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Why the lasso method in multinomial logistic regression differ from the traditional method using maximum likelihood? I found that the significant coefficients in lasso have different values against the regular one. The significant coefficients mean the coefficient included in the model. If i'm using the p value (sig.) of Wald test, the significant coefficient have p-value under 0.05(my alpha). The coefficient included using lasso and the traditional multinomial logistic regression are different, and have different values.

Why did that happened?

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  • $\begingroup$ What is the regular method? What does "significant coefficient" mean in both cases? $\endgroup$ – Matthew Drury Oct 16 '17 at 23:58
  • $\begingroup$ It means the usual method using maximum likelihood. $\endgroup$ – Hafid W. Ramadhan Oct 19 '17 at 3:53
  • $\begingroup$ The significant coefficients mean the coefficient included in the model. If we're using the p value (sig.) of Wald test, the significant coefficients have $\endgroup$ – Hafid W. Ramadhan Oct 19 '17 at 3:55
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LASSO forces the sum of the absolute values of the coefficients to be below some value. This will, naturally, affect their values. Why would you expect otherwise?

LASSO does this in order to counter the well-known problems with many other methods of variable selection, in particular such methods as stepwise, forward, backward and bivariate screeing. One of the problems with those methods is that coefficient estimates will be biased away from 0, another is that p values will be too small.

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