`ipynb source code <linearAnalysisCensoredData.ipynb>`_

Linear model analysis with censored data
========================================

.. code:: python

    # import relevant module
    import openturns as ot
    import otpod
    # enable display figure in notebook
    %matplotlib inline

Generate data
-------------

.. code:: python

    N = 100
    ot.RandomGenerator.SetSeed(123456)
    defectDist = ot.Uniform(0.1, 0.6)
    # normal epsilon distribution
    epsilon = ot.Normal(0, 1.9)
    defects = defectDist.getSample(N)
    signalsInvBoxCox = defects * 43. + epsilon.getSample(N) + 2.5
    # Inverse Box Cox transformation
    invBoxCox = ot.InverseBoxCoxTransform(0.3)
    signals = invBoxCox(signalsInvBoxCox)

Run analysis with Box Cox
-------------------------

.. code:: python

    noiseThres = 60.
    saturationThres = 1700.
    analysis = otpod.UnivariateLinearModelAnalysis(defects, signals, noiseThres,
                                                   saturationThres, boxCox=True)

Get some particular results
---------------------------

Result values are given for both analysis performed on filtered data
(uncensored case) and on censored data.

.. code:: python

    print(analysis.getIntercept())
    print(analysis.getR2())
    print(analysis.getKolmogorovPValue())


.. parsed-literal::

    [Intercept for uncensored case : 4.777, Intercept for censored case : 4.1614]
    [R2 for uncensored case : 0.869115, R2 for censored case : 0.860722]
    [Kolmogorov p-value for uncensored case : 0.477505, Kolmogorov p-value for censored case : 0.505919]


Print all results of the linear regression and all tests on the residuals
-------------------------------------------------------------------------

.. code:: python

    # Results are displayed for both case
    print(analysis.getResults())


.. parsed-literal::

    --------------------------------------------------------------------------------
             Linear model analysis results
    --------------------------------------------------------------------------------
    Box Cox parameter :                                      0.18              
                                                                               
                                                       Uncensored      Censored
                                                                               
    Intercept coefficient :                                  4.78          4.16
    Slope coefficient :                                     18.15         19.94
    Standard error of the estimate :                         0.97          1.03
                                                                               
    Confidence interval on coefficients                                        
    Intercept coefficient :                          [4.19, 5.36]              
    Slope coefficient :                             [16.63, 19.67]              
    Level :                                                  0.95              
                                                                               
    Quality of regression                                                      
    R2 (> 0.8):                                              0.87          0.86
    --------------------------------------------------------------------------------
    
    --------------------------------------------------------------------------------
             Residuals analysis results
    --------------------------------------------------------------------------------
    Fitted distribution (uncensored) :              Normal(mu = -2.19492e-15, sigma = 0.968046)              
    Fitted distribution (censored) :                Normal(mu = -0.0237409, sigma = 0.998599)              
                                                                               
                                                       Uncensored      Censored
    Distribution fitting test                                                  
    Kolmogorov p-value (> 0.05):                             0.48          0.51
                                                                               
    Normality test                                                             
    Anderson Darling p-value (> 0.05):                       0.06          0.08
    Cramer Von Mises p-value (> 0.05):                       0.07          0.09
                                                                               
    Zero residual mean test                                                    
    p-value (> 0.05):                                         1.0          0.83
                                                                               
    Homoskedasticity test (constant variance)                                  
    Breush Pagan p-value (> 0.05):                           0.69          0.71
    Harrison McCabe p-value (> 0.05):                         0.6          0.51
                                                                               
    Non autocorrelation test                                                   
    Durbin Watson p-value (> 0.05):                          0.43          0.48
    --------------------------------------------------------------------------------
    
    


Save all results in a csv file
------------------------------

.. code:: python

    analysis.saveResults('results.csv')

Show graphs
-----------

The linear regression model with data for the uncensored case (default case)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code:: python

    # draw the figure for the uncensored case and save it as png file
    fig, ax = analysis.drawLinearModel(name='figure/linearModelUncensored.png')
    fig.show()


.. parsed-literal::

    /home/dumas/anaconda2/lib/python2.7/site-packages/matplotlib/figure.py:397: UserWarning: matplotlib is currently using a non-GUI backend, so cannot show the figure
      "matplotlib is currently using a non-GUI backend, "



.. image:: linearAnalysisCensoredData_files/linearAnalysisCensoredData_14_1.png


The linear regression model with data for the censored case
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code:: python

    # draw the figure for the censored case and save it as png file
    fig, ax = analysis.drawLinearModel(model='censored', name='figure/linearModelCensored.png')
    fig.show()



.. image:: linearAnalysisCensoredData_files/linearAnalysisCensoredData_16_0.png