comparing the logit marginal effects to LPN coefficient

[Sunniva]

Dear Stata users,
I am using a logit model to calculate the average marginal effect (AME) of my independent variables on a dichotomous dummy variable (completed education VS non-completed education). Independent variables: 1.gen immigrant, 2.gen immigrant. I am comparing the logit marginal effects to the coefficient obtained by a linear probability model using OLS. The differences in percent points between the natives and the two immigrant group are not similar in these to analysis (AME from logit and coefficient from LPN). Are not the marginal effects from the logit models comparable to the OLS coefficients from the linear probability model? I dont, undersatnd why I get different results?
All the best,
Sunniva

[daniel klein]

Please show data (if possible), commands, and results you are asking about.

[Sunniva]

Please find the results below:

OLS (LPN)

1.gen	-0.064254
2.gen	-0.105847
constant	0.88476

LOGIT:

1.gen	-0.518517
2.gen	-0.778956
constant	2.038298

AME after logit:
dydx

1.gen	-0.056208
2.gen	-0.084441

As you see from the results AME after logit gives differnt estimates comaped to LPN.

[Maarten Buis]

If you have a single categorical variable, then the coefficients should not be just similar but exactly the same, as it is a saturated model. The standard errors are different, as it is a different estimator, but the coefficients are exactly the same, as you can see in the example below.

. // open example data
. sysuse nlsw88, clear
(NLSW, 1988 extract)

.
. // prepare the data
.
. gen byte occat = cond(occupation < 3, 1,                    ///
>                  cond(inlist(occupation,5, 6, 8, 9), 2, 3)) ///
>                  if !missing(occupation)
(9 missing values generated)

. label variable occat "occupational category"

. label define occat 1 "white collar" ///
>                    2 "skilled"      ///
>                    3 "unskilled"

. label value occat occat

.
. // estimate the logit with AMEs
. qui logit union i.occat

. margins, dydx(*)

Conditional marginal effects                             Number of obs = 1,869
Model VCE: OIM

Expression: Pr(union), predict()
dy/dx wrt:  2.occat 3.occat

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       occat |
    skilled  |   .1024781   .0266427     3.85   0.000     .0502593    .1546969
  unskilled  |   .1022039   .0224706     4.55   0.000     .0581624    .1462455
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

.
. // estimate the LPM
. reg union i.occat

      Source |       SS           df       MS      Number of obs   =     1,869
-------------+----------------------------------   F(2, 1866)      =     10.39
       Model |  3.81797888         2  1.90898944   Prob > F        =    0.0000
    Residual |  342.966398     1,866  .183797641   R-squared       =    0.0110
-------------+----------------------------------   Adj R-squared   =    0.0099
       Total |  346.784377     1,868  .185644741   Root MSE        =    .42872

------------------------------------------------------------------------------
       union | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       occat |
    skilled  |   .1024781   .0276142     3.71   0.000     .0483201    .1566361
  unskilled  |   .1022039   .0239401     4.27   0.000     .0552517    .1491562
             |
       _cons |   .1710262   .0192306     8.89   0.000     .1333105    .2087418
------------------------------------------------------------------------------

If you have other explanatory/control variables in your model, then the result will differ somewhat. Differences in results you have shown would be a bit high, but still within the limits of what I would expect.

[daniel klein]

Well, you should not expect the LPM coefficients to match AMEs, exactly. Why would you? The mathematics are vastly different. OLS analytically minimizes the sums of squares; AMEs approximate a linear change in a non-linear model by averaging predictions at observed covariate values.

I would say, 5.6 percentage points are pretty close to 6.4 percentage points (the CIs will probably overlap); so are 8.4 p.p. and 10.6 p.p. But that judgment obviously depends on the context. If you tell us more about why you are asking those questions, we might be able to give advice.

Edit:

Maarten provides a much more elaborate answer. I was assuming that there are additional covariates, which I really cannot tell from what you have (not) shown.

[Sunniva]

Many thanks, this was very helpful.

[daniel klein]

As to differences that might or might not be expected, I use Maartens example and add a single continuous covariate (and change the link-functin for the non.linear model) to obtain:

. 
. estimates table AME_logit LPM AME_probit

-----------------------------------------------------
    Variable | AME_logit       LPM       AME_probit  
-------------+---------------------------------------
       occat |
    skilled  |  .19039135    .20256645    .18547717  
  unskilled  |  .14882826    .16475509    .14462052  
             |
        wage |  .02111908    .02286942    .02131575  
       _cons |              -.05758609               
-----------------------------------------------------

[Sunniva]

Many thanks for your help. There are no other covariates in my model, so then my results shold be exactly the same in the LPN and AME after logit, or have I misunderstood?

[daniel klein]

There are no other covariates in my model, so then my results shold be exactly the same in the LPN and AME after logit

Yes. If the results differ, something is wrong. Because you did neither show the code you used nor the complete output, we cannot tell what is wrong.

btw. it is LPM, the M stands for model.

[Sunniva]

I apologize for the typo error in my post, yes it should be LPM.
We no discovered that the reason for why we get different results in the two models is because we have used a marginal effect at the mean (MEM) and not AME. Thanks for useful help.