Thanks for the awesome package. Cristian.

For implementation of WTP Space models, having reasonable starting values may be critical. My attempt to estimate my own data resulted in convergence issue: " Nonpositive definiteness in Cholesky factorization in formt; refresh the lbfgs memory and restart the iteration." The log likelihood is poor, indicating that the algorithm was stuck somewhere.

My intuition is that with proper starting values, the issues of local maxima or flat regions can be tackled. Is it possible to provide starting values to the procedure?

Further, Greene and Hensher (2010; Trasnportation Part D) and Fiebig et al. (2010; Marketing Science) have shown that WTP Space can be implemented with GMNL. The advantage of that is that the price parameter follows a log normal distribution. I wonder how the present set up of xlogit compares to/allow this specification.

Again, thanks for the awesome package. Xlogit is unrivalled in speed. It would be great to complete it with more useful features. This is a lot to ask. I would help if I can overcome the learning curve of programming it.

I am trying to use xlogit in cases where I have variation in alternatives available to each individual. It appears that in these cases, the code will return the following error:

"raise ValueError('inconsistent alts values in long format')"

I believe from looking at the code, this is because the "_check_long_format_consistency" function in the "_choice_model" code checks whether the total number of observations equals the product of individuals times the number of unique alternatives. From what I can tell, this is not strictly necessary from a theoretical or a coding basis. Could someone verify this?

Would is be possible to remove this check in the next edition of the xlogit? In the meantime, is there some sort of workaround for this? Thanks for any comments.

The current version does not support mixed logit models. In general, the current code is ready to be expanded for this functionality, the major change required is to develop the gradient for the random parameters. This could be done by following some of the strategies implemented in this paper or in the mlogit package for R.

Hi Cristian Arteaga,

I was wondering if your program allows you to set a subset of parameters to a given value while optimizing the rest of the parameters.

In particular, I am trying to set the cost coefficients to -1 to immediately read the Value of Time (VoT) from time coefficients.

Is that possible?

Best regards!
Álvaro

Hi Cristian Arteaga,

Thank you for your package.
I encounter a problem with standard errors when I run my code with version 0.2.6. The issue is that all of them are reported to be equal to 1, but when I run the same code and data on version 0.2.4. I do not have this problem. Am I missing something with the new version maybe?

Thanks in advance.
Best,
Max

@arteagac Very much thankful to you for this wonderful package. Is there a way to get the marginal effects or elasticities of the model variables?

Dear Cristian Arteaga,
First of all, thank you for developing such a great package. I have been using it extensively and I think it works just great!

However, I think I found a weird behavior (most likely a bug) when predicting probabilities from a MIXL model.

I was trying to re-create the Log-likelihood (LL) of the model from its predicted probabilities using equation (6) in your article:

Unfortunately, noticed that I was not able to replicate them, and the differences were rather large. (see the first chunk of code below). Additionally, weirdly enough, when using only 1 draw, I am able to replicate the LL value. (see the second chunk of code below)

I haven't had time to go through your source code, but I think there is something wrong with the .predict() method for the MIXL models, since, for MNL models, I checked that my method of retrieving the LL works just fine (not included here).

First chunk

#%%
# 
import pandas as pd
import numpy as np
from xlogit.utils import wide_to_long
from xlogit import MixedLogit
# from your example
df_wide = pd.read_table("http://transp-or.epfl.ch/data/swissmetro.dat", sep='\t')
# Keep only observations for commute and business purposes that contain known choices
df_wide = df_wide[(df_wide['PURPOSE'].isin([1, 3]) & (df_wide['CHOICE'] != 0))]
df_wide['custom_id'] = np.arange(len(df_wide))  # Add unique identifier
df_wide['CHOICE'] = df_wide['CHOICE'].map({1: 'TRAIN', 2:'SM', 3: 'CAR'})
df = wide_to_long(df_wide, id_col='custom_id', alt_name='alt', sep='_',
                  alt_list=['TRAIN', 'SM', 'CAR'], empty_val=0,
                  varying=['TT', 'CO', 'HE', 'AV', 'SEATS'], alt_is_prefix=True)
df['ASC_TRAIN'] = np.ones(len(df))*(df['alt'] == 'TRAIN')
df['ASC_CAR'] = np.ones(len(df))*(df['alt'] == 'CAR')
df['TT'], df['CO'] = df['TT']/100, df['CO']/100  # Scale variables
annual_pass = (df['GA'] == 1) & (df['alt'].isin(['TRAIN', 'SM']))
df.loc[annual_pass, 'CO'] = 0  # Cost zero for pass holders
varnames=['ASC_CAR', 'ASC_TRAIN', 'CO', 'TT']


# Model building 
model = MixedLogit()
model.fit(X=df[varnames], 
          y=df['CHOICE'], 
          varnames=varnames,
          alts=df['alt'], 
          ids=df['custom_id'],
           avail=df['AV'],
          panels=df["ID"], randvars={'TT': 'n'}, 
          n_draws=100,
          optim_method='L-BFGS-B')


# Create predictions 
predictions = model.predict(X=df[varnames], 
              varnames=varnames,
                alts=df['alt'], 
                ids=df['custom_id'], 
                avail=df['AV'],
                panels=df["ID"], 
                n_draws=100,
                return_proba = True) 
# Recovering the predicted probabilities
pred_proba = predictions[1]

# transform the df['CHOICE'] variable into a dummy variable
chosen = np.array(df_wide['CHOICE'].map({'TRAIN': 0, 'SM': 1, 'CAR': 2})).reshape(-1, 1)
# Select the probability of the chosen alternative
proba_chosen = np.take_along_axis(pred_proba, chosen, axis=1)
# Compute the negative log-likelihood
recreated_LL = np.sum(np.log(proba_chosen))
print("recreated LL:",recreated_LL)
print("model's LL  :",model.loglikelihood)

# recreated LL: -5293.024645448918
# model's LL  : -4360.226616589964

Second chunk

# The same again but with 1 draw only.
model.fit(X=df[varnames], 
          y=df['CHOICE'], 
          varnames=varnames,
          alts=df['alt'], 
          ids=df['custom_id'],
           avail=df['AV'],
          panels=df["ID"], randvars={'TT': 'n'}, 
          n_draws=1,
          optim_method='L-BFGS-B')


# Create predictions 
predictions = model.predict(X=df[varnames], 
              varnames=varnames,
                alts=df['alt'], 
                ids=df['custom_id'], 
                avail=df['AV'],
                panels=df["ID"], 
                n_draws=1,
                return_proba = True) 
# Recovering the predicted probabilities
pred_proba = predictions[1]

# transform the df['CHOICE'] variable into a dummy variable
chosen = np.array(df_wide['CHOICE'].map({'TRAIN': 0, 'SM': 1, 'CAR': 2})).reshape(-1, 1)
# Select the probability of the chosen alternative
proba_chosen = np.take_along_axis(pred_proba, chosen, axis=1)
# Compute the negative log-likelihood
recreated_LL = np.sum(np.log(proba_chosen))
print("recreated LL:",recreated_LL)
print("model's LL  :",model.loglikelihood)


#recreated LL: -5331.206129776281
#model's LL  : -5331.206129776281

Thank you in advance!

Álvaro

Hi Cristian,

Hope you're well! Just wanted to let you know that there is a small bug in the predict method. For the multinomial login class on line 283-284, it reads as follows:

if weights is not None: # Reshape weights to match input data weights = weights[y.ravel().astype(bool)]

but it should read as follows to prevent operation on None y values:
if weights is not None and not predict_mode: # Reshape weights to match input data weights = weights[y.ravel().astype(bool)]

xlogit needed a logo, so I asked DALLE-mini to generate one.

I selected firs one in the third column and added a transparent background:

Added some text, and done!

"wights" should be renamed to "weights". Otherwise, weighted estimation is broken.

I am coming over from R and the mlogit package and I have the data formatted in the same way. It seems like xlogit is expecting that when in long format there's the same number of alt rows for each id group. Is this expected behavior for xlogit? Am I attempting to do something that just isn't possible?

model = MultinomialLogit()
model.fit(X=df[vars], y=df['result'], varnames=vars, ids=df['id'], alts=df['alt_id'])
model.summary()

@arteagac, xlogit looks amazing, thanks for your work on this!

As @crforsythe noted in issue #3 on implementing WTP space models, I'm the author of the logitr R package. It seems both packages have very similar functionality (except for the WTP space implementation, which shouldn't be too hard to add if you're interested in adding it). logitr is considerably faster than most of the other R packages you benchmark against, but I don't think it's speed will scale with very large numbers of draws like xlogit. It'd be great to see it added to your benchmarking. I was actually in the process of attempting to benchmark it myself, but since you've already got yours setup it should be pretty easy to add it. I believe xlogit and logitr use the same data structure too - the UI looks quite similar.

Really nice work you've done here!

A vector of weights should be given and processed. See for instance the weights parameter in mlogit for R package.

The temporary branch addit implements an additive term in the utility formulation. This additive term can help model coefficients kept at a fixed value as well as alternative specific fixed values. The additive term can be included in the fit and predict functions as follows:

model.fit(..., addit= -1*df['cost'], ...)

which would result in the following utility specification that simulates a coefficient of -1 for the cost coefficient kept fixed throughout the estimation (the portion in squared brackets is the addit term):

$$ U_{j} = \beta_0 + \beta_{1j} x_{1j} + ... + [-1\cdot x_{cost j}]$$

Note that you can also add multiple terms by simple pre-computing the addit term.

Love seeing this new contribution to choice modeling software! Very impressive work. I was wondering if you had any intention to expand xlogit's ability to allow for nonlinear utility specification, such as WTP space estimation a la Train and Weeks (2005)?

First of all: Thanks a lot for this very useful package!

I was wondering whether it would be possible to estimate the random utility models in Bruhin et al. (2019) as mixed logits using xlogit? The authors already estimate the utility models as standard logits and finite mixtures. Specifically, they estimate simple social preference models based on a panel of binary dictator and reciprocity games. In a binary dictator game, the subject is randomly matched with another subject and has to choose between two allocations. The utility of a given allocation is given by:

In a binary reciprocity game, the subject is faced with the same decision, but the matched subject performs either a kind or unkind decision beforehand. Hence, the utility here is given by:

Based on this, the probability of choosing one allocation over the other is given by:

It is not clear to me whether such a functional form, both as standard logit and mixed logit, can be estimated by xlogit.

Many thanks and best,
Jesper