Statsmodels Methods Overview

[1]:

# This cells setups the environment when executed in Google Colab.
try:
    import google.colab
    !curl -s https://raw.githubusercontent.com/ibs-lab/cedalion/dev/scripts/colab_setup.py -o colab_setup.py
    # Select branch with --branch "branch name" (default is "dev")
    %run colab_setup.py
except ImportError:
    pass

Cedalion uses statsmodels for its GLM fitting functionality, and this notebook gives an overview of some common statsmodels methods. The glm.fit function returns an xr.DataArray of statsmodels RegressionResults objects with dimensions (channel, chromo). Any RegressionResults method can be called on this DataArray using the .sm accessor. A full list of available methods and attribute can be found in the statsmodels documentation.

In this notebook, we’ll assume that we have already loaded our data and set up the GLM. See the other GLM notebooks for details on setup.

We’ll start by fitting the GLM and displaying the resulting object.

[3]:

results = glm.fit(ts_long, dms)
display(results)

 67%|██████▋   | 2/3 [00:00<00:00, 154.85it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 158.68it/s]
 50%|█████     | 1/2 [00:00<00:00, 82.40it/s]
 50%|█████     | 1/2 [00:00<00:00, 84.03it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 157.67it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 168.49it/s]
 50%|█████     | 1/2 [00:00<00:00, 84.39it/s]
 50%|█████     | 1/2 [00:00<00:00, 86.31it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 166.11it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 161.85it/s]
 50%|█████     | 1/2 [00:00<00:00, 87.25it/s]
 50%|█████     | 1/2 [00:00<00:00, 86.61it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 168.74it/s]
 67%|██████▋   | 2/3 [00:00<00:00, 167.89it/s]
 50%|█████     | 1/2 [00:00<00:00, 84.58it/s]
 50%|█████     | 1/2 [00:00<00:00, 87.11it/s]

The results object is a DataArray of statsmodels RegressionResults: one for each channel/chromophore. In order to call a method on our results object, we just use the accessor .sm, followed by the RegressionResults method. Cedalion handles calling the method on each individual RegressionResults object in the results DataArray, and returns the outputs in a new DataArray with the appropriate dimensions. This allows us to get information on all channels simply and concisely.

Statsmodels Methods Overview

Beta Coefficients (params)

Standard Error

Confidence Intervals (conf_int)

Covariance and Variance

Statistical Tests - T-values, P-values

Plotting Uncertainty Bands