Mixed logit model

Below is documentation for the Matlab code in “mixed_logit” folder at this GitHub directory. The code uses full-info NNE to estimate a mixed logit model. Because the likelihood for mixed logit is relatively easy to simulate, full-info NNE shows no advantages in accuracy or computation here. But this setting is a good example to illustrate how full-info NNE works in practice.

Workflow

The following commands run a Monte Carlo experiment that estimates the mixed logit model on a simulated dataset.

>> monte_carlo_data        % simulate a dataset using mixed logit model and save it in data.mat
>> nne_gen                 % generate the training examples
>> nne_train               % train a neural net and apply it to the data

Description of each file

model_mixed_logit.m

This function codes the mixed logit model.

Y = mix_logit_model(rs, par, X, consumer_idx)

• Inputs:

  • rs: a random stream (to control randomness)

  • par: mixed logit model parameter vector

  • X: product attributes

  • consumer_idx: indices of consumers

• Outputs:

  • Y: dummies indicating if products are bought

monte_carlo_data.m

This script creates a dataset for Monte Carlo experiment. It uses model_mixed_logit.m to simulate the dataset under a “true” parameter vector, and then saves the dataset in data.mat.

nne_gen.m

This script generates the training, validation, and test examples. It uses model_mixed_logit.m to simulate the examples.

nne_train.m

This script trains a neural net, using the examples from nne_gen.m.

• Validation loss is reported. We can use this loss to choose neural net hyperparameters (e.g., numbers of hidden nodes).

• It draws the parameter recovery plots using the test examples.

• It applies the trained neural net on data.mat.

• It saves the trained neural net to trained_nne.mat.

learn.m

This function codes the training loop, and is used by nne_train.m. This is a custom training loop based on Matlab’s built-in back-propagation and adam algorithms.

[ema_net, train_pred, val_pred, test_pred] = ...
            learn(net, opt, nne, train_dataY, train_label, val_dataY, val_label, test_dataY)

• Inputs:

  • net: the initial neural net

  • opt: training options such as batch size, number of iterations, etc.

  • nne: a structure storing some settings of NNE, created by nne_gen.m.

  • train_dataY, train_label: training examples

  • val_dataY, val_label: validation examples

  • test_dataY: test examples

• Outputs:

  • ema_net: the final trained neural net

  • train_pred: predictions for training examples

  • val_pred: predictions for validation examples

  • test_pred: predictions for test examples