Univariate pattern identification for dyadic Markov chains

Computes empirical transition counts, estimates transition probabilities by maximum likelihood, and performs likelihood-ratio tests against the actor-only and partner-only constrained models to identify the univariate pattern of interaction.

Usage

univariatePattern(chainFM, chainSM, states, alpha = 0.05)

Arguments

chainFM

Numeric vector of observed states for the first member (FM). Values must be integers. Must have the same length as chainSM.

chainSM

Numeric vector of observed states for the second member (SM). Values must be integers. Must have the same length as chainFM.

states

A single integer >= 2 giving the number of states.

alpha

A single number in (0, 1) giving the significance level. Default is 0.05.

Value

A list with class c("dyadic_pattern", "list") containing two htest objects (TEST.AM, TEST.PM), the retained input sequences chainFM and chainSM, a string pattern, and metadata fields alpha, states, and call. It remains usable as an ordinary list.

Details

The nested full/restricted comparisons form the univariate likelihood-ratio test (LRT) procedure. dyadicMarkov evaluates each LRT comparison using Pearson's chi-squared statistic, $$X^2 = \sum_{ij} (O_{ij} - E_{ij})^2 / E_{ij},$$ where \(O\) and \(E\) are the empirical and theoretical transition counts. A comparison is treated as rejected when \(p \leq \alpha\). Pattern labels summarize which structure is retained by the tests: IM (A0) denotes an independence pattern, APM (A1) an actor-partner pattern, AM (A2) an actor-only pattern, and PM (A3) a partner-only pattern.

Examples

chainFM <- c(1L, 2L, 1L, 2L, 2L, 1L)
chainSM <- c(2L, 1L, 2L, 1L, 1L, 2L)
univariatePattern(chainFM, chainSM, states = 2L, alpha = 0.05)
#> Dyadic interaction pattern
#> Pattern: IM (A0)
#> Alpha: 0.05
#> States: 2