pymc.OrderedLogistic

class pymc.OrderedLogistic(name, *args, compute_p=True, **kwargs)

Wrapper class for Ordered Logistic distributions.

Useful for regression on ordinal data values whose values range from 1 to K as a function of some predictor, \(\eta\). The cutpoints, \(c\), separate which ranges of \(\eta\) are mapped to which of the K observed dependent variables. The number of cutpoints is K - 1. It is recommended that the cutpoints are constrained to be ordered.

\[\begin{split}f(k \mid \eta, c) = \left\{ \begin{array}{l} 1 - \text{logit}^{-1}(\eta - c_1) \,, \text{if } k = 0 \\ \text{logit}^{-1}(\eta - c_{k - 1}) - \text{logit}^{-1}(\eta - c_{k}) \,, \text{if } 0 < k < K \\ \text{logit}^{-1}(\eta - c_{K - 1}) \,, \text{if } k = K \\ \end{array} \right.\end{split}\]

Parameters:

etatensor_like of float

The predictor.

cutpointstensor_like of array

The length K - 1 array of cutpoints which break \(\eta\) into ranges. Do not explicitly set the first and last elements of \(c\) to negative and positive infinity.

compute_p: boolean, default True

Whether to compute and store in the trace the inferred probabilities of each categories, based on the cutpoints’ values. Defaults to True. Might be useful to disable it if memory usage is of interest.

Examples

# Generate data for a simple 1 dimensional example problem
n1_c = 300; n2_c = 300; n3_c = 300
cluster1 = np.random.randn(n1_c) + -1
cluster2 = np.random.randn(n2_c) + 0
cluster3 = np.random.randn(n3_c) + 2

x = np.concatenate((cluster1, cluster2, cluster3))
y = np.concatenate((1*np.ones(n1_c),
                    2*np.ones(n2_c),
                    3*np.ones(n3_c))) - 1

# Ordered logistic regression
with pm.Model() as model:
    cutpoints = pm.Normal("cutpoints", mu=[-1,1], sigma=10, shape=2,
                          transform=pm.distributions.transforms.ordered)
    y_ = pm.OrderedLogistic("y", cutpoints=cutpoints, eta=x, observed=y)
    idata = pm.sample()

# Plot the results
plt.hist(cluster1, 30, alpha=0.5);
plt.hist(cluster2, 30, alpha=0.5);
plt.hist(cluster3, 30, alpha=0.5);
posterior = idata.posterior.stack(sample=("chain", "draw"))
plt.hist(posterior["cutpoints"][0], 80, alpha=0.2, color='k');
plt.hist(posterior["cutpoints"][1], 80, alpha=0.2, color='k');

Methods

OrderedLogistic.dist(*args, **kwargs)