bisection.update {gIPFrm} | R Documentation |
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 |
ObsTbl |
a vector of observed cell frequencies of length |
tolerance |
tolerance used in stopping criteria. |
Value
gamma.tilde |
the adjustment factor under the precision given by |
model.tilde |
the value returned by |
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)