# dIC: Difference in information criteria In gRapfa: Acyclic Probabilistic Finite Automata

## Description

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

## Usage

 `1` ```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

The node symbol array corresponding to G may be supplied to increase speed

## 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.

## Value

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

## Author(s)

Smitha Ankinakatte and David Edwards.

## 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

 ```1 2 3 4 5 6``` ```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)) ```

gRapfa documentation built on May 2, 2019, 6:54 a.m.