"""
File: 03-initial_condition.py

Michel Bierlaire
Thu Aug 07 2025, 17:56:30
"""

import biogeme.biogeme_logging as blog

# The objective of this laboratory is to illustrate the initial condition problem when estimating dynamic models with
# a partial temporal observation period.

# We are performing the same analysis as for the
# previous laboratory. The difference is that we observe the individuals only
# between the age of 45 and the age of 55.

# We have generated synthetic data as follows. We postulate a true model
# for the data generation process. It is a mixture of logit models with
# two alternatives: `smoking` and `not smoking`. The utility for individual $n$ associated with `not smoking`
# in year $t$ is
# $$
# U_{0nt}= \varepsilon_{0nt}
# $$
#  and the utility associated with `smoking` is
# $$
# U_{1nt}= \beta_{nt} y_{n,t-1} + \beta^p_{nt} P_{t} + c_n + \varepsilon_{1nt},
# $$
# where
#
# - $\beta_{nt} = 10$,
# - $y_{n,t-1}=1$ if $n$ is smoking at time $t-1$, $0$ otherwise,
# - $\beta^p_{nt} = -0.1$,
# - $P_t$ is the price of cigarettes at time $t$,
# - $c_n$ is an individual specific constant that captures the a priori, intrinsic attraction of each individual
#   towards smoking. It is assumed to be normally distributed in the population, with zero mean and standard deviation
#   50: $N(0, 50^2)$, and constant over $t$.
#
#
# We have generated a sample of 1000 individuals, and we simulate their smoking behavior between the age of 16 until
# the age of 100.
#
# The date of birth of each individual is uniformly distributed between 2000 and 2020.
# The price of cigarettes in 2000 is supposed to be 10. The price of cigarettes in year $t$ is $$P_t =
# 10 \cdot 1.02^{t-2000},$$
# which represents a price increase of 2% per year.
#
# The data file is `smoking55.dat`.
#
#
# 1. Estimate a simple static model.
# 2. Estimate a dynamic Markov model.
# 3. Estimate a static model accounting for serial correlation.
# 4. Estimate a dynamic Markov model accounting for serial correlation.
# 5. Compare and discuss the results.


# As the estimation time may be long, we ask Biogeme to report the details of the iterations.
logger = blog.get_screen_logger(level=blog.INFO)

# **Tip:**<div class="alert alert-block alert-info">It is advised to start working with a low number of draws,
# until the script is working well. Then, increase the number of draws to 10000, say. Then, execute the script
# overnight.  </div>
number_of_draws = 10