Computing interaction effects and standard errors in logit and probit models

Computing interaction effects and standard errors in logit and probit models

2004 | Edward C. Norton, Hua Wang, Chunrong Ai
The paper explains why computing the marginal effect of a change in two variables is more complex in nonlinear models than in linear models. The Stata command inteff computes the correct marginal effect of a change in two interacted variables for a logit or probit model, as well as the correct standard errors. The inteff command graphs the interaction effect and saves the results for further investigation. Interaction terms are used in nonlinear models like logit and probit. However, the intuition from linear regression does not apply. The marginal effect of changing both interacted variables is not equal to the marginal effect of changing just the interaction term. The sign of the interaction effect may vary across observations, and the statistical significance cannot be determined from the z-statistic. The odds-ratio interpretation of logit coefficients does not apply to interaction terms. Most applied researchers misinterpret the coefficient of the interaction term in nonlinear models. A review of 13 economics journals found that none correctly interpreted the interaction term. The inteff command computes the correct interaction effect and standard errors for logit and probit models. It works for continuous, dummy, or mixed variables. It also graphs the interaction effect and saves results. In linear models, the interaction effect is straightforward. In nonlinear models, the interaction effect is the cross-partial derivative of the expected value of the dependent variable. The interaction effect is conditional on the independent variables and may have different signs for different values of covariates. The test for the statistical significance of the interaction effect must be based on the estimated cross-partial derivative, not the coefficient of the interaction term. The inteff command is easier to use than predictnl and leads to fewer user errors. It calculates the correct interaction effect and standard errors for logit and probit models. The paper provides examples of using inteff with logit and probit models. The results show that interaction effects can be positive or negative, and their statistical significance varies. The inteff command is important for applied researchers to correctly compute and interpret interaction effects in nonlinear models.The paper explains why computing the marginal effect of a change in two variables is more complex in nonlinear models than in linear models. The Stata command inteff computes the correct marginal effect of a change in two interacted variables for a logit or probit model, as well as the correct standard errors. The inteff command graphs the interaction effect and saves the results for further investigation. Interaction terms are used in nonlinear models like logit and probit. However, the intuition from linear regression does not apply. The marginal effect of changing both interacted variables is not equal to the marginal effect of changing just the interaction term. The sign of the interaction effect may vary across observations, and the statistical significance cannot be determined from the z-statistic. The odds-ratio interpretation of logit coefficients does not apply to interaction terms. Most applied researchers misinterpret the coefficient of the interaction term in nonlinear models. A review of 13 economics journals found that none correctly interpreted the interaction term. The inteff command computes the correct interaction effect and standard errors for logit and probit models. It works for continuous, dummy, or mixed variables. It also graphs the interaction effect and saves results. In linear models, the interaction effect is straightforward. In nonlinear models, the interaction effect is the cross-partial derivative of the expected value of the dependent variable. The interaction effect is conditional on the independent variables and may have different signs for different values of covariates. The test for the statistical significance of the interaction effect must be based on the estimated cross-partial derivative, not the coefficient of the interaction term. The inteff command is easier to use than predictnl and leads to fewer user errors. It calculates the correct interaction effect and standard errors for logit and probit models. The paper provides examples of using inteff with logit and probit models. The results show that interaction effects can be positive or negative, and their statistical significance varies. The inteff command is important for applied researchers to correctly compute and interpret interaction effects in nonlinear models.
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