dyadicMarkov implements an R workflow for identifying
patterns of interaction in categorical dyadic sequences using transition
matrices. The package is designed for situations in which one or two
categorical variables are observed repeatedly for both members of one
dyad, so that the analysis accounts for both temporal dependence and
dyadic dependence.
dyadicMarkov is based on three methodological papers on
dyadic pattern analysis with the Longitudinal Actor-Partner
Interdependence Model (L-APIM) and Markov chains. The univariate
single-case method is described by Bollenrücher
et al. (2023). The visualization and clustering methodology
described by Bollenrücher et al. (2024)
provides a complementary analysis of similar dyadic behaviors. The
bivariate single-case method is described by Böllenrücher et al. (in press).
The package is intended for ordered categorical observations collected from two members of a dyad. In practice, such sequences may arise from coded interaction data, daily diary studies, repeated binary responses, or intensive longitudinal designs. For example, researchers may code whether each partner shows a given behavior at each measurement occasion, whether a parent and child are in one of several interaction states, or whether two individuals report the presence or absence of a response across repeated observations.
The package summarizes how the next state of the analyzed sequence is associated with its own previous state and with the previous state of the partner. The resulting pattern labels help describe whether the observed transitions are better characterized by actor dependence, partner dependence, actor-partner dependence, independence, or, in the bivariate workflow, by partial or complete bivariate dependence structures.
The example datasets included in the package are synthetic. They are used to make the required input structure reproducible and easy to inspect. They should be read as small stand-ins for real ordered dyadic sequences, not as substantive empirical datasets.
The package works with categorical dyadic sequences. In the univariate case, one categorical variable is observed over time for two members of a dyad. For each function call, the first member is the member whose next state is modeled, and the second member supplies the partner sequence. The roles can be reversed to analyze the other member.
In the bivariate case, two categorical variables are observed over
time for both members of the dyad. The current implementation supports
binary variables (states = 2). The corresponding empirical
count matrix has 16 rows and 2 columns. Each row represents one of the
16 possible lagged combinations formed by the first member and the
second member on the main variable and on the second variable. The two
columns represent the possible next states of the first member on the
main variable.
The state-space scope differs between the two methods. The univariate
workflow supports any integer number of categorical
states ≥ 2, whereas the bivariate workflow currently
supports states = 2 only.
The package separates estimation from identification. Estimation summarizes the observed sequences as empirical transition counts and maximum-likelihood transition probabilities. Identification compares the observed transition structure with restricted transition structures corresponding to interpretable patterns of interaction.
In the univariate workflow, the relevant patterns are actor-partner,
actor-only, partner-only and independence. In the bivariate workflow,
the analysis first identifies the global case as trivial, univariate,
partial bivariate or complete bivariate. A trivial case has no
subsequent local pattern. A univariate case is followed by
univariatePattern() on the main-variable sequences. Partial
and complete cases are followed by partialPattern() and
completePattern(), respectively.
The comparison statistics also differ by step. The univariate
pattern-identification procedure uses the Likelihood-Ratio Test (LRT)
nomenclature of the underlying method; dyadicMarkov
evaluates these comparisons using Pearson’s chi-squared statistic, \(X^2 = \sum (O-E)^2/E\). The global
bivariate approach compares nested models within the same LRT framework.
bivariateCase() performs two chi-squared tests involving
the actor-partner pattern A1 and the partial actor-partner pattern B1.
The local partial and complete bivariate procedures instead compute the
G-squared deviance, \(G^2 = 2\sum
O\log(O/E)\), and then calculate \(AIC
= G^2 + 2k\) for each candidate structure.
The user-facing workflow is organized around seven exported functions:
countEmp() computes empirical transition counts for the
first member sequence in a univariate dyadic sequence. Returned objects
have class dyadic_counts and provide print(),
summary(), and utils::toLatex() methods.mleEstimation() estimates transition probabilities from
empirical count matrices. Returned objects have class
dyadic_mle and provide print(),
summary(), and utils::toLatex() methods.univariatePattern() identifies the univariate
interaction pattern. Returned objects have class
dyadic_pattern and provide print(),
summary(), and plot() methods.countEmpBivariate() computes empirical transition
counts for the first member sequence in a bivariate dyadic sequence.
Returned objects have class dyadic_counts and provide
print(), summary(), and
utils::toLatex() methods.bivariateCase() identifies the global dependence case
for the analyzed sequence. Returned objects have class
dyadic_case and provide print(),
summary(), and plot() methods.partialPattern() selects a local pattern for a partial
bivariate case. Returned objects have class dyadic_pattern
and provide print(), summary(), and
plot() methods.completePattern() selects a local pattern for a
complete bivariate case. Returned objects have class
dyadic_pattern and provide print(),
summary(), and plot() methods.The workflow assumes categorical states coded by integers from 1 to
states, equal chain lengths, ordered repeated observations,
and a first-order homogeneous transition process. Inputs containing
NA are rejected; missing observations are not deleted or
imputed automatically because they break the construction of transition
pairs.
Based on the sensitivity analysis reported in Böllenrücher et al. (in
press), a minimum sequence length of 90 measurement points is
recommended for applying the method. Pattern-identification accuracy
improves with longer sequences; for shorter sequences, particularly at
30 measurement points, the procedure often results in a trivial pattern,
whereas from 90 measurement points onward the occurrence of trivial
patterns diminishes significantly. This is methodological guidance
rather than a hard input requirement in dyadicMarkov.
This introduction explains the scope and structure of the package.
The univariate workflow vignette shows the use of
countEmp(), mleEstimation(), and
univariatePattern(). The bivariate workflow vignette shows
the use of countEmpBivariate(),
bivariateCase(), partialPattern(), and
completePattern(). The sensitivity analysis vignette
examines how sequence length affects pattern identification using the
fixed simulation datasets distributed with the package.