If I want to test the equality of the coefficients of two IVs in the same regression (same DV) I can do a Wald test. If I want to test the equality of the coefficients of the same IV in two different regressions (seemingly unrelated regressions with different DVs), I can do this kind of wizardry. But what if I need to compare the coefficients of the same IV for two different levels of a nominal variable in a multinomial logit regression? How do I test whether $\beta_1 = \beta_2$?
Let's say in:
multinom(formula = dv ~ iv, data = df)
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Dependent variable:
------------------------------
dv_l1 dv_l2
(1) (2)
------------------------------------------------
iv 0.736*** 0.658***
(0.023) (0.021)
Constant -5.757*** -4.396***
(0.036) (0.018)
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Observations 245,698 245,698
Log Likelihood -21,432.162 -21,432.162
Akaike Inf. Crit. 42,872.320 42,872.320
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Note: *p<0.05; **p<0.01; ***p<0.001
How do I test whether the difference between the coefficients for iv
is statistically significant (is 0.736 - 0.658 = 0.078 significantly different from zero)?