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, Darwiche, and
Antonietti (2023). The extension to visualization and clustering of
similar dyadic behaviors is described by Bollenrücher, Darwiche, and
Antonietti (2024). The bivariate single-case method is described by
Böllenrücher, Darwiche, and Antonietti (in press). The visualization and
clustering methodology of Bollenrücher, Darwiche, and Antonietti (2024)
is methodological background; it is not currently part of the exported
package API.
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 of the
bivariate workflow supports binary variables (states = 2).
This leads to a bivariate empirical count matrix with 16 rows and 2
columns: the 16 rows represent the four binary lagged components: the
first member on the main variable, the second member on the main
variable, the first member on the second variable and the second member
on the second variable. The 2 columns represent the possible next states
of the first member on the main variable.
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 user-facing workflow is organized around seven exported functions:
countEmp() computes empirical transition counts for the
first member sequence in a univariate dyadic sequence.mleEstimation() estimates transition probabilities from
empirical count matrices.univariatePattern() identifies the univariate
interaction pattern.countEmpBivariate() computes empirical transition
counts for the first member sequence in a bivariate dyadic
sequence.bivariateCase() identifies the global dependence case
for the member sequence analyzed.partialPattern() selects a local pattern for a partial
bivariate case.completePattern() selects a local pattern for a
complete bivariate case.The workflow assumes categorical states coded as 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.
The bivariate functions currently support the binary-state case. With
two binary variables observed for two members, the previous state is
described by four binary components, producing 2^4 = 16 previous-state
combinations. Generalizing this workflow beyond states = 2
would require extending the bivariate restriction structures and their
implementation.
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().
Bollenrücher, Mégane, Joëlle Darwiche, and Jean-Philippe Antonietti. 2023. “Dyadic Pattern Analysis Using Longitudinal Actor-Partner Interdependence Model with Markov Chains for Unique Case Analysis.” The Quantitative Methods for Psychology 19 (3): 230-43. https://doi.org/10.20982/tqmp.19.3.p230.
Bollenrücher, Mégane, Joëlle Darwiche, and Jean-Philippe Antonietti. 2024. “Methodology for Identification, Visualization, and Clustering of Similar Behaviors in Dyadic Sequences Analyzed Through the Longitudinal Actor-Partner Interdependence Model with Markov Chains.” The Quantitative Methods for Psychology 20 (1): 17-32. https://doi.org/10.20982/tqmp.20.1.p017.
Böllenrücher, Mégane, Joëlle Darwiche, and Jean-Philippe Antonietti. in press. “Bivariate Dyadic Patterns Analysis Using Longitudinal Actor-Partner Interdependence Model and Markov Chains for Single-Case.” Quantitative and Computational Methods in Behavioral Sciences, in press. https://doi.org/10.23668/psycharchives.22174.