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st: -clogit-, -asclogit- and marginal effects


From   "Timothy Dang" <tpondang@gmail.com>
To   stata <statalist@hsphsun2.harvard.edu>
Subject   st: -clogit-, -asclogit- and marginal effects
Date   Sun, 28 Oct 2007 11:37:12 -0700

Hello-

I'm using -asclogit- on some panel data from an economics experiment.
I'm using -asclogit- so that
I can put in dummies for the experimental run as a bit of a control on
correlation.

In any case, I find myself confused about the reported marginal
effects. To try to clarify things, I've
run a regression with -clogit-, and one with -asclogit- without any
case variables. As I understand it,
these should be the same. The reported coefficients are the same, but
the marginal effects appear
different.

Here's part of the results. To keep things pithy, I'm clipping lots of
stuff, leaving the results reported
for one variable "r_lagadjco~t":

For -clogit-:
-------------------------------------------------------------------------------------------------------
.         gen NotOO = cat2+cat3+cat4   // NotOO is 1 for anything
other than outside option
.         clogit y NotOO r_price r_minprice r_switchflag r_baseflag
r_lagadjcount, group(id)

Iteration 0:   log likelihood = -337.69779
Iteration 1:   log likelihood =  -227.3159
Iteration 2:   log likelihood = -215.49176
Iteration 3:   log likelihood = -214.81565
Iteration 4:   log likelihood =  -214.8147
Iteration 5:   log likelihood =  -214.8147

Conditional (fixed-effects) logistic regression   Number of obs   =       3648
                                                  LR chi2(6)      =    2098.97
                                                  Prob > chi2     =     0.0000
Log likelihood =  -214.8147                       Pseudo R2       =     0.8301

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       NotOO |   2.769809   .5627178     4.92   0.000     1.666902    3.872715
     r_price |  -.9380129    .114137    -8.22   0.000    -1.161717   -.7143086
  r_minprice |   .4793116    .273653     1.75   0.080    -.0570383    1.015662
r_switchflag |  -3.132582   .2163795   -14.48   0.000    -3.556678   -2.708486
  r_baseflag |   3.001386   .3403266     8.82   0.000     2.334358    3.668414
r_lagadjco~t |   .5978349   .0704545     8.49   0.000     .4597467    .7359232
------------------------------------------------------------------------------

.         mfx, predict(pu0)

Marginal effects after clogit
      y  = Pr(y|fixed effect is 0) (predict, pu0)
         =  .54073355
------------------------------------------------------------------------------
variable |      dy/dx    Std. Err.     z    P>|z|  [    95% C.I.   ]      X
---------+--------------------------------------------------------------------
   NotOO*|   .5732462      .10516    5.45   0.000   .367135  .779358       .75
 r_price |  -.2329469      .03304   -7.05   0.000  -.297697 -.168197   2.79388
r_minp~e*|   .1167234      .06427    1.82   0.069  -.009248  .242695   .223684
r_swit~g*|  -.6519393      .03705  -17.60   0.000  -.724549  -.57933   .500822
r_base~g*|   .6084147      .06649    9.15   0.000   .478103  .738726      .375
r_laga~t |   .1484668      .01924    7.72   0.000    .11075  .186183   1.74424
------------------------------------------------------------------------------
(*) dy/dx is for discrete change of dummy variable from 0 to 1

-------------------------------------------------------------------------------------------------------


For -asclogit-:
-------------------------------------------------------------------------------------------------------
.asclogit y NotOO r_price r_minprice r_switchflag r_baseflag
r_lagadjcount, case(id) alternatives(n) basealternative(0) casevars()
nocons

note: variable r_minprice has 96 cases that are not
alternative-specific: there is no within-case variability
note: variable r_baseflag has 114 cases that are not
alternative-specific: there is no within-case variability

Iteration 0:   log likelihood = -337.69779
Iteration 1:   log likelihood =  -227.3159
Iteration 2:   log likelihood = -215.49176
Iteration 3:   log likelihood = -214.81565
Iteration 4:   log likelihood =  -214.8147
Iteration 5:   log likelihood =  -214.8147

Alternative-specific conditional logit         Number of obs      =       3648
Case variable: id                              Number of cases    =        912

Alternative variable: n                        Alts per case: min =          4
                                                              avg =        4.0
                                                              max =          4

                                                  Wald chi2(6)    =     381.94
Log likelihood =  -214.8147                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
n            |
       NotOO |   2.769809   .5627178     4.92   0.000     1.666902    3.872715
     r_price |  -.9380129    .114137    -8.22   0.000    -1.161717   -.7143086
  r_minprice |   .4793116    .273653     1.75   0.080    -.0570383    1.015662
r_switchflag |  -3.132582   .2163795   -14.48   0.000    -3.556678   -2.708486
  r_baseflag |   3.001386   .3403266     8.82   0.000     2.334358    3.668414
r_lagadjco~t |   .5978349   .0704545     8.49   0.000     .4597467    .7359232
------------------------------------------------------------------------------

.         estat mfx

Equation Name           Alternative
--------------------------------------------------
n1                      0
n2                      1
n3                      2
n4                      3


Pr(choice = 0|1 selected) = .03259311
-------------------------------------------------------------------------------
variable     |   dp/dx   Std. Err.    z     P>|z|  [    95% C.I.    ]       X
-------------+-----------------------------------------------------------------

<snip>
-------------+-----------------------------------------------------------------
r_lagadjco~t |
          n1 |   .01885   .008401    2.24   0.025   .002385   .035315         0
          n2 | -.000014   .000012   -1.14   0.255  -.000038    .00001    2.0954
          n3 | -.016744   .007509   -2.23   0.026  -.031461  -.002027     2.602
          n4 | -.002092   .000977   -2.14   0.032  -.004007  -.000177    2.2796
-------------------------------------------------------------------------------
(*) dp/dx is for discrete change of indicator variable from 0 to 1

Pr(choice = 1|1 selected) = .00072116
-------------------------------------------------------------------------------
variable     |   dp/dx   Std. Err.    z     P>|z|  [    95% C.I.    ]       X
-------------+-----------------------------------------------------------------
<snip>
-------------+-----------------------------------------------------------------
r_lagadjco~t |
          n1 | -.000014         .       .       .         .         .         0
          n2 |  .000431         .       .       .         .         .    2.0954
          n3 |  -.00037         .       .       .         .         .     2.602
          n4 | -.000046         .       .       .         .         .    2.2796
-------------------------------------------------------------------------------
(*) dp/dx is for discrete change of indicator variable from 0 to 1

Pr(choice = 2|1 selected) = .85932034
-------------------------------------------------------------------------------
variable     |   dp/dx   Std. Err.    z     P>|z|  [    95% C.I.    ]       X
-------------+-----------------------------------------------------------------
<snip>
-------------+-----------------------------------------------------------------
r_lagadjco~t |
          n1 | -.016744   .007509   -2.23   0.026  -.031461  -.002027         0
          n2 |  -.00037   .000265   -1.40   0.162  -.000889   .000148    2.0954
          n3 |  .072272   .010197    7.09   0.000   .052285   .092258     2.602
          n4 | -.055157   .007935   -6.95   0.000   -.07071  -.039604    2.2796
-------------------------------------------------------------------------------
(*) dp/dx is for discrete change of indicator variable from 0 to 1

Pr(choice = 3|1 selected) = .10736539
-------------------------------------------------------------------------------
variable     |   dp/dx   Std. Err.    z     P>|z|  [    95% C.I.    ]       X
-------------+-----------------------------------------------------------------
<snip>
-------------+-----------------------------------------------------------------
r_lagadjco~t |
          n1 | -.002092         .       .       .         .         .         0
          n2 | -.000046         .       .       .         .         .    2.0954
          n3 | -.055157         .       .       .         .         .     2.602
          n4 |  .057295         .       .       .         .         .    2.2796
-------------------------------------------------------------------------------
(*) dp/dx is for discrete change of indicator variable from 0 to 1
-------------------------------------------------------------------------------------------------------

OK, so the regression results are the same, as I figure they should be
(-asclogit- with -casevars()- should be the same thing as -clogit-,
right?). So far, so good.

Then it seems I don't know how to read one or the other of the
marginal effects. -mfx, preduct(pu0)- for -clogit- gives a marginal
effect of 0.1484668 for r_lagadjco~t. I interpret that as:

All else equal, at the mean of the independent variables, an increase
of 1 in r_lagadjco~t (for outcome n) will increase the probability of
outcome n by approx 0.148

Then for -asclogit- there's a bunch of different marginal effects,
because while -clogit- assumes symmetry -asclogit- doesn't. I
interpret the results of -estat mfx- as:

All else equal, at the mean of the independent variables, an increase of 1 in
   r_lagadjco~t (for outcome n2) will increase the probability of
outcome n2 by approx .000431
   r_lagadjco~t (for outcome n3) will increase the probability of
outcome n3 by approx .072272
   r_lagadjco~t (for outcome n4) will increase the probability of
outcome n4 by approx .057295

I don't see much relation between the marginal effects from the two
different postestimation commands. Any help in correcting my
interpretation would be very appreciated.

Possibly related, The probabilities given:
Pr(choice = 0|1 selected) = .03259311
Pr(choice = 1|1 selected) = .00072116
Pr(choice = 2|1 selected) = .85932034
Pr(choice = 3|1 selected) = .10736539


...don't match the data at all. In fact, the fractions in the data are:
choice = 1: .3059211
choice = 2: .3695175
choice = 3: .3190789

Thanks

-Timothy

-- 
------------------------------
Timothy O'Neill Dang / Cretog8
623-587-0532
One monkey don't stop no show.
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