Calculating marginal effects at different values for a squared term in a logit

[Courtney R. Yarbrough]

I'm having trouble calculating marginal effects at different values of a variable var1 that I have included as a continuous independent variable in a logit regression along with its square as c.var1##c.var1.

For example, I've written my command as:
xi: logit depvar c.var1##c.var1 var2 var3 i.year, vce(bootstrap)

When I attempt to have STATA calculate marginal effects of var1 over a range of values of var1, STATA tells me it is inestimable. However, STATA will calculate marginal effects for var2 and var3, indicating that it is having an issue because of the squared term. The command I have used for calculating marginal effects is:
margins, dydx(var1) at(var1==(0(10)100))

Can you tell me why STATA is unable to do marginal effects for the squared term and how I might get it to work?

Many thanks.

[Richard Williams]

Don't use the xi: prefix. It isn't necessary and it confuses margins.

For more on margins, and margins for continuous variables, see

http://www3.nd.edu/~rwilliam/stats3/Margins01.pdf

http://www3.nd.edu/~rwilliam/stats3/Margins03.pdf

Also, for a good discussion of why you don't get marginal effects for interactions and squared terms,

http://www.stata.com/statalist/archi.../msg00263.html

[Courtney R. Yarbrough]

I removed the xi:, and unfortunately I'm having the same problem (inestimable). STATA will calculate marginal effects for variables not included in an interaction but not for the variable that is interacted.

I may have misspoken before. I'm not trying to calculate the marginal effect for the interaction term (c.var1##c.var1). Rather, I need it for var1 itself. Is that possible in STATA, or do I have to do it manually?

Thanks for the help.

[daniel klein]

Can you show us the output?

It is not the squared term per se that is causing the problems, as this little example shows

. sysuse nlsw88
(NLSW, 1988 extract)

. logit union c.age##c.age c.wage ,vce(boot)
(running logit on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50

Logistic regression                             Number of obs      =      1878
                                                Replications       =        50
                                                Wald chi2(3)       =     46.87
                                                Prob > chi2        =    0.0000
Log likelihood = -1026.2595                     Pseudo R2          =    0.0195

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0830317   .5094544     0.16   0.871    -.9154805    1.081544
             |
 c.age#c.age |  -.0009451   .0064221    -0.15   0.883    -.0135322     .011642
             |
        wage |   .0779428   .0117173     6.65   0.000     .0549773    .1009083
       _cons |  -3.530711   10.04165    -0.35   0.725    -23.21198    16.15056
------------------------------------------------------------------------------

. su age

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
         age |      2246    39.15316    3.060002         34         46

. sysuse nlsw88
(NLSW, 1988 extract)

. logit union c.age##c.age c.wage ,vce(boot)
(running logit on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50

Logistic regression                             Number of obs      =      1878
                                                Replications       =        50
                                                Wald chi2(3)       =     71.17
                                                Prob > chi2        =    0.0000
Log likelihood = -1026.2595                     Pseudo R2          =    0.0195

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
       union |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0830317   .5751146     0.14   0.885    -1.044172    1.210236
             |
 c.age#c.age |  -.0009451   .0072629    -0.13   0.896    -.0151801    .0132899
             |
        wage |   .0779428   .0096715     8.06   0.000      .058987    .0968986
       _cons |  -3.530711   11.31371    -0.31   0.755    -25.70518    18.64376
------------------------------------------------------------------------------

. margins ,dydx(age) at(age = (30(5)50))

Average marginal effects                          Number of obs   =       1878
Model VCE    : Bootstrap

Expression   : Pr(union), predict()
dy/dx w.r.t. : age

1._at        : age             =          30

2._at        : age             =          35

3._at        : age             =          40

4._at        : age             =          45

5._at        : age             =          50

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age          |
         _at |
          1  |   .0043974   .0219566     0.20   0.841    -.0386366    .0474315
          2  |   .0029835   .0119592     0.25   0.803     -.020456    .0264231
          3  |   .0013528   .0031051     0.44   0.663    -.0047332    .0074388
          4  |  -.0003719   .0147131    -0.03   0.980    -.0292091    .0284653
          5  |   -.002071    .026725    -0.08   0.938    -.0544511     .050309
------------------------------------------------------------------------------

.

Best
Danie


Please read the FAQs, especially 6. and 18. And please use the code environment to post code and results - this makes it much easier to read.

[Richard Williams]

I think we need to see your exact code and output. This example seems similar to me, and it runs fine:

webuse nhanes2f, clear
logit diabetes weight i.female c.age##c.age, vce(bootstrap)
margins, dydx(age) at(age=(20 (5) 70)) vsquish

When entering the code and output, please do it like I just did. When typing the message, click on the underlined A on the upper right, then click #. Copy and paste your code and output between the two code tags.

Also, does it work if you don't specify a range?

[Courtney R. Yarbrough]

I appreciate your help very much. Here is the code and the output.

Courtney Yarbrough

use "`datadir'/DTCfinal.dta", clear;

****rx7 IS REFERENCE****;


********INSTRUMENTS*******;
global instr osteoporosis_iv osteoporosis_iv2 offpatent mark_share unitprice drugcount combsales
enroll rank unemp rx1 rx2 rx3 rx4 rx5 rx6 rx8 rx9 rx10 rx11 rx12 ; 

********INDEPEDNENT VARS*******;
global indep offpatent mark_share unitprice 
drugcount combsales enroll rank unemp rx1 rx2 rx3 rx4 rx5 rx6 rx8 rx9 rx10 rx11 rx12;


****** RUN FIRST STAGE OF 2SRI MODEL ******;
****** RUN FIRST STAGE OF 2SRI MODEL ******;
****** RUN FIRST STAGE OF 2SRI MODEL ******;
xi: reg dtctv $instr i.year i.state_id;
predict ehat1, r;
est store iv_coef;
label var ehat1 "IV Residual for Own DTC";
est save "`studydir'/iv_coef.ster", replace;

xi: reg pct_dtctv $instr  i.year i.state_id;
predict ehat2, r;
est store iv_coef2;
label var ehat2 "IV Residual for Percent Own DTC";
est save "`studydir'/iv_coef2.ster", replace;


****** RUN SECOND STAGE OF 2SRI MODEL ******;
****** RUN SECOND STAGE OF 2SRI MODEL ******;
****** RUN SECOND STAGE OF 2SRI MODEL ******;


********YEAR AND STATE FIXED EFFECTS*******;
logit tier3 c.dtctv##c.dtctv c.comp_dtctv##c.comp_dtctv pct_dtctv 
$indep ehat1 ehat2 i.year i.state_id, vce(bootstrap);
est store tier3_coef_endog;
est save "`studydir'/tier3_coef_endog.ster", replace;

margins, dydx(dtctv comp_dtctv pct_dtctv offpatent mark_share unitprice drugcount enroll rank unemp) post;
est store tier3_me_endog;
est save "`studydir'/tier3_me_endog.ster", replace;



estimates restore tier3_coef_endog;
margins, dydx(dtctv) at(dtctv==(0(5)65));
marginsplot, 
title("Marginal Effect of Lagged TV DTC") 
subtitle("by DTC spending level")
ytitle("Change in the Pr(Drug is on Tier 3)", size (medsmall) )
xtitle("Lagged Statin TV DTC - in millions of dollars", size(medsmall))
ylabel(, labsize(small))
xlabel(, labsize(small))
yline(0)
saving("`resultsdir'/ME for pre-DTC across levels.gph", replace);

.

********YEAR AND STATE FIXED EFFECTS*******;
. logit tier3 c.dtctv##c.dtctv c.comp_dtctv##c.comp_dtctv pct_dtctv 
> $indep ehat1 ehat2 i.year i.state_id, vce(bootstrap);
note: 2009.year omitted because of collinearity
(running logit on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50

Logistic regression                             Number of obs      =     92294
                                                Replications       =        50
                                                Wald chi2(49)      =         .
                                                Prob > chi2        =         .
Log likelihood = -46236.562                     Pseudo R2          =    0.2772

-------------------------------------------------------------------------------
              |   Observed   Bootstrap                         Normal-based
        tier3 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
        dtctv |  -.3240426   .0302156   -10.72   0.000     -.383264   -.2648211
              |
      c.dtctv#|
      c.dtctv |   .0006589    .000126     5.23   0.000      .000412    .0009057
              |
   comp_dtctv |   .1688027   .0296938     5.68   0.000     .1106039    .2270016
              |
 c.comp_dtctv#|
 c.comp_dtctv |  -.0004517   .0001133    -3.99   0.000    -.0006736   -.0002297
              |
    pct_dtctv |     .39543   .0343691    11.51   0.000     .3280679    .4627921
    offpatent |    2.34081   .2140492    10.94   0.000     1.921281    2.760338
   mark_share |  -.0323753   .0083993    -3.85   0.000    -.0488375    -.015913
    unitprice |   .2216178    .034591     6.41   0.000     .1538207    .2894149
    drugcount |  -.2445509   .0126496   -19.33   0.000    -.2693436   -.2197581
    combsales |   .0001148   .0000275     4.17   0.000     .0000609    .0001687
       enroll |   .0004406    .000313     1.41   0.159    -.0001728     .001054
         rank |   .0046341   .0002837    16.33   0.000      .004078    .0051902
        unemp |  -.0779873   .0223815    -3.48   0.000    -.1218542   -.0341204
          rx1 |  -7.439726   1.171668    -6.35   0.000    -9.736152     -5.1433
          rx2 |   -13.5757   1.493084    -9.09   0.000    -16.50209   -10.64931
          rx3 |  -1.371345   .5427068    -2.53   0.012    -2.435031   -.3076594
          rx4 |  -9.003761   .8499758   -10.59   0.000    -10.66968   -7.337839
          rx5 |  -7.123702   1.146536    -6.21   0.000     -9.37087   -4.876534
          rx6 |  -6.406982   1.186145    -5.40   0.000    -8.731783    -4.08218
          rx8 |  -11.28036    .837652   -13.47   0.000    -12.92213   -9.638591
          rx9 |  -11.09249   1.342224    -8.26   0.000     -13.7232   -8.461778
         rx10 |  -9.611291   1.115936    -8.61   0.000    -11.79848   -7.424097
         rx11 |  -3.011886   .5797944    -5.19   0.000    -4.148262    -1.87551
         rx12 |  -6.901231   .8364846    -8.25   0.000    -8.540711   -5.261751
        ehat1 |   .2676613    .011839    22.61   0.000     .2444574    .2908653
        ehat2 |  -.3624523   .0208636   -17.37   0.000    -.4033442   -.3215604
              |
         year |
        2007  |   1.074457   .1153425     9.32   0.000     .8483896    1.300524
        2008  |  -.8511964   .1590708    -5.35   0.000    -1.162969   -.5394234
        2009  |          0  (omitted)
              |
     state_id |
           2  |   .3057444   .1131611     2.70   0.007     .0839526    .5275362
           4  |   .4211974   .0828566     5.08   0.000     .2588015    .5835933
           5  |   .5328415   .0726966     7.33   0.000     .3903587    .6753242
           6  |   .2025526   .0798412     2.54   0.011     .0460667    .3590386
           7  |   .1261486   .0808892     1.56   0.119    -.0323915    .2846886
           8  |   .2577842    .087231     2.96   0.003     .0868145    .4287538
           9  |   .1392999   .0621256     2.24   0.025      .017536    .2610637
          10  |   .4041623   .0758896     5.33   0.000     .2554215    .5529031
          11  |  -.1107206   .0970095    -1.14   0.254    -.3008557    .0794146
          12  |  -.0016339   .0880818    -0.02   0.985    -.1742711    .1710033
          13  |   .1913869   .0846261     2.26   0.024     .0255228     .357251
          14  |   .0842027   .0764746     1.10   0.271    -.0656848    .2340903
          15  |   .1456644    .072709     2.00   0.045     .0031573    .2881715
          16  |   .2565955    .085889     2.99   0.003     .0882563    .4249348
          17  |    .099478   .1090289     0.91   0.362    -.1142147    .3131707
          18  |   .2209883   .0777587     2.84   0.004      .068584    .3733926
          19  |   .2094426   .0779416     2.69   0.007     .0566798    .3622054
          20  |    .303627   .0828313     3.67   0.000     .1412807    .4659733
          21  |   .6070566   .0840972     7.22   0.000      .442229    .7718841
          22  |   .1800938   .1156869     1.56   0.120    -.0466485     .406836
          23  |   .3034836   .0822912     3.69   0.000     .1421957    .4647714
          24  |   .2504132   .1102354     2.27   0.023     .0343558    .4664707
          25  |   .2131395   .0902913     2.36   0.018     .0361718    .3901071
          26  |   .1462796   .0853793     1.71   0.087    -.0210609      .31362
          27  |   .0648055   .0845458     0.77   0.443    -.1009012    .2305122
          28  |   .2753373   .0847793     3.25   0.001     .1091729    .4415017
          29  |   .0438266   .1061926     0.41   0.680     -.164307    .2519603
          30  |     .54294   .0750654     7.23   0.000     .3958146    .6900654
          31  |   .4416992   .0830936     5.32   0.000     .2788388    .6045597
          32  |   .0908294   .0678199     1.34   0.180    -.0420951    .2237539
          33  |  -.1810277    .090979    -1.99   0.047    -.3593433   -.0027122
          34  |   .1498803   .0993012     1.51   0.131    -.0447464    .3445071
          35  |   .4267741   .0822993     5.19   0.000     .2654705    .5880778
          36  |   .1402126   .0840615     1.67   0.095    -.0245449      .30497
          37  |   .2565708   .0955218     2.69   0.007     .0693515      .44379
          38  |   .4930436   .0755505     6.53   0.000     .3449673    .6411199
          39  |   .4555804   .1057377     4.31   0.000     .2483384    .6628224
          40  |   .4016865   .0900511     4.46   0.000     .2251896    .5781833
          41  |   .0551261   .0947821     0.58   0.561    -.1306434    .2408957
          42  |   .2570303    .086772     2.96   0.003     .0869604    .4271003
          43  |   .1267611   .0698514     1.81   0.070    -.0101451    .2636673
          44  |   .0760076   .0744966     1.02   0.308    -.0700031    .2220182
          45  |   .0502561   .1019381     0.49   0.622    -.1495389    .2500511
          46  |   .0289844   .0818703     0.35   0.723    -.1314785    .1894473
          47  |   .2415181   .0815765     2.96   0.003      .081631    .4014052
          49  |   .4311747   .0803313     5.37   0.000     .2737282    .5886211
          50  |   .3378018   .0836816     4.04   0.000     .1737888    .5018148
          51  |   .0639106    .092097     0.69   0.488    -.1165962    .2444175
              |
        _cons |  -1.818922   1.460472    -1.25   0.213    -4.681395     1.04355
-------------------------------------------------------------------------------

. est store tier3_coef_endog;

. est save "`studydir'/tier3_coef_endog.ster", replace;
file /Users/moxiemoo/Dropbox/DTC and Formularies/Analysis/Results/tier3_coef_endo
> g.ster saved

. margins, dydx(dtctv comp_dtctv pct_dtctv offpatent mark_share unitprice drugcou
> nt enroll rank unemp) post;

Average marginal effects                          Number of obs   =      92294
Model VCE    : Bootstrap

Expression   : Pr(tier3), predict()
dy/dx w.r.t. : dtctv comp_dtctv pct_dtctv offpatent mark_share unitprice
               drugcount enroll rank unemp

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       dtctv |  -.0502009   .0044055   -11.40   0.000    -.0588356   -.0415663
  comp_dtctv |   .0098243   .0005216    18.84   0.000      .008802    .0108466
   pct_dtctv |   .0653218   .0056396    11.58   0.000     .0542685    .0763751
   offpatent |   .3866826   .0351711    10.99   0.000     .3177484    .4556167
  mark_share |  -.0053481   .0013875    -3.85   0.000    -.0080676   -.0026287
   unitprice |   .0366094   .0056954     6.43   0.000     .0254466    .0477723
   drugcount |  -.0403978   .0020393   -19.81   0.000    -.0443947   -.0364009
      enroll |   .0000728   .0000517     1.41   0.159    -.0000285    .0001741
        rank |   .0007655   .0000459    16.67   0.000     .0006755    .0008555
       unemp |  -.0128829   .0037012    -3.48   0.001    -.0201371   -.0056287
------------------------------------------------------------------------------

. est store tier3_me_endog;

. est save "`studydir'/tier3_me_endog.ster", replace;
file /Users/moxiemoo/Dropbox/DTC and Formularies/Analysis/Results/tier3_me_endog.
> ster saved

. estimates restore tier3_coef_endog;
(results tier3_coef_endog are active now)

. margins, dydx(dtctv) at(dtctv==(0(5)65));

Average marginal effects                          Number of obs   =      92294
Model VCE    : Bootstrap

Expression   : Pr(tier3), predict()
dy/dx w.r.t. : dtctv

1._at        : dtctv           =           0

2._at        : dtctv           =           5

3._at        : dtctv           =          10

4._at        : dtctv           =          15

5._at        : dtctv           =          20

6._at        : dtctv           =          25

7._at        : dtctv           =          30

8._at        : dtctv           =          35

9._at        : dtctv           =          40

10._at       : dtctv           =          45

11._at       : dtctv           =          50

12._at       : dtctv           =          55

13._at       : dtctv           =          60

14._at       : dtctv           =          65

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
dtctv        |
         _at |
          1  |          .  (not estimable)
          2  |          .  (not estimable)
          3  |          .  (not estimable)
          4  |          .  (not estimable)
          5  |          .  (not estimable)
          6  |          .  (not estimable)
          7  |          .  (not estimable)
          8  |          .  (not estimable)
          9  |          .  (not estimable)
         10  |          .  (not estimable)
         11  |          .  (not estimable)
         12  |          .  (not estimable)
         13  |          .  (not estimable)
         14  |          .  (not estimable)
------------------------------------------------------------------------------

. marginsplot, 
> title("Marginal Effect of Lagged TV DTC") 
> subtitle("by DTC spending level")
> ytitle("Change in the Pr(Drug is on Tier 3)", size (medsmall) )
> xtitle("Lagged Statin TV DTC - in millions of dollars", size(medsmall))
> ylabel(, labsize(small))
> xlabel(, labsize(small))
> yline(0)
> saving("`resultsdir'/ME for pre-DTC across levels.gph", replace);

[Richard Williams]

You still have a bunch of unnecessary xi: commands in there. They may not be causing the main problem but they aren't helping either.

This is an incredibly complicated problem, much more complicated than what you first presented. My general advice in a situation like this is to start with a minimal number of variables, and then gradually build up. i.e.start with something like you first presented.