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I trying to estimate the willingness to pay for a specific product. To do so, I am running a multinomial logit in willingness to pay space.

I am doing something like this using the logitr package

# upload package and data
library(logitr)
data(yogurt)
# estimate the model
mnl_wtp <- logitr(
  data     = yogurt,
  outcome  = "choice",
  obsID    = "obsID",
  pars     = c("feat", "brand"),
  scalePar = "price"
)
# report results
summary(mnl_wtp)
Call:
logitr(data = yogurt, outcome = "choice", obsID = "obsID", pars = c("feat", 
    "brand"), scalePar = "price")

Frequencies of alternatives:
       1        2        3        4 
0.402156 0.029436 0.229270 0.339138 

Exit Status: 3, Optimization stopped because ftol_rel or ftol_abs was reached.
                                 
Model Type:     Multinomial Logit
Model Space:   Willingness-to-Pay
Model Run:                 1 of 1
Iterations:                    38
Elapsed Time:         0h:0m:0.02s
Algorithm:         NLOPT_LD_LBFGS
Weights Used?:              FALSE
Robust?                     FALSE

Model Coefficients: 
               Estimate Std. Error  z-value  Pr(>|z|)    
scalePar       0.366583   0.024366  15.0448 < 2.2e-16 ***
feat           1.340593   0.355867   3.7671 0.0001651 ***
brandhiland  -10.135764   0.576089 -17.5941 < 2.2e-16 ***
brandweight   -1.749083   0.179898  -9.7226 < 2.2e-16 ***
brandyoplait   2.003821   0.142377  14.0740 < 2.2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
                                     
Log-Likelihood:         -2656.8878779
Null Log-Likelihood:    -3343.7419990
AIC:                     5323.7757559
BIC:                     5352.7168000
McFadden R2:                0.2054148
Adj McFadden R2:            0.2039195
Number of Observations:  2412.0000000

I wonder, what is the correct way to test the difference across coefficients? For example is the effect of feat (1.341) statistically different from the effect on brandyoplait (2.004)?

If anyone could help me I would be extremely grateful

Best

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The two coefficients are not entirely independent; the presence of one predictor in the model influences the coefficient for the other. I would test the difference by creating a model with feat and without brand; a model with brand but not with feat; and by using AIC or BIC -- or performance on cross-validation -- to test the difference between the two. (It may be tempting to use anova() for this purpose, but it would not apply since the two models would not be nested.)

Edit: there is a Vuong Non-Nested Hypothesis Test for comparing non-nested models with same response variable. It can be obtained using the nonnest2 or pscl library in R.

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  • $\begingroup$ Dear Rolando, thank you very much for your help on this matter! it is really helpful. I wonder would you be able to provide a working example of the non test? It does not appear to be working with logitr coefficients $\endgroup$ Commented Jul 18 at 13:08
  • $\begingroup$ pscl::vuong(m1,m2) # where m1 and m2 are the two models. A large, positive test statistic provides evidence of the superiority of model 1 over model 2, while a large, negative test statistic is evidence of the superiority of model 2 over model 1. $\endgroup$ Commented Jul 19 at 14:36

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