# API reference¶

## Markov Methods¶

 giddy.markov.Markov(class_ids[, classes, …]) Classic Markov Chain estimation. giddy.markov.Spatial_Markov(y, w[, k, m, …]) Markov transitions conditioned on the value of the spatial lag. giddy.markov.LISA_Markov(y, w[, …]) Markov for Local Indicators of Spatial Association Full Rank Markov in which ranks are considered as Markov states rather than quantiles or other discretized classes. Geographic Rank Markov. Kullback information based test of Markov Homogeneity. Prais conditional mobility measure. giddy.markov.homogeneity(transition_matrices) Test for homogeneity of Markov transition probabilities across regimes. giddy.markov.sojourn_time(p[, summary]) Calculate sojourn time based on a given transition probability matrix. Generalized function for calculating the steady state distribution for a regular or reducible Markov transition matrix P. giddy.ergodic.fmpt(P[, fill_empty_classes]) Generalized function for calculating first mean passage times for an ergodic or non-ergodic transition probability matrix. Variances of first mean passage times for an ergodic transition probability matrix.

## Directional LISA¶

 giddy.directional.Rose(Y, w[, k]) Rose diagram based inference for directional LISAs.

## Economic Mobility Indices¶

 giddy.mobility.markov_mobility(p[, measure, ini]) Markov-based mobility index.

## Exchange Mobility Methods¶

 giddy.rank.Theta(y, regime[, permutations]) Regime mobility measure. giddy.rank.Tau(x, y) Kendall’s Tau is based on a comparison of the number of pairs of n observations that have concordant ranks between two variables. giddy.rank.SpatialTau(x, y, w[, permutations]) Spatial version of Kendall’s rank correlation statistic. Local version of the classic Tau. giddy.rank.Tau_Local_Neighbor(x, y, w[, …]) Neighbor set LIMA. giddy.rank.Tau_Local_Neighborhood(x, y, w[, …]) Neighborhood set LIMA. giddy.rank.Tau_Regional(x, y, regime[, …]) Inter and intraregional decomposition of the classic Tau.

## Alignment-based Sequence Methods¶

 giddy.sequence.Sequence(y[, subs_mat, …]) Pairwise sequence analysis.

## Utility Functions¶

 Random permutation of rows and columns of a matrix giddy.util.get_lower(matrix) Flattens the lower part of an n x n matrix into an n*(n-1)/2 x 1 vector. Assign 1 to diagonal elements which fall in rows full of 0s to ensure the transition probability matrix is a stochastic one.