sirt (version 1.5-0)

sia.sirt: Statistical Implicative Analysis (SIA)

Description

This function is a simplified implementation of statistical implicative analysis (Gras & Kuntz, 2008) which aims at deriving implications $X_i \rightarrow X_j$. This means that solving item $i$ implies solving item $j$.

Usage

sia.sirt(dat, significance = 0.85)

Arguments

dat

Data frame with dochotomous item responses

significance

Minimum implicative probability for inclusion of an arrow in the graph. The probability can be interpreted as a kind of significance level, i.e. higher probabilities indicate more probable implications.

Value

• A list with following entries
• adj.matrix
  Adjacency matrix of the graph. Transitive and symmetric implications (arrows) have been removed.
• adj.pot
  Adjacency matrix including all potencies, i.e. all direct and indirect paths from item $i$ to item $j$.
• adj.matrix.trans
  Adjacency matrix including transitive arrows.
• desc
  List with descriptive statistics of the graph.
• desc.item
  Descriptive statistics for each item.
• impl.int
  Implication intensity (probability) as the basis for deciding the significance of an arrow
• impl.t
  Corresponding $t$ values of impl.int
• impl.significance
  Corresponding $p$ values (significancies) of impl.int
• conf.loev
  Confidence according to Loevinger (see Gras & Kuntz, 2008). This values are just conditional probabilities $P( X_j=1|X_i=1)$.
• graph.matr
  Matrix containing all arrows. Can be used for example for the Rgraphviz package.
• graph.edges
  Vector containing all edges of the graph, e.g. for the Rgraphviz package.
• igraph.matr
  Matrix containing all arrows for the igraph package.
• igraph.obj
  An object of the graph for the igraph package.

Details

The test statistic for selection an implicative relation follows Gras and Kuntz (2008). Transitive arrows (implications) are removed from the graph. If some implications are symmetric, then only the more probable implication will be retained.

References

Gras, R., & Kuntz, P. (2008). An overview of the statistical implicative analysis (SIA) development. In R. Gras, E. Suzuki, F. Guillet, & F. Spagnolo (Eds.). Statistical Implicative Analysis (pp. 11-40). Springer, Berlin Heidelberg.

See Also

See also the IsingFit package for calculating a graph for dichotomous item responses using the Ising model.

Examples

#############################################################################
# EXAMPLE 1: SIA for data.read
#############################################################################

data(data.read)
dat <- data.read

res <- sia.sirt(dat , significance=.85 )

#*** plot results with igraph package
library(igraph)
plot( res$igraph.obj ) # , vertex.shape="rectangle" , vertex.size=30 )

#*** plot results with qgraph package
library(qgraph)
qgraph::qgraph( res$adj.matrix )

#*** plot results with Rgraphviz package
# Rgraphviz can only be obtained from Bioconductor
# If it should be downloaded, select TRUE for the following lines
if (FALSE){
     source("http://bioconductor.org/biocLite.R")
     biocLite("Rgraphviz")
            }
# define graph
grmatrix <- res$graph.matr
res.graph <- new("graphNEL", nodes= res$graph.edges , edgemode="directed")
# add edges
RR <- nrow(grmatrix)
for (rr in 1:RR){
    res.graph <- Rgraphviz::addEdge(grmatrix[rr,1], grmatrix[rr,2], res.graph , 1)
                    }                                                          
# define cex sizes and shapes
V <- length(res$graph.edges)
size2 <- rep(16,V)
shape2 <- rep("rectangle" , V )
names(shape2) <- names(size2) <- res$graph.edges
# plot graph
Rgraphviz::plot( res.graph, nodeAttrs =list("fontsize" = size2 , "shape" = shape2) )