pistar.ct: The Mixture Index of Fit for a Contingency Table

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

The Mixture Index of Fit for a Contingency Table

Description

pistar.ct is used to find the value of the pi* for any user-supplied model fit to a contingency table. The only requirements are (1) that the model inputs only a contingency table with non-negative continuous cell values, and (2) outputs a named list in which the predicted values are a contingency table named "fit". Optionally parameter estimates of interest can be outputed as a vector named "param" in the output list.

pi* for the model of interest is estimated using the algorithm of Rudas, Clogg, and Lindsay (1994). Standard errors for pi* and any other parameter estimates of interest can be obtained by jackknife as proposed by Dayton (2003).

Usage

pistar.ct(data, fn, from = .Machine$double.neg.eps^0.25, 
          to = 1 - .Machine$double.neg.eps^0.25, jack = FALSE, 
          method = "uniroot", u_iter = 1e3, zeta = 1, 
          lr_eps = .Machine$double.neg.eps^0.25, 
          max_dif = .Machine$double.neg.eps, chi_stat = 0, verbose = TRUE)

Arguments

data	a contingency table.
fn	a user supplied function that estimates the model of interests. Must input only the observed values as a contingency table containging non-negative continuous cell values. Must output the predicted values as a contingency table as item named "fit" in a named list. Optionally can output parameter estimates of interest as a vector named "param" in the output named list.
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?
method	character: method with to look for pi*. "uniroot" uses uniroot, can be expected to be faster "split" uses a simple binary search from rcl.s.
u_iter	maximum number of iterations for method uniroot if method "uniroot".
zeta	weighing constant; default is 1. The EM algorithm might crash due to very low cell values and in such case increasing the zeta might help.
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 and rcl.s.
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*.
verbose	logical: print during estimation?

Details

The EM algorithm implemented here was proposed by Rudas, Clogg and Lindsay (1994). The jackknife procedure was proposed by Dayton (2003). The function is developed from J.M.Grego's clr and clr.root functions.

Value

Object of class "Pistar", "PistarCT", and "PistarRCL" 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	an array with 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

piplot.ct rcl.em rcl.s

Examples

	#	load data
	data(Fienberg1980a)

	#	define a function: log-linear model of independence in a
	#	2-way table
	mf <- function(x){
		loglin(table=x, margin=list(1,2), fit=TRUE, print=FALSE)
	}

	#	find pi*
	p <- pistar(proc="ct", data=Fienberg1980a, fn=mf, jack=FALSE)

	p

	summary(p)

	plot(p)

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