Contingency table analysis is performed based on maximum likelihood (ML) fitting of multinomial-Poisson homogeneous (MPH) models (Lang, 2004) and homogeneous linear predictor (HLP) models (Lang, 2005). Objects computed include model goodness-of-fit statistics; likelihood-based (cell- and link-specific) residuals; and cell probability and expected count estimates along with standard errors. This package can also compute test-inversion--e.g. Wald, profile likelihood, score, power-divergence--confidence intervals for contingency table estimands, when table probabilities are potentially subject to equality constraints. See Lang (2008) and Zhu (2020) for test-inversion intervals.
Please call the following two R functions in this cta package.
mph.fit: Computes maximum likelihood estimates and fit statistics for MPH and HLP models for contingency tables.
ci.table: Constructs test-inversion approximate confidence intervals for estimands in contingency tables with or without equality constraints.
Lang, J. B. (2004) Multinomial-Poisson homogeneous models for contingency tables, Annals of Statistics, 32, 340--383.
Lang, J. B. (2005) Homogeneous linear predictor models for contingency tables, Journal of the American Statistical Association, 100, 121--134.
Lang, J. B. (2008) Score and profile likelihood confidence intervals for contingency table parameters, Statistics in Medicine, 27, 5975--5990.
Zhu, Q. (2020) "On improved confidence intervals for parameters of discrete distributions." PhD dissertation, University of Iowa.