Interpreting results from multinomial logistic model

[Linh Nguyen]

Hi everyone,

The dependent variable is "decision" take 0 for no action, 1 for equity issues, 3 for debt issues.

The main independent variable: mis_mbm1=ln(market value of equity/book value of equity)

I run the following code:

. global x_list tan1 ebitda1 size1

. // Get estimated coefficients 
. mlogit decision mis_mbm1                        $x_list, b(0) vce(cluster id)

Iteration 0:   log pseudolikelihood = -1656.4934  
Iteration 1:   log pseudolikelihood = -1612.5628  
Iteration 2:   log pseudolikelihood = -1612.2417  
Iteration 3:   log pseudolikelihood = -1612.2417  

Multinomial logistic regression                 Number of obs     =      1,644
                                                Wald chi2(8)      =      47.48
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -1612.2417               Pseudo R2         =     0.0267

                                   (Std. Err. adjusted for 219 clusters in id)
------------------------------------------------------------------------------
             |               Robust
    decision |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0            |  (base outcome)
-------------+----------------------------------------------------------------
1            |
    mis_mbm1 |   .3654429   .1797999     2.03   0.042     .0130416    .7178443
        tan1 |   1.896081   .7475029     2.54   0.011     .4310023     3.36116
     ebitda1 |  -10.41082   3.184291    -3.27   0.001    -16.65192   -4.169728
       size1 |  -.2413481   .0848461    -2.84   0.004    -.4076435   -.0750528
       _cons |  -.1678774   1.017706    -0.16   0.869    -2.162545     1.82679
-------------+----------------------------------------------------------------
3            |
    mis_mbm1 |   .6849597   .1390506     3.72   0.000     .2449119    .7899802
        tan1 |   .1355039   .4106839     0.33   0.741    -.6694218    .9404295
     ebitda1 |  -5.916909    2.42404    -2.44   0.015    -10.66794   -1.165878
       size1 |  -.3576047   .0658636    -5.43   0.000     -.486695   -.2285144
       _cons |    2.31299   .6238702     3.71   0.000     1.090226    3.535753
------------------------------------------------------------------------------


. // Get margin effects
. qui mlogit decision mis_mbm1                        $x_list, b(0) vce(cluster id)

. eststo mlogit

. foreach o in 1 3 {
  2.     qui margins, dydx(*) atmeans predict(outcome(`o')) post
  3.     eststo, title(Outcome `o')
  4.     estimates restore mlogit
  5. }
(est2 stored)
(results mlogit are active now)
(est3 stored)
(results mlogit are active now)

. eststo drop mlogit
(mlogit dropped)

. esttab, noobs b(3) z(3) star(* 0.10 ** 0.05 *** 0.010) mtitles nonumbers title(Average Marginal Effects)
(tabulating estimates stored by eststo; specify "." to tabulate the active results)

Average Marginal Effects
--------------------------------------------
                Outcome 1       Outcome 3   
--------------------------------------------
mis_mbm1            0.025           0.112***
                  (1.185)         (3.747)   

tan1                0.265***       -0.071   
                  (2.666)        (-0.874)   

ebitda1            -1.179***       -0.704   
                 (-2.843)        (-1.544)   

size1              -0.016          -0.063***
                 (-1.540)        (-5.520)   
--------------------------------------------
z statistics in parentheses
* p<0.10, ** p<0.05, *** p<0.010

. 
end of do-file

My explanation about estimated coefficients:

when there is a 10% shift in the market value relative to the book value, e.g. a rise from 1 to 1.1, the change in MIS_MBM is ln(market value/book value = 1.10) = 0.095 which is associated with an increase in the odds ratio for debt issues relative to no action of e^0.685×0.095 = 1.067 (where 0.685 is the coefficient of MIS_MBM and 0.095 is the change in MIS_ MBM). This means that the odds of being a debt issue is 1.067 times (or 7.6% higher than) that of no financing alternative at all when there is a 10% increase in misvaluation

and about marginal effects:

when there is a 0.095 increase in MIS_MBM, the probability of a debt issue in a certain period increases on average about 0.112×0.095 = 1.07 percentage points given all other predictor variables in the model are held constant.

Do I explain coefficients and marginal effects correctly?

I would really appreciate all the help I can get.

Best regards

[Clyde Schechter]

when there is a 0.095 increase in MIS_MBM, the probability of a debt issue in a certain period increases on average about 0.112×0.095 = 1.07 percentage points given all other predictor variables in the model are held constant.

should be "...given all other predictor variables in the model are held constant at their sample means."

-mlogit- is a non-linear model, so the marginal effects change with different values of the variables. If you were to hold all the predictor variables constant at some other values, the marginal effects would be, in general, different.

[Linh Nguyen]

Thank you so much Clyde.

[Linh Nguyen]

Clyde Schechter: Dear Clyde,

The dependent variable is "eqissu" take 0 for no action, 1 for equity issues. The main independent variable: mis_mbm1=ln(market value of equity/book value of equity).

I run -aextlogit- to calculate average semi elasticities rather than marginal effects in -xtlogit, fe-

aextlogit eqissumis_mbm_fm1 tan1 ebitda1 size1
note: multiple positive outcomes within groups encountered.
note: 138 groups (615 obs) dropped because of all positive or
      all negative outcomes.

Iteration 0:   log likelihood = -159.57945  
Iteration 1:   log likelihood = -145.64694  
Iteration 2:   log likelihood = -145.31023  
Iteration 3:   log likelihood = -145.30693  
Iteration 4:   log likelihood = -145.30693  

Conditional fixed-effects logistic regression   Number of obs      =       545
Group variable: id                              Number of groups   =        79
                                                Obs per group: min =         2
                                                               avg = 6.8987342
Log likelihood  = -145.30693                                   max =        16

                   Average (semi) elasticities of Pr(y=1|x,u)
------------------------------------------------------------------------------
      eqissu |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     mis_mbm |   .2672099   .0555997     4.81   0.000     .1582365    .3761834
        tan1 |    .773218    .213595     3.62   0.000     .3545795    1.191856
     ebitda1 |   2.073535    .986045     2.10   0.035     .1409224    4.006148
       size1 |  -.1188548   .0438158    -2.71   0.007    -.2047321   -.0329774
------------------------------------------------------------------------------

My explanation about average semi elasticities:

when there is a 1% increase in MIS_MBM, on average the probability of being equity issues goes up by 26.7%.

Do I explain the economic significance of average semi elasticities correctly?

I would really appreciate all the help I can get.

Best regards