I am now working with an econometrics project, where the dataset contains lots of binary(dummy) variables. Since the linear probability model (LPM) I constructed by directly regressing independent variables on a dependent variable (which is binary also) does not violate the mathematical principle (probabilities should be within 0 and 1), I try to keep that result, as well as compare that result to Probit and Logistic models' estimators, and observe all of their significance levels.

One interaction term that I designed added is significant at 5% level in the LPM, but when I work with Probit and Logistic models it turns to be insignificant.

How could I explain this thing happening? Can I still keep that interaction term (though that is significant at 10% level in Probit/Logistic)? If not, which result should I prefer: LPM or Probit/Logistic? Why? Thanks!

  • $\begingroup$ Did you use robust / Huber white sandwich estimators for the standard errors in the LPM? $\endgroup$ Mar 12 '17 at 15:49
  • $\begingroup$ @MaartenBuis I use robust on my LPM but for Huber White estimator, I haven't learned that yet:( $\endgroup$
    – Can Liang
    Mar 12 '17 at 20:15
  • $\begingroup$ These are just different names for the same thing. $\endgroup$ Mar 12 '17 at 21:36
  • $\begingroup$ Okay. For my LPM I got all predicted probabilities within 0% - 100%. So compared with Logistic and Probit, which model's interpretations should I trust the most? $\endgroup$
    – Can Liang
    Mar 12 '17 at 21:39

Ordinary linear regression uses the assumption of a continuous dependent variable, and is poorly equipped for a binary dependent variable. In particular, it's liable to make absurd predictions, such as saying that the probability of the event occurring is above 100% or below 0%. Stick to your logistic model or probit model instead.

  • $\begingroup$ Thank you for your response! My LPM model predicts the probability within 0%-100%, does that mean that LPM works? If so, which model is more reliable? Do you mean that Probit/Logistic are better always? Thanks again! $\endgroup$
    – Can Liang
    Mar 12 '17 at 20:17
  • $\begingroup$ @CanLiang Probit and logistic regression are always better for a binary dependent variable than linear regression, yes. Or at least, it's very hard to imagine a real-world scenario where ordinary linear regression would serve you better. $\endgroup$ Mar 12 '17 at 23:36
  • $\begingroup$ The coefficients I obtained are similar but for a specific interaction term I added, it is significant in LPM but not in Probit/Logistic. Since Probit/Logistic are better I should use interpretations from their results. Thanks! $\endgroup$
    – Can Liang
    Mar 12 '17 at 23:38
  • $\begingroup$ @CanLiang You're welcome. If I answered your question to your satisfaction, you can accept my answer by clicking the check mark under the voting arrows. $\endgroup$ Mar 12 '17 at 23:58
  • $\begingroup$ Already accepted! First time using Cross Validated, very helpful! Thanks again! $\endgroup$
    – Can Liang
    Mar 12 '17 at 23:59

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