Beta modal regression with measurement error

Import data

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import pybetareg as pyb

## Beta Modal Regression in Python.

df1 = pd.read_csv("data.csv")
df1.head()

##           Y      Wbar    SigmaW   Z1
## 0  0.186046 -2.289838  1.732051  0.0
## 1  0.391666 -0.535476  1.732051  0.0
## 2  0.883178  2.071954  1.732051  1.0
## 3  0.727209 -0.578447  1.732051  0.0
## 4  0.269854 -0.926259  1.732051  0.0

y = df1['Y'].to_numpy()
w = df1['Wbar'].to_numpy()
z = df1['Z1'].to_numpy()
z = np.column_stack([np.ones(z.shape[0]),z])
sigmaw = df1['SigmaW'].to_numpy()

Fit model

model2 = pyb.reg_measurement_error(y=y,w=w,z=z,
                                   sigmaw=sigmaw,
                                   initial=[10,1,1,1],
                                   CUDA = True,
                                   column_names = ['b1','b0','b2'])
model2fit = model2.fit()
model2fit.summary()

## -----------------------Model fitting completes------------------------
## Success:True
## Optimization terminated successfully.
## """
##                   Beta Modal Regression Results With                  
##                      Measurement Error Adjustment                     
## ======================================================================
##                 coef   std err         z     P>|z|    [0.025    0.975]
## ----------------------------------------------------------------------
## m            12.3424     3.791     3.256     0.001     4.913    19.772
## b1            0.9733     0.453     2.150     0.032     0.086     1.860
## b0            1.0646     0.436     2.444     0.015     0.211     1.918
## b2            0.9807     0.442     2.217     0.027     0.114     1.847
## ======================================================================
## """

Hotelling's T² statistic and parametric bootstrap p-value.

Use hotelling_p(50) function to calculate Hotelling's T² statistic and parametric bootstrap p-value across 50 iterations.

model2.hotelling_p(50)

## Hotelling's T^2 statistic and parametric bootstrap p-value.      
## ======================================================================
## Hotelling's T^2 statistic: 0.5063
## parametric bootstrap p-value: 0.7000
## ======================================================================

Beta modal regression without measurement error

Import data

df2 = pd.read_csv("data2.csv")
df2.head()

##           Y   X0        X1   X2
## 0  0.133439  1.0 -2.223525  0.0
## 1  0.315374  1.0 -1.415762  0.0
## 2  0.845555  1.0  1.218485  1.0
## 3  0.977328  1.0  1.690799  1.0
## 4  0.811748  1.0  0.076872  0.0

Fit model

x = df2[['X0','X1','X2']]
y = df2['Y']
model1 = pyb.reg(x=x, y=y, initial = [10,1,1,1])
model1fit = model1.fit()
model1fit.summary()

## Link function:logit
## Columns names are not given.
## Success:True
## Optimization terminated successfully.
## """
##                     Beta Modal Regression Results                     
## ======================================================================
##                 coef   std err         z     P>|z|    [0.025    0.975]
## ----------------------------------------------------------------------
## m            11.1426     1.253     8.891     0.000     8.686    13.599
## beta0         0.9453     0.113     8.373     0.000     0.724     1.167
## beta1         0.8837     0.084    10.571     0.000     0.720     1.048
## beta2         1.1198     0.182     6.158     0.000     0.763     1.476
## ======================================================================
"""