Note
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Discrete mixture with panel data
- Example of a discrete mixture of logit models, also called latent
class model. The datafile is organized as panel data.
- author:
Michel Bierlaire, EPFL
- date:
Mon Apr 10 11:53:06 2023
import biogeme.biogeme_logging as blog
import biogeme.biogeme as bio
from biogeme import models
from biogeme.expressions import (
Beta,
bioDraws,
PanelLikelihoodTrajectory,
MonteCarlo,
log,
)
See the data processing script: Panel data preparation for Swissmetro.
from swissmetro_panel import (
database,
CHOICE,
SM_AV,
CAR_AV_SP,
TRAIN_AV_SP,
TRAIN_TT_SCALED,
TRAIN_COST_SCALED,
SM_TT_SCALED,
SM_COST_SCALED,
CAR_TT_SCALED,
CAR_CO_SCALED,
)
logger = blog.get_screen_logger(level=blog.INFO)
logger.info('Example b15panel_discrete.py')
Example b15panel_discrete.py
Parameters to be estimated. One version for each latent class.
NUMBER_OF_CLASSES = 2
B_COST = [Beta(f'B_COST_class{i}', 0, None, None, 0) for i in range(NUMBER_OF_CLASSES)]
Define a random parameter, normally distributed across individuals, designed to be used for Monte-Carlo simulation
B_TIME = [Beta(f'B_TIME_class{i}', 0, None, None, 0) for i in range(NUMBER_OF_CLASSES)]
It is advised not to use 0 as starting value for the following parameter.
B_TIME_S = [
Beta(f'B_TIME_S_class{i}', 1, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
B_TIME_RND = [
B_TIME[i] + B_TIME_S[i] * bioDraws(f'B_TIME_RND_class{i}', 'NORMAL_ANTI')
for i in range(NUMBER_OF_CLASSES)
]
We do the same for the constants, to address serial correlation.
ASC_CAR = [
Beta(f'ASC_CAR_class{i}', 0, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
ASC_CAR_S = [
Beta(f'ASC_CAR_S_class{i}', 1, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
ASC_CAR_RND = [
ASC_CAR[i] + ASC_CAR_S[i] * bioDraws(f'ASC_CAR_RND_class{i}', 'NORMAL_ANTI')
for i in range(NUMBER_OF_CLASSES)
]
ASC_TRAIN = [
Beta(f'ASC_TRAIN_class{i}', 0, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
ASC_TRAIN_S = [
Beta(f'ASC_TRAIN_S_class{i}', 1, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
ASC_TRAIN_RND = [
ASC_TRAIN[i] + ASC_TRAIN_S[i] * bioDraws(f'ASC_TRAIN_RND_class{i}', 'NORMAL_ANTI')
for i in range(NUMBER_OF_CLASSES)
]
ASC_SM = [Beta(f'ASC_SM_class{i}', 0, None, None, 1) for i in range(NUMBER_OF_CLASSES)]
ASC_SM_S = [
Beta(f'ASC_SM_S_class{i}', 1, None, None, 0) for i in range(NUMBER_OF_CLASSES)
]
ASC_SM_RND = [
ASC_SM[i] + ASC_SM_S[i] * bioDraws(f'ASC_SM_RND_class{i}', 'NORMAL_ANTI')
for i in range(NUMBER_OF_CLASSES)
]
Class membership probability.
prob_class0 = Beta('prob_class0', 0.5, 0, 1, 0)
prob_class1 = 1 - prob_class0
In class 0, it is assumed that the time coefficient is zero.
B_TIME_RND[0] = 0
Utility functions.
V1 = [
ASC_TRAIN_RND[i] + B_TIME_RND[i] * TRAIN_TT_SCALED + B_COST[i] * TRAIN_COST_SCALED
for i in range(NUMBER_OF_CLASSES)
]
V2 = [
ASC_SM_RND[i] + B_TIME_RND[i] * SM_TT_SCALED + B_COST[i] * SM_COST_SCALED
for i in range(NUMBER_OF_CLASSES)
]
V3 = [
ASC_CAR_RND[i] + B_TIME_RND[i] * CAR_TT_SCALED + B_COST[i] * CAR_CO_SCALED
for i in range(NUMBER_OF_CLASSES)
]
V = [{1: V1[i], 2: V2[i], 3: V3[i]} for i in range(NUMBER_OF_CLASSES)]
Associate the availability conditions with the alternatives.
av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}
The choice model is a discrete mixture of logit, with availability conditions We calculate the conditional probability for each class.
prob = [
PanelLikelihoodTrajectory(models.logit(V[i], av, CHOICE))
for i in range(NUMBER_OF_CLASSES)
]
Conditional to the random variables, likelihood for the individual.
probIndiv = prob_class0 * prob[0] + prob_class1 * prob[1]
We integrate over the random variables using Monte-Carlo.
logprob = log(MonteCarlo(probIndiv))
Create the Biogeme object. As the objective is to illustrate the syntax, we calculate the Monte-Carlo approximation with a small number of draws. To achieve that, we provide a parameter file different from the default one.
the_biogeme = bio.BIOGEME(database, logprob, parameter_file='few_draws.toml')
the_biogeme.modelName = 'b15panel_discrete'
File few_draws.toml has been parsed.
Estimate the parameters.
results = the_biogeme.estimate()
*** Initial values of the parameters are obtained from the file __b15panel_discrete.iter
Cannot read file __b15panel_discrete.iter. Statement is ignored.
Optimization algorithm: hybrid Newton/BFGS with simple bounds [simple_bounds]
** Optimization: Newton with trust region for simple bounds
Iter. ASC_CAR_S_class ASC_CAR_S_class ASC_CAR_class0 ASC_CAR_class1 ASC_SM_S_class0 ASC_SM_S_class1 ASC_TRAIN_S_cla ASC_TRAIN_S_cla ASC_TRAIN_class ASC_TRAIN_class B_COST_class0 B_COST_class1 B_TIME_S_class1 B_TIME_class1 prob_class0 Function Relgrad Radius Rho
0 1.3 1.2 -0.094 0.17 1.5 1.2 1.3 1.2 -0.67 -0.92 -0.47 -0.6 2 -1 0 4.1e+03 0.031 10 0.9 ++
1 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 1e+02 0.92 ++
2 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 50 -0.003 -
3 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 25 -0.0064 -
4 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 12 -0.012 -
5 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 6.2 -0.019 -
6 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 3.1 -0.019 -
7 1.3 2 -0.11 0.12 1.6 1.6 1.3 1.7 -0.65 -1.4 -0.46 -2.1 2.5 -2.7 0 3.8e+03 0.02 1.6 0.016 -
8 1.4 3.1 -0.24 0.43 1.6 1.5 1.4 2.6 -0.54 -0.65 -0.066 -3.6 3.5 -4.2 8.7e-10 3.7e+03 0.032 1.6 0.18 +
9 1.4 3.1 -0.24 0.43 1.6 1.5 1.4 2.6 -0.54 -0.65 -0.066 -3.6 3.5 -4.2 8.7e-10 3.7e+03 0.032 0.78 -0.049 -
10 1.4 3.5 -0.26 0.22 1.6 1.6 1.4 2.3 -0.53 -0.81 -0.048 -2.8 3.4 -4.8 9.6e-10 3.6e+03 0.012 0.78 0.21 +
11 1.4 3.5 -0.26 0.22 1.6 1.6 1.4 2.3 -0.53 -0.81 -0.048 -2.8 3.4 -4.8 9.6e-10 3.6e+03 0.012 0.39 -0.24 -
12 1.4 3.3 -0.28 0.35 1.6 1.6 1.4 2.3 -0.51 -0.63 -0.034 -3.2 3.5 -4.9 4.2e-09 3.6e+03 0.025 0.39 0.65 +
13 1.5 3.3 -0.32 0.32 1.5 1.7 1.4 2.1 -0.47 -0.46 -0.0055 -3.1 3.7 -5.3 7.8e-09 3.6e+03 0.0036 3.9 0.99 ++
14 1.7 3.7 -1 0.23 1.2 1.9 1.3 1.4 0.26 -0.12 -0.27 -3.4 4 -5.7 1.6e-08 3.6e+03 0.0062 39 1.5 ++
15 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 39 0.59 +
16 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 20 -2.3 -
17 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 9.8 -3.9 -
18 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 4.9 -5.5 -
19 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 2.4 -5.6 -
20 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 1.2 -1.2 -
21 1.9 4.5 -1.4 0.014 1.2 2.2 1 -0.2 0.25 -0.14 -0.02 -4 4.4 -6.2 3.1e-08 3.6e+03 0.014 0.61 -0.41 -
22 1.9 3.8 -1.4 0.38 1.2 2.2 0.98 0.24 0.26 0.016 -0.084 -3.9 4.4 -6.2 6.3e-08 3.6e+03 0.007 0.61 0.67 +
23 2 3.9 -1.7 0.34 1.1 2 0.73 0.22 0.25 -0.0093 -0.2 -3.7 4.3 -6.1 1.3e-07 3.6e+03 0.00099 6.1 1.1 ++
24 2.1 4 -2.3 0.4 0.87 2.1 0.51 0.23 0.011 0.033 -0.091 -3.8 4.4 -6.2 2.5e-07 3.6e+03 0.00076 61 1.2 ++
25 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 6.1e+02 1.2 ++
26 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 3.1e+02 -0.085 -
27 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 1.5e+02 -0.1 -
28 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 76 -0.13 -
29 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 38 -0.18 -
30 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 19 -0.26 -
31 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 9.5 -0.32 -
32 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 4.8 -0.37 -
33 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 2.4 -0.37 -
34 2.1 3.9 -2.7 0.35 0.5 2.1 0.33 0.23 -0.2 -0.0038 -0.31 -3.7 4.3 -6.1 5e-07 3.6e+03 0.00092 1.2 -0.25 -
35 2.1 4 -3.6 0.41 -0.7 2.1 -0.26 0.23 -0.9 0.051 -0.002 -3.8 4.5 -6.3 1e-06 3.6e+03 0.0017 1.2 0.12 +
36 2 3.8 -4.1 0.34 0.5 2.1 -0.23 0.25 -0.54 0.022 -0.81 -3.7 4.4 -6.2 2.1e-06 3.6e+03 0.0053 1.2 0.14 +
37 2 3.8 -4.1 0.34 0.5 2.1 -0.23 0.25 -0.54 0.022 -0.81 -3.7 4.4 -6.2 2.1e-06 3.6e+03 0.0053 0.6 -0.33 -
38 2 4 -4.2 0.27 0.49 2.1 -0.18 0.2 -0.72 -0.039 -0.21 -3.8 4.4 -6.1 4.3e-06 3.6e+03 0.00061 0.6 0.88 +
39 2 4 -4.4 0.27 -0.11 2.1 0.03 0.18 -0.77 -0.026 -0.57 -3.8 4.3 -6.1 8.5e-06 3.6e+03 0.00073 6 0.94 ++
40 1.8 4 -5.5 0.31 0.81 2.1 -0.2 0.25 -1.2 -0.0055 -0.42 -3.8 4.4 -6.2 1.7e-05 3.6e+03 0.0005 6 0.67 +
41 1.8 4 -5.5 0.31 0.81 2.1 -0.2 0.25 -1.2 -0.0055 -0.42 -3.8 4.4 -6.2 1.7e-05 3.6e+03 0.0005 3 -0.36 -
42 1.8 4 -5.5 0.31 0.81 2.1 -0.2 0.25 -1.2 -0.0055 -0.42 -3.8 4.4 -6.2 1.7e-05 3.6e+03 0.0005 1.5 0.035 -
43 1.6 4 -6.3 0.25 -0.68 2.1 0.07 0.2 -1.1 -0.034 -0.84 -3.8 4.3 -6.1 3.3e-05 3.6e+03 0.0012 1.5 0.5 +
44 1.6 4 -6.3 0.25 -0.68 2.1 0.07 0.2 -1.1 -0.034 -0.84 -3.8 4.3 -6.1 3.3e-05 3.6e+03 0.0012 0.75 -0.22 -
45 1.4 4 -6.7 0.3 0.066 2.1 -0.045 0.18 -1.5 -0.029 -0.38 -3.8 4.4 -6.2 5e-05 3.6e+03 0.00074 0.75 0.35 +
46 0.86 4 -7.5 0.26 -0.56 2 0.16 0.22 -2.3 -0.0077 -1.1 -3.8 4.4 -6.1 0.00011 3.6e+03 0.0011 0.75 0.8 +
47 0.17 4 -8.2 0.34 -0.21 1.9 0.45 0.22 -2.9 0.053 -0.75 -3.9 4.3 -6.1 0.00029 3.6e+03 0.0018 0.75 0.79 +
48 0.066 3.9 -8.6 0.39 0.43 2 0.1 0.25 -2.6 0.0051 -1.5 -3.9 4.3 -6.1 0.00063 3.6e+03 0.0034 0.75 0.3 +
49 0.066 3.9 -8.6 0.39 0.43 2 0.1 0.25 -2.6 0.0051 -1.5 -3.9 4.3 -6.1 0.00063 3.6e+03 0.0034 0.37 -0.13 -
50 0.067 3.8 -8.7 0.49 0.43 2 0.093 0.079 -2.6 0.043 -1.1 -4 4.4 -6.1 0.0016 3.6e+03 0.0028 3.7 1.2 ++
51 0.002 3.7 -12 0.55 -2.2 2 -0.15 -0.11 -3.4 0.089 -1.6 -3.9 4.4 -6.1 0.0034 3.6e+03 0.0079 3.7 0.73 +
52 0.002 3.7 -12 0.55 -2.2 2 -0.15 -0.11 -3.4 0.089 -1.6 -3.9 4.4 -6.1 0.0034 3.6e+03 0.0079 1.9 -3.8 -
53 0.002 3.7 -12 0.55 -2.2 2 -0.15 -0.11 -3.4 0.089 -1.6 -3.9 4.4 -6.1 0.0034 3.6e+03 0.0079 0.93 -0.18 -
54 -0.0018 3.6 -12 0.6 -1.7 2.1 0.024 -1 -3 0.075 -1.1 -3.9 4.4 -6.2 0.0068 3.6e+03 0.0033 0.93 0.55 +
55 -0.0018 3.6 -12 0.6 -1.7 2.1 0.024 -1 -3 0.075 -1.1 -3.9 4.4 -6.2 0.0068 3.6e+03 0.0033 0.47 -0.7 -
56 -0.0017 3.5 -12 0.64 -1.7 2.2 0.052 -0.58 -2.9 -0.13 -1.5 -4 4.1 -5.8 0.013 3.6e+03 0.0056 0.47 0.3 +
57 -0.0011 3.5 -12 0.7 -1.7 2.1 0.084 -1 -2.8 -0.1 -1.6 -3.9 4.2 -6 0.022 3.6e+03 0.0015 4.7 0.96 ++
58 -0.0011 3.5 -12 0.7 -1.7 2.1 0.084 -1 -2.8 -0.1 -1.6 -3.9 4.2 -6 0.022 3.6e+03 0.0015 2.3 -3.9 -
59 -0.0011 3.5 -12 0.7 -1.7 2.1 0.084 -1 -2.8 -0.1 -1.6 -3.9 4.2 -6 0.022 3.6e+03 0.0015 1.2 -1.5 -
60 -0.0011 3.5 -12 0.7 -1.7 2.1 0.084 -1 -2.8 -0.1 -1.6 -3.9 4.2 -6 0.022 3.6e+03 0.0015 0.58 -0.3 -
61 -0.0011 3.4 -12 0.73 -2 2.1 -0.08 -0.65 -2.2 -0.071 -1.7 -3.8 4.1 -5.9 0.034 3.6e+03 0.0023 0.58 0.67 +
62 -0.0019 3.5 -12 0.84 -2.4 2.2 -0.43 -1.2 -1.8 -0.21 -1.7 -3.9 4.3 -6.1 0.052 3.6e+03 0.0023 0.58 0.76 +
63 -0.0019 3.5 -12 0.84 -2.4 2.2 -0.43 -1.2 -1.8 -0.21 -1.7 -3.9 4.3 -6.1 0.052 3.6e+03 0.0023 0.29 -0.12 -
64 -0.0031 3.4 -12 0.8 -2.5 1.9 -0.45 -1.5 -1.6 -0.34 -1.8 -3.6 4.2 -5.8 0.059 3.6e+03 0.031 0.29 0.5 +
65 -0.0035 3.1 -12 0.81 -2.6 2 -0.44 -1.8 -1.6 -0.29 -1.8 -3.6 4 -6 0.06 3.6e+03 0.014 0.29 0.55 +
66 -0.0069 3 -12 0.84 -2.6 2.1 -0.34 -2 -1.5 -0.58 -1.8 -3.6 3.8 -5.8 0.067 3.6e+03 0.0014 2.9 0.99 ++
67 -0.0069 3 -12 0.84 -2.6 2.1 -0.34 -2 -1.5 -0.58 -1.8 -3.6 3.8 -5.8 0.067 3.6e+03 0.0014 1.5 -0.87 -
68 -0.0069 3 -12 0.84 -2.6 2.1 -0.34 -2 -1.5 -0.58 -1.8 -3.6 3.8 -5.8 0.067 3.6e+03 0.0014 0.73 -0.31 -
69 -0.023 3 -12 0.88 -3 2.1 0.39 -2 -0.86 -0.71 -1.9 -3.5 3.8 -5.9 0.078 3.6e+03 0.0027 0.73 0.19 +
70 -0.056 2.9 -13 0.83 -2.8 2.1 0.67 -1.9 -1.2 -0.63 -1.9 -3.5 3.8 -5.8 0.073 3.6e+03 0.00064 7.3 0.92 ++
71 -0.056 2.9 -13 0.83 -2.8 2.1 0.67 -1.9 -1.2 -0.63 -1.9 -3.5 3.8 -5.8 0.073 3.6e+03 0.00064 3.6 -1.5 -
72 -0.056 2.9 -13 0.83 -2.8 2.1 0.67 -1.9 -1.2 -0.63 -1.9 -3.5 3.8 -5.8 0.073 3.6e+03 0.00064 1.8 -1.7 -
73 -0.056 2.9 -13 0.83 -2.8 2.1 0.67 -1.9 -1.2 -0.63 -1.9 -3.5 3.8 -5.8 0.073 3.6e+03 0.00064 0.91 -1.3 -
74 -0.056 2.9 -13 0.83 -2.8 2.1 0.67 -1.9 -1.2 -0.63 -1.9 -3.5 3.8 -5.8 0.073 3.6e+03 0.00064 0.45 0.032 -
75 -0.059 2.9 -13 0.82 -3.2 2 0.96 -1.9 -0.72 -0.66 -2.1 -3.5 3.7 -5.7 0.076 3.6e+03 0.00045 4.5 1.1 ++
76 -0.059 2.9 -13 0.82 -3.2 2 0.96 -1.9 -0.72 -0.66 -2.1 -3.5 3.7 -5.7 0.076 3.6e+03 0.00045 2.3 -3.8 -
77 -0.059 2.9 -13 0.82 -3.2 2 0.96 -1.9 -0.72 -0.66 -2.1 -3.5 3.7 -5.7 0.076 3.6e+03 0.00045 1.1 -0.22 -
78 -0.059 2.9 -13 0.82 -3.2 2 0.96 -1.9 -0.72 -0.66 -2.1 -3.5 3.7 -5.7 0.076 3.6e+03 0.00045 0.57 -0.11 -
79 -0.062 2.9 -13 0.81 -3 2 1.5 -2 -0.78 -0.7 -2 -3.5 3.7 -5.7 0.074 3.6e+03 0.0004 0.57 0.35 +
80 -0.2 2.9 -14 0.81 -2.7 2.1 1.4 -1.9 -0.42 -0.69 -2.2 -3.5 3.7 -5.7 0.075 3.6e+03 0.002 0.57 0.57 +
81 -0.29 2.9 -14 0.81 -2.9 2 1.6 -1.9 -0.49 -0.68 -2.3 -3.5 3.7 -5.7 0.075 3.6e+03 0.00026 5.7 1.1 ++
82 -0.5 2.9 -17 0.81 -3.1 2 1.6 -1.9 -0.62 -0.68 -2.6 -3.5 3.7 -5.7 0.076 3.6e+03 0.00011 57 1.2 ++
83 -0.33 2.9 -18 0.82 -3.3 2 1.5 -1.9 -0.8 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 9.2e-05 57 0.8 +
84 -0.31 2.9 -19 0.82 -3.2 2 1.5 -1.9 -0.75 -0.67 -2.7 -3.5 3.7 -5.7 0.076 3.6e+03 5.8e-05 5.7e+02 1.1 ++
85 -0.27 2.9 -19 0.82 -3.2 2 1.5 -1.9 -0.71 -0.68 -2.7 -3.5 3.7 -5.7 0.076 3.6e+03 3.4e-05 5.7e+03 1.1 ++
86 -0.25 2.9 -19 0.82 -3.2 2 1.5 -1.9 -0.76 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 4.7e-05 5.7e+04 0.97 ++
87 -0.23 2.9 -19 0.82 -3.2 2 1.5 -1.9 -0.73 -0.68 -2.7 -3.5 3.7 -5.7 0.076 3.6e+03 3.1e-05 5.7e+05 1.1 ++
88 -0.22 2.9 -19 0.82 -3.3 2 1.5 -1.9 -0.76 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 3.9e-05 5.7e+06 0.99 ++
89 -0.2 2.9 -19 0.82 -3.2 2 1.5 -1.9 -0.74 -0.67 -2.7 -3.5 3.7 -5.7 0.076 3.6e+03 2.8e-05 5.7e+07 1.1 ++
90 -0.19 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.77 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 3.4e-05 5.7e+08 1 ++
91 -0.18 2.9 -20 0.82 -3.2 2 1.5 -1.9 -0.75 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.5e-05 5.7e+09 1 ++
92 -0.17 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.77 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 3e-05 5.7e+10 1 ++
93 -0.16 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.75 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.3e-05 5.7e+11 1 ++
94 -0.15 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.78 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.6e-05 5.7e+12 1 ++
95 -0.14 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.76 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.1e-05 5.7e+13 1 ++
96 -0.13 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.78 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.3e-05 5.7e+14 1 ++
97 -0.13 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.76 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 1.9e-05 5.7e+15 1 ++
98 -0.12 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.78 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 2.1e-05 5.7e+16 1 ++
99 -0.12 2.9 -20 0.82 -3.3 2 1.5 -1.9 -0.77 -0.67 -2.8 -3.5 3.7 -5.7 0.076 3.6e+03 1.7e-05 5.7e+17 1 ++
It seems that the optimization algorithm did not converge. Therefore, the results may not correspond to the maximum likelihood estimator. Check the specification of the model, or the criteria for convergence of the algorithm.
Results saved in file b15panel_discrete.html
Results saved in file b15panel_discrete.pickle
print(results.short_summary())
Results for model b15panel_discrete
Nbr of parameters: 15
Sample size: 752
Observations: 6768
Excluded data: 3960
Final log likelihood: -3578.193
Akaike Information Criterion: 7186.386
Bayesian Information Criterion: 7255.727
pandas_results = results.getEstimatedParameters()
pandas_results
Total running time of the script: (11 minutes 58.663 seconds)