[Limdep Nlogit List] Standard Error Issue Solved - Two Final Questions
William Greene
wgreene at stern.nyu.edu
Fri Mar 20 23:27:48 EST 2009
David.
(1) nlogit.chm is for Windows Vista users. It replaces the internal Help file.
(2) (a) I do not understand this question. MEs are always computed "over the
RHS variables." The value given is the partial effect of the X on the indicated
probability. I'm not sure what you mean by "the whole marginal effect." Partial
effects, by definition, apply to a single variable.
(b) The problem discussed on R10-11 is a discussion of what MEs are. There is
no "solution" as such. The ME is a mixture of all of the parameters in the
model. As such, one wants to be a little cautious about interpreting tests of
significance.
(c) Go to the Stern/Economics website and make your way to the working paper
series. I have a 2008 working paper on ordered choice models that contains a
very long discussion about marginal effects.
/Bill Greene
----- Original Message -----
From: "David Tufte" <tufte at suu.edu>
To: limdep at limdep.itls.usyd.edu.au
Sent: Thursday, March 19, 2009 9:23:14 PM GMT -05:00 US/Canada Eastern
Subject: [Limdep Nlogit List] Standard Error Issue Solved - Two Final Questions
I pasted a successful run (of a somewhat fatter model) below from the new nlogit.exe.
1) Should I also copy over the nlogit.chm file that came in the zip file?
2) I think I understand this output, but it is different from the manual I have, so I need some pointers. Am I right in thinking that:
a) The standard errors of the marginal effects are now calculated over the RHS variables' influence on each marginal effect rather than on effects themselves? (So in this model, the output says nothing about whether the whole marginal effect on Y=00 was significant, but it does show that the effect of ln_sal on Y=00 was significant while none of the other variables were.)
b) Is this a "solution/improvement" to the problem discussed in the 2nd full paragraph of R10-10,11; namely that the "marginal effect is a hodgepodge" and the standard error of the (whole) marginal effect can only be more so?
c) Can you point me to some cites? This is new stuff to me, and not in my area.
--> oprobit;full;
marginal effects;
lhs=inverse;
rhs=one,age,age_sq,hrswk,ln_sal$
Normal exit from iterations. Status=0. F= 1031.560
+---------------------------------------------+
| Ordered Probability Model |
| Maximum Likelihood Estimates |
| Dependent variable INVERSE |
| Weighting variable None |
| Number of observations 1015 |
| Iterations completed 10 |
| Log likelihood function -1031.560 |
| Number of parameters 7 |
| Info. Criterion: AIC = 2.04642 |
| Finite Sample: AIC = 2.04653 |
| Info. Criterion: BIC = 2.08037 |
| Info. Criterion:HQIC = 2.05932 |
| Restricted log likelihood -1037.590 |
| McFadden Pseudo R-squared .0058121 |
| Chi squared 12.06121 |
| Degrees of freedom 4 |
| Prob[ChiSqd > value] = .1690184E-01 |
| Model estimated: Mar 19, 2009, 07:04:17PM |
| Underlying probabilities based on Normal |
+---------------------------------------------+
+--------------------------------------------------------------------+
| TABLE OF CELL FREQUENCIES FOR ORDERED PROBABILITY MODEL |
+--------------------------------------------------------------------+
| Frequency Cumulative < = Cumulative > = |
|Outcome Count Percent Count Percent Count Percent |
|----------- ------- --------- ------- --------- ------- --------- |
|INVERSE=00 24 2.3645 24 2.3645 1015 100.0000 |
|INVERSE=01 90 8.8670 114 11.2315 991 97.6355 |
|INVERSE=02 482 47.4877 596 58.7192 901 88.7685 |
|INVERSE=03 419 41.2808 1015 100.0000 419 41.2808 |
+--------------------------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
+--------+Index function for probability |
|Constant| .40483 .68400355 .592 .5540 |
|AGE | .00999 .02678558 .373 .7093 43.174384|
|AGE_SQ |-.75872D-04 .00029319 -.259 .7958 1968.6345|
|HRSWK | .00172 .00325914 .528 .5973 43.867980|
|LN_SAL | .11381*** .04012893 2.836 .0046 10.872970|
+--------+Threshold parameters for index |
|Mu(1) | .77660*** .04822083 16.105 .0000 |
|Mu(2) | 2.22136*** .05510768 40.309 .0000 |
+--------+------------------------------------------------------------+
| Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. |
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
========================================================================
||Summary of Marginal Effects for Ordered Probability Model (probit) ||
||Effects computed at means. Effectsfor binary variables are ||
||computed as differences of probabilities, other variables at means. ||
========================================================================
|| Continuous Variable ONE Continuous Variable AGE
|| ============================== ==============================
Outcome Effect dPy<=nn/dX dPy>=nn/dX Effect dPy<=nn/dX dPy>=nn/dX
======= ============================== ==============================
Y = 00 .00000 .00000 .00000 -.00054 -.00054 .00000
Y = 01 .00000 .00000 .00000 -.00135 -.00189 .00054
Y = 02 .00000 .00000 .00000 -.00200 -.00389 .00189
Y = 03 .00000 .00000 .00000 .00389 .00000 .00389
========================================================================
|| Continuous Variable AGE_SQ Continuous Variable HRSWK
|| ============================== ==============================
Outcome Effect dPy<=nn/dX dPy>=nn/dX Effect dPy<=nn/dX dPy>=nn/dX
======= ============================== ==============================
Y = 00 .00000 .00000 .00000 -.00009 -.00009 .00000
Y = 01 .00001 .00001 .00000 -.00023 -.00033 .00009
Y = 02 .00002 .00003 -.00001 -.00035 -.00067 .00033
Y = 03 -.00003 .00000 -.00003 .00067 .00000 .00067
========================================================================
|| Continuous Variable LN_SAL
|| ==============================
Outcome Effect dPy<=nn/dX dPy>=nn/dX
======= ==============================
Y = 00 -.00615 -.00615 .00000
Y = 01 -.01534 -.02149 .00615
Y = 02 -.02281 -.04430 .02149
Y = 03 .04430 .00000 .04430
========================================================================
+----------------------------------------------------+
| Marginal effects for ordered probability model |
| These are the effects on Prob[Y=00] at means. |
| M.E.s for dummy variables are Pr[y|x=1]-Pr[y|x=0] |
| Names for dummy variables are marked by *. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|Constant| .000*** ......(Fixed Parameter)....... |
|AGE | -.00054 .00144819 -.373 .7094 43.174384|
|AGE_SQ | .41001D-05 .158474D-04 .259 .7958 1968.6345|
|HRSWK |-.93050D-04 .00017637 -.528 .5978 43.867980|
|LN_SAL | -.00615*** .00223477 -2.752 .0059 10.872970|
+--------+------------------------------------------------------------+
| Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. |
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
+---------------------------------------------------------------------+
|Fixed Parameter... indicates a parameter that is constrained to equal|
|a fixed value (e.g., 0) or a serious estimation problem. If you did |
|not impose a restriction on the parameter, check for previous errors.|
+---------------------------------------------------------------------+
+----------------------------------------------------+
| Marginal effects for ordered probability model |
| These are the effects on Prob[Y=01] at means. |
| M.E.s for dummy variables are Pr[y|x=1]-Pr[y|x=0] |
| Names for dummy variables are marked by *. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|Constant| .000*** ......(Fixed Parameter)....... |
|AGE | -.00135 .00361137 -.373 .7093 43.174384|
|AGE_SQ | .10229D-04 .395284D-04 .259 .7958 1968.6345|
|HRSWK | -.00023 .00043951 -.528 .5974 43.867980|
|LN_SAL | -.01534*** .00542693 -2.827 .0047 10.872970|
+--------+------------------------------------------------------------+
| Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. |
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
+---------------------------------------------------------------------+
|Fixed Parameter... indicates a parameter that is constrained to equal|
|a fixed value (e.g., 0) or a serious estimation problem. If you did |
|not impose a restriction on the parameter, check for previous errors.|
+---------------------------------------------------------------------+
+----------------------------------------------------+
| Marginal effects for ordered probability model |
| These are the effects on Prob[Y=02] at means. |
| M.E.s for dummy variables are Pr[y|x=1]-Pr[y|x=0] |
| Names for dummy variables are marked by *. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|Constant| .000*** ......(Fixed Parameter)....... |
|AGE | -.00200 .00537165 -.373 .7095 43.174384|
|AGE_SQ | .15204D-04 .587742D-04 .259 .7959 1968.6345|
|HRSWK | -.00035 .00065388 -.528 .5977 43.867980|
|LN_SAL | -.02281*** .00834611 -2.732 .0063 10.872970|
+--------+------------------------------------------------------------+
| Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. |
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
+---------------------------------------------------------------------+
|Fixed Parameter... indicates a parameter that is constrained to equal|
|a fixed value (e.g., 0) or a serious estimation problem. If you did |
|not impose a restriction on the parameter, check for previous errors.|
+---------------------------------------------------------------------+
+----------------------------------------------------+
| Marginal effects for ordered probability model |
| These are the effects on Prob[Y=03] at means. |
| M.E.s for dummy variables are Pr[y|x=1]-Pr[y|x=0] |
| Names for dummy variables are marked by *. |
+----------------------------------------------------+
+--------+--------------+----------------+--------+--------+----------+
|Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| Mean of X|
+--------+--------------+----------------+--------+--------+----------+
|Constant| .000*** ......(Fixed Parameter)....... |
|AGE | .00389 .01042719 .373 .7093 43.174384|
|AGE_SQ |-.29533D-04 .00011413 -.259 .7958 1968.6345|
|HRSWK | .00067 .00126878 .528 .5973 43.867980|
|LN_SAL | .04430*** .01566667 2.828 .0047 10.872970|
+--------+------------------------------------------------------------+
| Note: nnnnn.D-xx or D+xx => multiply by 10 to -xx or +xx. |
| Note: ***, **, * = Significance at 1%, 5%, 10% level. |
+---------------------------------------------------------------------+
+---------------------------------------------------------------------+
|Fixed Parameter... indicates a parameter that is constrained to equal|
|a fixed value (e.g., 0) or a serious estimation problem. If you did |
|not impose a restriction on the parameter, check for previous errors.|
+---------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Cross tabulation of predictions. Row is actual, column is predicted. |
| Model = Probit . Prediction is number of the most probable cell. |
+------+-----+-----+-----+-----+-----+-----------------------------------------+
|y(i,j)| 0 | 1 | 2 | 3 |Total| |
+------+-----+-----+-----+-----+-----+ |
| 0 | 0| 0| 22| 2| 24| |
| 1 | 0| 0| 85| 5| 90| |
| 2 | 0| 0| 429| 53| 482| |
| 3 | 0| 0| 337| 82| 419| |
+------+-----+-----+-----+-----+-----+ |
| Total| 0| 0| 873| 142| 1015| |
+------------------------------------------------------------------------------+
+------------------------------------------------------------------------------+
| Cross tabulation of outcomes and predicted probabilities. Row = actual |
| Column = Prediction, Model = Probit , Value(j,m)=Sum(i=1,N)y(i,j)*p(i,m)|
+------+-----+-----+-----+-----+-----+-----------------------------------------+
|y(i,j)| 0 | 1 | 2 | 3 |Total| |
+------+-----+-----+-----+-----+-----+ |
| 0 | 1| 2| 12| 9| 24| |
| 1 | 2| 8| 43| 37| 90| |
| 2 | 12| 43| 229| 198| 482| |
| 3 | 10| 36| 197| 175| 419| |
+------+-----+-----+-----+-----+-----+ |
| Total| 24| 90| 482| 419| 1015| |
+------------------------------------------------------------------------------+
| Column totals may not match sum of cells because of rounding error. |
+------------------------------------------------------------------------------+
David Tufte
Associate Professor
Department of Economics and Finance
School of Business
Southern Utah University
351 W. University Blvd.
Cedar City UT 84720
351 W. University Blvd.
Cedar City UT 847820
351 West Center St.
Cedar City, UT 84720
Office: (435) 586-5407
Fax: (435) 586-5493
http://www.suu.edu/faculty/tufte
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