The DASSOC program uses the modified Newton-Raphson algorithm for association models described in the Haberman 1994 paper, ”Computation of Maximum-Likelihood Estimates in Association Models.”: In association models for cross-classified data, computation of maximum likelihood estimates (MLE’s) is relatively difficult due to the nonlinear constraints on the parameters. Currently available procedures based on the scoring algorithm for constrained maximum likelihood are relatively unreliable, and other cyclic procedures are relatively slow and do not provide estimated asymptotic standard deviations as by-products of calculations. To facilitate computations, it is noted that in standard association models removal of constraints results in underidentification of parameters but does not affect the model itself, so that the MLE’s of cell probabilities and conditional probabilities are unaffected. Given this observation, maximum likelihood estimation may be accomplished by unconstrained maximization of an objective function with two components: a log-likelihood ratio and a sum of squares representing deviations of parameters from their constraints. The objective function is then maximized by using a modification of the Newton-Raphson algorithm that ensures that successive iterations increase the objective function whenever a local maximum has not been reached. The proposed algorithm is shown to be reliable and relatively rapid. In addition, it is shown that the proposed technique may be used to estimate asymptotic standard deviations of parameter estimates. Use of the algorithm in practice is illustrated through some standard examples of association models.
Keywords for this software
References in zbMATH (referenced in 8 articles , 1 standard article )
Showing results 1 to 8 of 8.
- Anderson, Carolyn J.: Multidimensional item response theory models with collateral information as Poisson regression models (2013)
- Beh, Eric J.; Farver, Thomas B.: An evaluation of non-iterative methods for estimating the linear-by-linear parameter of ordinal log-linear models (2009)
- Iliopoulos, G.; Kateri, M.; Ntzoufras, I.: Bayesian estimation of unrestricted and order-restricted association models for a two-way contingency table (2007)
- de Rooij, Mark; Heiser, Willem J.: Graphical representations and odds ratios in a distance-association model for the analysis of cross-classified data (2005)
- Liu, Ivy; Agresti, Alan: The analysis of ordered categorical data: An overview and a survey of recent developments. (With discussion) (2005)
- Aït-Sidi-Allal, M. L.; Baccini, A.; Mondot, A. M.: A new algorithm for estimating the parameters and their asymptotic covariance in correlation and association models (2004)
- Croft, J.; Smith, J. Q.: Discrete mixtures in Bayesian networks with hidden variables: a latent time budget example (2003)
- Haberman, Shelby J.: Computation of maximum likelihood estimates in association models (1995)