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

In gIPFrm: Generalized Iterative Proportional Fitting for Relational Models

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.

Author(s)

Anna Klimova, Tamas Rudas

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

### 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)

gIPFrm documentation built on May 1, 2019, 9:16 p.m.