pymc.OrderedMultinomial

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

Wrapper class for Ordered Multinomial distributions.

Useful for regression on ordinal data whose values range from 1 to K as a function of some predictor, \(\eta\), but which are _aggregated_ by trial, like multinomial observations (in contrast to pm.OrderedLogistic, which only accepts ordinal data in a _disaggregated_ format, like categorical observations). 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 float

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.

ntensor_like of int

The total number of multinomial trials.

compute_pbool, 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
true_cum_p = np.array([0.1, 0.15, 0.25, 0.50, 0.65, 0.90, 1.0])
true_p = np.hstack([true_cum_p[0], true_cum_p[1:] - true_cum_p[:-1]])
fake_elections = np.random.multinomial(n=1_000, pvals=true_p, size=60)

# Ordered multinomial regression
with pm.Model() as model:
    cutpoints = pm.Normal(
        "cutpoints",
        mu=np.arange(6) - 2.5,
        sigma=1.5,
        initval=np.arange(6) - 2.5,
        transform=pm.distributions.transforms.ordered,
    )

    pm.OrderedMultinomial(
        "results",
        eta=0.0,
        cutpoints=cutpoints,
        n=fake_elections.sum(1),
        observed=fake_elections,
    )

    trace = pm.sample()

# Plot the results
arviz.plot_posterior(trace_12_4, var_names=["complete_p"], ref_val=list(true_p));

Methods

OrderedMultinomial.dist(*args, **kwargs)