gIPFrm (version 3.1)

bisection.update: Search for the adjustment factor corresponding to the MLE using the bisection method

Description

bisection.update computes the segment that is known to contain the adjustment factor corresponding to the MLE and finds this adjustment factor using the bisection method. It is needed only for relational models for probabilities.

Usage

bisection.update(ModelMx, ObsTbl, tolerance)

Arguments

ModelMx

an I by J model matrix of a relational model. Here I is the number of observations and J is the number of generating subsets.

ObsTbl

a vector of observed cell frequencies of length I.

tolerance

tolerance used in stopping criteria.

Value

gamma.tilde

the adjustment factor under the precision given by tolerance.

model.tilde

the value returned by ipf.gamma() with the adjustment factor gamma equal to gamma.tilde.

References

A. Klimova, Coordinate-Free Exponential Families on Contingency Tables. PhD thesis. Advisers: Tamas Rudas and Thomas Richardson.

D. Bertsekas, Non-Linear Programming. Athena Scientific, 1999.

Examples

# NOT RUN {
### Multiplicative model from Aitchison and Silvey (1960)

A = matrix(c(1, 0, 0, 1, 0, 1, 1, 
             0, 1, 0, 1, 1, 0, 1,
             0, 0, 1, 0, 1, 1, 1), byrow=TRUE, nrow=3) ## the model matrix 

y = c(46,24,7,15,3,4,1) ## the observed data

bisection.update(A, y, 1e-4)



## The model of independence for a 2 by 2 contingency table

A = matrix(c( 1,1,0,0,
              0,0,1,1,
              1,0,1,0,
              0,1,0,1), byrow=TRUE, nrow=4) ## the model matrix

y = c(1,2,3,4)  ## the observed data


bisection.update(A, y, 1e-5)

# }