ApolloChoiceModelling forum

Just a quick follow-up question on the interpretation of the log-normally Distributed cost parameter; what does the delta-Method output tell? It tells that the actual cost parameter is approximately zero (as shown in the output script), but the very high Rob t-ratio provided by the deltMethod - what does that mean?

I wouldn't really look at the t-ratio in that case. It's clear that the original parameter is not well estimated, see the NaN for the classical standard error for cost_sig. But your cost coefficient here is clearly not different from zero

stephanehess wrote: ↑18 Aug 2020, 10:37 Hi

there could be many reasons for this, and it's difficult to diagnose without seeing your outputs, and also how they compare to the model with Normals. A Normal distribution for cost of course makes no sense, so you're right to try negative Lognormals. One thing to consider is whether your starting values for the negative Lognormal are appropriate. I would advise starting cost_B_mu at something like -3 or even -5

Best wishes

Stephane

Hi Stephane,

Following this discussion, would you recommend specifying vtts and b_cost using different distributions for time and cost in the WTP space.

For example, suppose I specify betta_fare as negative log-normal and vtts as normal,

Assuming the utility to be additive, Is it correct to specify the utility function for alternative 1 as,
V[["alt1"]] =... + betta_fare(vtts * TT_1 + cost_1)

Hi

to me, Normal does not make sense for VTT - see for example https://doi.org/10.1016/j.tra.2004.09.007 and https://doi.org/10.1016/j.trb.2016.11.002

But if you use two lognormals, then there is no need for wtp space as the results in preference space will be the same



Stephane

Thanks and happy holidays.

Regards

Masimba

Good day, David and Stephane,

I hope you're all doing well.

I am estimating a mixed logit for a public transport mode choice study with 3-time components, fare, and seating arrangement as variables. Like you advised the last time regarding how it doesn't make sense to assume Normal distribution for fare and time components, I tried to specify as lognormal and log uniform distribution and my LL keeps getting worse as I increase the number of draws, which would mean that I am estimating the wrong model. However, normal & uniform specifications seem to work just fine in that context, and my estimates for the fare:

Normal distribution
mean = -0.11153 (-13.32228)
sigma = 0.06084 (12.3186)

• 3.3% non-zero probability of positive coefficient

Uniform
a = -0.006285(-0.9827)
b = -0.218420(-11.2865)

The uniform seems to be behaviourally sound. My question is regarding the normal distribution; I have students in my data who I assume might not be sensitive to fare, would you advise allowing continuous distribution within a group. For instance,
betta_fare_student follows N(b_fare_student_mean, b_fare_student_sigma).

I seem not to find literature on that type of specification besides latent class models.

Thanks and regards

Masimba.

Hi

you say "my LL keeps getting worse as I increase the number of draws, which would mean that I am estimating the wrong model". Why do you think that means you are estimating the wrong model? As explained in the frequently asked questions, your LL will stabilise once you use a large enough number of draws. How many are you using?

Stephane

I started with 200,500 then 1000
LL(note) : -3172.792
LL(200) : -1540.384
LL(500) : -1541.772
LL(1000) : -1542.743
LL(note) : -3172.792
LL(200) : -1541.001
LL(500) : -1544.171

Hi

okay, so where exactly is the issue? These are still fluctuating, which is quite normal

Stephane

Thank you

I thought the LL should have improved when I used 1000 draws from 500.
Let men keep on trying with more draws.

Regards

Masimba