gRapfa (version 1.0)

dIC: Difference in information criteria

Description

The function returns the difference in AIC or BIC associated with merging a node pair in an APFA igraph object.

Usage

dIC(G, nodeset, crit = "BIC", NS=NULL)

Arguments

G

APFA igraph object

nodeset

vector of length two, contain the names of the nodes to be merged.

crit

Information criterion, 'AIC' or 'BIC' or a positive numerical value for the tuning parameter.

NS

Node symbol array

Value

A numerical vector of length three containing d(IC), G^2 and the degrees of freedom.

Details

dIC is The penalized likelihood criterion, IC(A) = -2(A) + alpha*dim(A), where dim(A) is the number of free parameters under A, and 'alpha' is a tuning parameter. For the AIC, alpha=2 and for the BIC, alpha= log(N). BIC penalises the parameters more heavily and so selects simpler models.

The difference in IC is d(IC) = IC(A_0) - IC(A) = G^2 - alpha*df\ where A_0 is the APFA obtained after merging the two nodes in A, G^2 is the deviance statistic and d.f. is the associated degrees of freedom.

References

Thollard, F.; Dupont, P. & de la Higuera, C. Probabilistic DFA Inference using Kullback-Leibler Divergence and Minimality 17th International Conference on Machine Learning., 2000, 975-982

Ankinakatte, S. and Edwards, D. Modelling discrete longitudinal data using acyclic probabilistic finite automata. Submitted to C.S.D.A.

Examples

library(gRapfa)
data(Wheeze)
G <- st(Wheeze)
G.c <- contract.last.level(G)
dic1 <- dIC(G.c, nodeset=c(5,3))
dic2 <- dIC(G.c, nodeset=c(6,4))