sea.entailment {ldsa} | R Documentation |

Extracts the entailments from `x`

satisfying a given error threshold.

sea.entailment(x, thresh, measure = c("rate", "z-score", "binom.p"), req.str = TRUE, sea.table.precomp = NULL)

`x` |
a `data.frame` with observations on rows; missing data is permitted. |

`thresh` |
error threshold to employ when extracting entailments; only rules with error rates less than `thresh` are retained. |

`measure` |
error measure to use; `rate` for absolute error rates, `z-score` for z-scores, or `binom.p` for p-values under an exact Binomial test. |

`req.str` |
logical; should implications be required to satisfy White's “strong relationship” rule to be included? |

`sea.table.precomp` |
an object of class `sea.table` , computed on `x` (optional). |

The pairwise entailments for a pair of binary variables, *X* and *Y*, can be parameterized as follows:

*Implication:**X => Y*; violations occur where*X*and*!Y*are both true.*Exclusion:**X => !Y*; violations occur where*X*and*Y*are both true.*Coexhaustion:**!X => Y*; violations occur where*!X*and*!Y*are both true.

Note that implication is directed, while exclusion and coexhaustion are undirected. Thus, for each pair of variables, there are two implications, an exclusion, and a coexhaustion to be considered (hopefully not simultaneously!). The `sea.entailment`

seeks to identify rules of this kind within `x`

, by examining the frequency tables for all pairs of variables for violations (as described above). If `measure=="rate"`

, violations are evaluated in terms of observed rates within the associated excluded cells. If `measure=="z-score"`

, z-scores for the excluded cell frequencies (based on an asymptotic normal model conditional on row and column marginals) are used; `measure=="binom.p"`

instead uses the p-value value for a one-sided exact Binomial test of the conditional probability of error (given the precondition), versus the baseline probability due to the associated marginals. In all three cases, lower scores reflect a better “fit” to the data. For each variable pair, all dyadic entailments whose error scores are less than `thresh`

are retained, with implications being additionally subject to White's strength condition iff `req.str==TRUE`

. The entailments are stored in two-column form, with the first and second columns containing the numbers of the *X* and *Y* variables for the relationships (respectively).

Note that `sea.entailment`

does not check the resulting structure for completeness, nor for logical consistency. Thus, it is possible that additional entailments can be deduced from those extracted from the data – or, alternately, that no pattern of responses can satisfy the entailment set. Such results can occur, for instance, when a loose criterion is used to extract entailments from noisy data. For this reason, `sea.entailment`

is generally employed in conjunction with additional, statistical analyses (e.g., confirmatory latent class analysis).

An object of class `sea.entailment`

, containing the following elements:

`dep.imp ` |
A two-column matrix, whose rows contain the variable numbers for each respective implication |

`dep.excl ` |
A two-column matrix, whose rows contain the variable numbers for each respective exclusion |

`dep.coex ` |
A two-column matrix, whose rows contain the variable numbers for each respective coexhaustion |

`ndep.imp ` |
The number of implicative relationships |

`ndep.excl ` |
The number of exclusive relationships |

`ndep.coex ` |
The number of coexhaustive relationships |

`vars ` |
A vector of variable names (in the order used elsewhere in this function) |

`thresh ` |
The `thresh` argument |

`req.str ` |
The `req.str` argument |

`n ` |
The number of rows of `x` |

`measure ` |
The `measure` argument |

Carter T. Butts buttsc@uci.edu

White, D.R.; Burton, M.; and Brudner, L. 1977. “Entailment Theory and Method: A Cross-Cultural Analysis of the Sexual Division of Labor.” *Behavior Science Research,* 12:1-24.

`sea.enumerate`

, `sea.net`

, `sea.table`

, `binom.test`

[Package *ldsa* version 0.1-2 Index]