pistar.ll: The Mixture Index of Fit for Log-linear Models

In jmedzihorsky/pistar: Rudas, Clogg and Lindsay Mixture Index of Fit

The Mixture Index of Fit for Log-linear Models

Description

pistar.ll is used to find the value of the pi* index of fit for any log-linear model estimated with loglin; pi* is estimated using the algorithm of Rudas, Clogg, and Lindsay (1994). Standard errors for pi* and any other estimates of parameters of interest can be obtained by jackknife as proposed by Dayton (2003).

Usage

pistar.ll(data, margin = list(1, 2), start = rep(1, length(data)), eps = 0.1,
          iter = 1e3, param = TRUE, print = FALSE, 
          from = .Machine$double.neg.eps^0.25, 
          to = 1 - .Machine$double.neg.eps^0.25, jack = FALSE, 
          lr_eps = .Machine$double.neg.eps^0.25, 
          max_dif = .Machine$double.neg.eps, chi_stat = 0, u_iter = 1e3, 
          tol = .Machine$double.eps^0.25, verbose = TRUE)

Arguments

data	a contingency table.
margin	passed to loglin.
start	start argument of loglin.
eps	eps argument of loglin.
iter	maximum number of iterations for loglin.
param	logical: return parameter estimates?
print	logical: should loglin print during fitting?
from	numeric: lower bound of the interval of out-of-model proportions to be explored.
to	numeric: upper bound of the interval of out-of-model proportions to be explored.
jack	logical: perform jackknife?
lr_eps	penalty for finding pi*, the largest small positive number that can be still considered practically indistinguishable from 0.
max_dif	largest acceptable difference, passed to rcl.em.
chi_stat	Chi squared statistic penalty; default 0. Supply a different e.g. if you want to find the lower endpoint of a one-sided confidence interval for pi*.
u_iter	maximum number of iterations for method uniroot.
tol	tolerance passed to loglin.
verbose	logical: print during estimation?

Details

This is a version of the algorithm implemented in pistar.ct for log-linear models that is speed-optimized.

Value

Object of class "Pistar", "PistarCT", , "PistarRCL", and "PistarLL" with the following slots:

call	the matched call.
pistar	a list of estimated values of the mixture index of fit. est for the supplied data. jack vector of values from jackknife.
pred	a list of predicted values with three items: model the model component multiplied by (1-pi*) unres the unrestricted component multiplied by pi* combi the two-point mixture, i.e. (1-pi*)M + pi*U
data	the supplied data.
param	a list of requested estimates of the parameters of interest of the model fit to an unscaled model density, i.e. to M and not (1-pi) x M. est the estimated values. jack from each jackknife replication.
llrs	a list of values of log-likelihood ratio statistics est for the supplied data. jack vector of values from each jackknife.
iter	a list of the numbers of iterations of either uniroot or rcl.s est for the supplied data. jack from each jackknife replication.

Author(s)

Juraj Medzihorsky

Developed from J.M.Grego's clr and clr.root functions.

References

Dayton, C. M. (2003) Applications and computational strategies for the two-point mixture index of fit. British Journal of Mathematical & Statistical Psychology, 56, 1-13.

Grego, J. M. clr and clr.root functions available at http://www.stat.sc.edu/~grego/courses/stat770/CLR.txt

Rudas, T., Clogg, C. C., Lindsay, B. G. (1994) A New Index of Fit Based on Mixture Methods for the Analysis of Contingency Tables. Journal of the Royal Statistical Society. Series B (Methodological), Vol. 56, No. 4, 623-639.

Rudas, T. (2002) 'A Latent Class Approach to Measuring the Fit of a Statistical Model' in Hagenaars, J. A. and McCutcheon, A. L. (eds.) Applied Latent Class Analysis. Cambridge University Press. 345-365.

See Also

pistar.ct loglin

Examples

	data(HairEyeColor)

	#	check if the data is an "array"
	is(HairEyeColor, "array")

	#	it is not, so it first needs to be converted:
	HEC <- array(HairEyeColor, 
				 dim=dim(HairEyeColor), 
				 dimnames=dimnames(HairEyeColor))

	#	find pi* for independence in a 3-way table
	p <- pistar(proc="ll", data=HEC, margin=list(1, 2, 3), jack=FALSE)

	p

	summary(p)

	#	plot does not work for n-way tables if n > 2
	#	plot(p)

	
	#	create data
	H <- matrix((1:4)*1e1, byrow=TRUE, ncol=2)

	#	find pi* and model parameter estimates and perform jackknife
	h <- pistar(proc="ll", data=H, margin=list(1, 2), param=TRUE, jack=TRUE)

	h

	summary(h)

jmedzihorsky/pistar documentation built on June 4, 2022, 9:58 a.m.