 .0013 3.1164725
Z7 -.6770594854E-01 .60739793E-01 -1.115 .2650 4.1946755
Z8 .4577650236 .94870568E-01 4.825 .0000 3.9317804
ZIP
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
| Conditional Mean at Sample Point .0063 |
| Scale Factor for Marginal Effects -.3438 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 2.899747536 .57896387 5.009 .0000
Z2 -.2523628400E-01 .12985077E-01 -1.943 .0520 32.487521
Z3 .9869128559E-01 .26718883E-01 3.694 .0002 8.1776955
Z5 -.2879288809 .85416029E-01 -3.371 .0007 3.1164725
Z7 .6436057742E-01 .46300314E-01 1.390 .1645 4.1946755
Z8 -.3437579550 .79602625E-01 -4.318 .0000 3.9317804
Tobit(0)
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
| Conditional Mean at Sample Point 1.1263 |
| Scale Factor for Marginal Effects .2338 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant 1.910805168 .65758415 2.906 .0037
Z2 -.4192088954E-01 .18444435E-01 -2.273 .0230 32.487521
Z3 .1295365140 .31167559E-01 4.156 .0000 8.1776955
Z5 -.3941718875 .93379144E-01 -4.221 .0000 3.1164725
Z7 .7621839725E-01 .59471639E-01 1.282 .2000 4.1946755
Z8 -.5341365577 .94896126E-01 -5.629 .0000 3.9317804
Tobit(0,4)
+-------------------------------------------+
| Partial derivatives of expected val. with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
| Conditional Mean at Sample Point .2257 |
| Scale Factor for Marginal Effects .1229 |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Constant .9712865866 .34346628 2.828 .0047
Z2 -.2183257607E-01 .95804001E-02 -2.279 .0227 32.487521
Z3 .6543718214E-01 .16101450E-01 4.064 .0000 8.1776955
Z5 -.1987000414 .48288948E-01 -4.115 .0000 3.1164725
Z7 .3985302304E-01 .31004563E-01 1.285 .1987 4.1946755
Z8 -.2713127494 .48803373E-01 -5.559 .0000 3.9317804