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st: interactions and economic significance in logit regression


From   Francesco Saverio Stentella Lopes <[email protected]>
To   [email protected]
Subject   st: interactions and economic significance in logit regression
Date   Fri, 08 Nov 2013 14:21:26 +0100

Coefficient    |Marginal effect
x1      | -0.03557      |-0.00283
x2      | -0.15448***|-0.01229***
x3      |  -0.01690     |-0.00134
x4      | 0.07181**   | 0.00571**
x5      | -0.00470      |-0.00037
x6      | 0.06316*     | 0.00503*
x2*x3| -0.03970      |-0.00340
x2*x4| -0.00257      |-0.00092
x2*x5| -0.08700**  |-0.00771**
x2*x6| 0.06842**   | 0.00548*

Dear Statalist,
The above table reports results from a logit model in which the dependent
variable  is a dummy variable. All the regressors are continuous variables.
The model also includes the interactions between the x2 and x3,x4,x5,x6.
All independent variables have been standardized. We are interested in the
moderator role of each one of the interacted x (x3 x4 x5 and x6) on the
relationship between x2 and our dependent variable (y). We report both
logit coefficients and marginal effects estimated holding other variables
at the mean values. For interaction terms, we follow the procedure
suggested by Norton et al. (2004), in order to calculate the corrected
interaction effect (the value reported in the table is the mean interaction
effect and its level of statistical significance). We are interested in
estimating the economic significance of our results. Namely we want to
understand how x3 x4 x5 and x6 (one by one) impact on the link between x2
and our dependent variable.
For example, focusing on control (x5), we would interpret our results as
such:
1) A decrease of 1 standard deviation in x2, irrespective the level of the
others rgressors, increases the probability of y by 1.229 percentage points (-0.01229***)
i.e. the estimated margin for x2;

2) Holding constant x2, an increase of one standard deviation in x5 would
increase the probability of y by 0.037 percentage points (i.e. the estimated margin for x5)
. However, the effect is not statistically significant and we do not
discuss it;


3)The effect of a decrease of 1 standard deviation in x2 is reinforced by a
contemporaneous increase of 1 standard deviation in  x5  (given that the
mean interaction effect has the same sign of the coefficient of  x2). The
economic effect on the probability of y becomes
(-0.01229-0.00771)=-0.02000, so that the probability of y would increase of
about 2 percentage points.

Is the third step correct? Can I simply add the marginal effect calculated
by the margin command (i.e the marginal effect calculated for x1...x6) with
the marginal effect calculated using inteff (i.e the marginal effect
calculated for x2*x3...x2*x6) in order to obtain the economic significance
of our results?
Many thanks for the precious help
Francesco
Reference
Norton, E., Wang H, Ai C. (2004) Computing interaction effects and standard errors in logit and probit models. Stata Journal, 4, pp. 103-116


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