Hello everyone,

I am using a multinomial logit regression with three categories. I want to calculate the economic significance of independent variables. Many papers refer to changes in odds in interpreting the economic significance of variables in multinomial regressions. According to these papers, the change in odds is the percentage change in the odds ratio for one standard deviation increase in explanatory variables. My questions are as follows.

Q1: Is the change in odds for multinomial regressions the same as the standard deviation interpretation for linear regressions?

Q2: I have difficulties in interpreting STATA outputs. For example, I have a dependent variable of three categories, 0, 1, and 2. The base case of the multinomial logit regression is category 0. That is, I have two regressions, 1 versus 0 and 2 versus 0. I want to know the change in odds of CR_year. I use the following codes to calculate the change in odds. My understanding is that e^bStdX gives the results of the change in odds. However, I am not sure which numbers to use. Are 0.9072 and 0.4431 the changes of odds for regressions 1 versus0 and 2 versus 0 respectively?

This may be a silly question...but I would appreciate your kind help.

Code:
. mlogit Security CR_year, base(0) ro

Iteration 0:   log pseudolikelihood = -3897.9265  
Iteration 1:   log pseudolikelihood = -3692.8119  
Iteration 2:   log pseudolikelihood = -3688.6424  
Iteration 3:   log pseudolikelihood = -3688.6368  
Iteration 4:   log pseudolikelihood = -3688.6368  

Multinomial logistic regression                 Number of obs     =      3,731
                                                Wald chi2(2)      =     338.51
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -3688.6368               Pseudo R2         =     0.0537

------------------------------------------------------------------------------
             |               Robust
    Security |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0            |  (base outcome)
-------------+----------------------------------------------------------------
1            |
     CR_year |  -.2081153   .0907458    -2.29   0.022    -.3859737   -.0302568
       _cons |  -.7551389   .0584756   -12.91   0.000    -.8697489   -.6405288
-------------+----------------------------------------------------------------
2            |
     CR_year |  -1.738738   .0956928   -18.17   0.000    -1.926292   -1.551184
       _cons |      .2518   .0440799     5.71   0.000     .1654051     .338195
------------------------------------------------------------------------------
. listcoef, help

mlogit (N=3731): Factor Change in the Odds of Security 

Variable: CR_year (sd=.46807845)

Odds comparing    |
Alternative 1     |
to Alternative 2  |      b         z     P>|z|     e^b   e^bStdX
------------------+---------------------------------------------
1       -2        |   1.53062   13.666   0.000   4.6211   2.0472
1       -0        |  -0.20812   -2.293   0.022   0.8121   0.9072
2       -1        |  -1.53062  -13.666   0.000   0.2164   0.4885
2       -0        |  -1.73874  -18.170   0.000   0.1757   0.4431
0       -1        |   0.20812    2.293   0.022   1.2314   1.1023
0       -2        |   1.73874   18.170   0.000   5.6902   2.2566
----------------------------------------------------------------
       b = raw coefficient
       z = z-score for test of b=0
   P>|z| = p-value for z-test
     e^b = exp(b) = factor change in odds for unit increase in X
 e^bStdX = exp(b*SD of X) = change in odds for SD increase in X