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[WIP] Add GLM example with the Negative Binomial distribution. #392

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[WIP] Add GLM example with the Negative Binomial distribution. #392

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7725bf1
Add example of using GLM with the Negative Binomial distribution.
geektoni Aug 16, 2020
d52bfc8
Update Negative Binomial regression example description.
geektoni Aug 18, 2020
214f900
Apply suggestions from code review.
geektoni Aug 18, 2020
b9b9ddd
Apply suggestions from code review 2.
geektoni Aug 18, 2020
972b2c3
FIX: bring it close to R example
jasmainak Aug 19, 2020
dbed52e
Update plot_negative_binomial.
geektoni Aug 19, 2020
6274c06
Add new example with Poisson and Negative Binomial distribution.
geektoni Oct 14, 2020
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Update plot_negative_binomial. 
* Add convergence graph;
* Add better information to show the program types;
* Add Poisson regression to compare the results;
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@geektoni
geektoni committed Aug 19, 2020
commit dbed52ea7809f20a2c072690b0552499973c80ec
53 changes: 40 additions & 13 deletions examples/plot_negative_binomial.py
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Expand Up @@ -28,14 +28,16 @@

This gives us an extra parameter which can be used to account for the over
dispersion.
"""

In this example, we will apply both Negative Binomial regression and
Poisson regression on the dataset.
"""

########################################################
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# Author: Titipat Achakulvisut <[email protected]>
# Giovanni De Toni <[email protected]>
# License: MIT


########################################################
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########################################################
# Import relevance libraries
Expand All @@ -49,6 +51,11 @@
# Read and preprocess data
df = pd.read_stata("https://stats.idre.ucla.edu/stat/stata/dae/nb_data.dta")

########################################################
# Change the program type to string (we don't need it)
df['prog'].replace({1:"General", 2:"Academic", 3:"Vocational"}, inplace=True)

########################################################
# Histogram of type of program they are enrolled
df.hist(column='daysabs', by=['prog'])
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plt.show()
Expand All @@ -64,18 +71,38 @@
X = df.drop('daysabs', axis=1)
y = df['daysabs'].values

########################################################
# design matrix
program_df = pd.get_dummies(df.prog)
Xdsgn = pd.concat((df['math'], program_df.drop(3.0, axis=1)), axis=1).values
program_df_cleaned = program_df.drop('Vocational', axis=1)[["General", "Academic"]]
Xdsgn = pd.concat((df['math'], program_df_cleaned), axis=1).values

########################################################
# Fit the model using the GLM
glm_neg_bino = GLM(distr='neg-binomial',
alpha=0.0,
reg_lambda=0.0,
score_metric='pseudo_R2',
verbose=True,
learning_rate=1e-6,
theta=1.032713156)
glm_neg_bino.fit(Xdsgn, y)
print(glm_neg_bino.beta0_, glm_neg_bino.beta_)
glm_nb = GLM(distr='neg-binomial',
alpha=0.0,
reg_lambda=0.0,
score_metric='pseudo_R2',
verbose=True,
learning_rate=1e-6,
theta=1.032713156)
glm_nb.fit(Xdsgn, y)
print(glm_nb.beta0_, glm_nb.beta_)

########################################################
# Fit the model using the Poisson regression instead
glm_poisson = GLM(distr='poisson',
alpha=0.0,
reg_lambda=0.0,
score_metric='pseudo_R2',
verbose=True,
learning_rate=1e-6)
glm_poisson.fit(Xdsgn, y)
print(glm_poisson.beta0_, glm_poisson.beta_)


########################################################
# Plot convergence information for both negative binomial and poisson
glm_nb.plot_convergence()
glm_poisson.plot_convergence()
plt.show()