pymc.OrderedMultinomial#
- class pymc.OrderedMultinomial(name, *args, compute_p=True, **kwargs)[source]#
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
- eta: float
The predictor.
- cutpoints: 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.
- n: int
The total number of multinomial trials.
- 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 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.__init__
(*args, **kwargs)OrderedMultinomial.dist
(*args, **kwargs)