Identifies the bivariate case as "trivial", "univariate",
"partial", or "complete" using two chi-squared tests
against constrained binary bivariate structures.
Arguments
- empirical
An empirical bivariate count matrix with 16 rows and 2 columns, as returned by
countEmpBivariate.- alpha
A single number in (0, 1) giving the significance level. Default is 0.05.
Value
A list with class c("dyadic_case", "list") containing
components testUnivariate, testPartial, case, and
metadata fields alpha and call. It remains usable as an
ordinary list. When empirical was created by
countEmpBivariate(), its stored sequence metadata is propagated so
that plot() can display the four observed state strips.
Details
The returned case corresponds to the global approach of the
binary bivariate method. The scientific method treats the global
comparisons as nested-model comparisons within a likelihood-ratio test
(LRT) framework. bivariateCase() implements the two chi-squared
tests for the A1 and B1 comparisons. dyadicMarkov evaluates these tests
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 global comparison is treated as rejected when
\(p \leq \alpha\). The result determines whether the sequence analyzed is
treated as trivial, univariate, partial bivariate, or complete bivariate before the
separate local AIC-based identification of the pattern of interaction.
Examples
chainFM_V1 <- c(1L, 2L, 1L, 2L, 2L, 1L)
chainSM_V1 <- c(2L, 1L, 2L, 1L, 1L, 2L)
chainFM_V2 <- c(1L, 1L, 2L, 2L, 1L, 2L)
chainSM_V2 <- c(2L, 2L, 1L, 1L, 2L, 1L)
emp <- countEmpBivariate(
chainFM_V1, chainSM_V1, chainFM_V2, chainSM_V2,
states = 2L
)
bivariateCase(emp, alpha = 0.05)
#> Bivariate dyadic case
#> Case: trivial
#> Alpha: 0.05