g.ipf: Generalized Iterative Proportional Fitting for Relational...

In gIPFrm: Generalized Iterative Proportional Fitting for Relational Models

Description

g.ipf computes the maximum likelihood estimates of the cell frequencies and of the model parameters under a relational model specified by a model matrix.

Usage

g.ipf(ModelMatrix, ObsTable, tol, estimand, adjustment)

Arguments

ModelMatrix	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.
ObsTable	a vector of observed cell frequencies of length I.
tol	tolerance used in stopping criteria.
estimand	set to "probabilities" in the case of multinomial sampling; set to "intensities" in the case of Poisson sampling.
adjustment	set to "grid" if a grid is used to update the adjustment factor; set to "bisection" if the bisection method is used to update the adjustment factor; set to "none" if estimand is "intensities".

Value

model.matrix	the model matrix.
observed.data	the vector of observed cell frequencies.
fitted.values	the maximum likelihood estimates of the cell frequencies.
estimated.total	the sum of the estimated cell frequencies.
adjustment.for.total	the estimated total divided by the observed total.
adjustment.for.subsets	the adjustment factor for the subset sums.
model.parameters	the maximum likelihood estimates for model parameters on the multiplicative scale.
degrees.of.freedom	the degrees of freedom of the relational model.
chisq.statistic	Pearson's chi-squared statistic.
p.value.chisq	the p-value, based on Pearson's chi-squared statistic.
log.likelihood.ratio.statistic	the log likelihood ratio statistic.
p.value.log.likelihood.ratio.statistic	the p-value, based on the log likelihood ratio statistic.
Bregman.statistic	the Bregman statistic.
p.value.Bregman.statistic	the p-value, based on the Bregman statistic.

Author(s)

Anna Klimova, Tamas Rudas

References

A.Klimova, T.Rudas, A.Dobra, Relational models for contingency tables. J. Multivariate Anal., 2012, 104, 159–173.

A.Klimova, T.Rudas, Iterative proportional scaling for curved exponential families. Scand. J. Statist., 2015, 42, 832–847.

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

A.Agresti, Categorical Data Analysis. Wiley, New York, 1990.

J.Aitchison, S.D.Silvey, Maximum-likelihood estimation procedures and associated tests of significance. J. Roy. Statist. Soc. Ser.B, 1960, 22, 154–171.

G.Kawamura, T.Matsuoka, T.Tajiri, M.Nishida, M.Hayashi, Effectiveness of a sugarcane-fish combination as bait in trapping swimming crabs. Fisheries Research, 1995, 22, 155–160.

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

g.ipf(A, y, 1e-6, "probabilities", "bisection")
g.ipf(A, y, 1e-4, "probabilities", "grid")



### Bait study in swimming crabs, see Kawamura at al. (1995) :  

A = matrix(c(1,1,0,1,0,1), 2,3,byrow=TRUE) ## the model matrix

y1 = c(36,2,11)  ## the observed data for Charybdis japonica
y2 = c(71,3,44)  ## the observed data for Portunuspelagicus 

## If the model is for intensities, the adjustemnt factor is equal to one;
## the adjustment parameter is redundant.

g.ipf(A, y1, 1e-6, "intensities", "none")
g.ipf(A, y2, 1e-6, "intensities", "none")

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