WTP estimation with "brand" dummies

[jonah-allen]

Hi John,

It’s me again—now running into a quirk implementing dummies. I currently have two dummy columns, crop_change and tech_change. These are analogous to the yogurt brands in your example, as each respondent receives three options in their survey question: no change, a cropping change, or a technology change to the farm. Here’s a snapshot of the data:

wtp_risk

# A tibble: 180 × 12
   version  risk loss_value id      original_choice Policy alt   choice obsID clusterID crop_change
   <fct>   <dbl>      <dbl> <chr>   <fct>            <dbl> <fct>  <dbl> <int>     <int>       <dbl>
 1 CO1         8         0  R_bf8T… c                    0 a          0    53         1           0
 2 CO1         4       113. R_bf8T… c                    0 b          0    53         1           1
 3 CO1         4       113. R_bf8T… c                    0 c          1    53         1           0
 4 CO1         8         0  R_2tnw… a                    0 a          1    27         1           0
 5 CO1         4       113. R_2tnw… a                    0 b          0    27         1           1
 6 CO1         4       113. R_2tnw… a                    0 c          0    27         1           0
 7 CO1         8         0  R_2S9c… c                    0 a          0    17         1           0
 8 CO1         4       113. R_2S9c… c                    0 b          0    17         1           1
 9 CO1         4       113. R_2S9c… c                    0 c          1    17         1           0
10 CO1         8         0  R_31F6… a                    0 a          1    29         1           0
# ℹ 170 more rows
# ℹ 1 more variable: tech_change <dbl>
# ℹ Use `print(n = ...)` to see more rows

Observations and Issues

1. NaNs in WTP Estimation When estimating WTP directly, I get the following warning:

Warning message: In sqrt(diag(stats::vcov(object))) : NaNs produced

And the model output is:

mnl_wtp <- logitr(
  data = wtp_risk, 
  outcome = "choice",
  obsID = "obsID", 
  pars = c("risk", "tech_change", "crop_change"),
  scalePar = "loss_value",
  options = list(numMultiStarts = 10) # ensures global solution
)

Model Coefficients: 
              Estimate Std. Error z-value            Pr(>|z|)    
scalePar      0.010608   0.010107  1.0496              0.2939    
risk        -10.505535   1.141731 -9.2014 <0.0000000000000002 ***
sd_scalePar  -0.050373        NaN     NaN                 NaN 

I suspect this issue might be due to the small data size (60 observations). However, the problem does not occur during preference-space estimation.

2. Large Standard Errors in WTP Estimation The standard errors for WTP estimation are very large, regardless of whether clustering is applied. Example output:

mnl_pref <- logitr(
  data = wtp_risk, 
  outcome = "choice",
  obsID = "obsID", 
  pars = c("loss_value", "risk", "crop_change", "tech_change")
)

wtp(mnl_pref, scalePar = "loss_value")
                  Estimate    Std. Error z-value Pr(>|z|)  
scalePar          0.0083484     0.0048013  1.7388  0.08208 .
risk            -25.6952811  7150.6716715 -0.0036  0.99713  
crop_change    -142.2892161 51064.3296005 -0.0028  0.99778  
tech_change     -80.8290757 43298.7631545 -0.0019  0.99851 

3. Differences Between WTP Estimation Methods WTP estimates differ substantially between direct estimation and preference-space estimation. Additionally, the dummy variables (crop_change and tech_change) do not appear in the direct WTP estimation, though this is probably expected. The direct estimation is the same as the results (on both approaches) without "brand" dummies.

I also tested the results with only only one dummy (tech_change), and the issues persist,

Questions

•   Could the NaNs issue be entirely due to the small data size, or might there be something else at play?
•   What might explain the large standard errors in the WTP estimation, even when clustering isn’t applied?
•   Is the difference between WTP estimation methods expected, or might it indicate an implementation issue?

Please let me know if you’d like a portion of my data to replicate these issues. Once again, thank you for this incredibly useful package!

Best, Jonah

[jhelvy]

This is almost certainly because the model is converging to a local minimum. What is the log-likelihood of the WTP space model, and what is it for the preference space model? A preference space MNL model has a convex log-likelihood function, so it will always converge to the global minimum. You can use this to compare - your WTP space LL should be the same. If it's not then you need to keep searching.

It also looks like you're using the outdata API for specifying multi-starts. It should be this (here I'm using 100 starts to search a broader space):

mnl_wtp <- logitr(
  data = wtp_risk, 
  outcome = "choice",
  obsID = "obsID", 
  pars = c("risk", "tech_change", "crop_change"),
  scalePar = "loss_value",
  numMultiStarts = 100
)