Showing papers on "Model selection published in 1973"
TL;DR: In this paper, the authors proposed a threefold classification of models that assume complete homogeneity among the tables: (i) models that allow complete heterogeneity, (ii) models with partial heterogeneity, and (iii) models without complete heterogeneity.
Abstract: The combined use of direct estimation (in saturated models) and indirect testing (of unsaturated models), proposed in [7, 8] for the analysis of a given multidimensional contingency table, is extended here to the analysis of a set of T multidimensional tables (T ≥ 2). For this set of tables, a three-fold classification of models is introduced: (1) models that assume “complete homogeneity” among the tables; (2) models that allow “complete heterogeneity” among the tables; and (3) models that allow “partial heterogeneity.” Stepwise procedures proposed in [8] for model selection are extended. “Guided” and “unguided” selection methods and “multidirectional” methods are introduced. For illustrative purposes, a set of two 4-way tables is analyzed.
45 citations
TL;DR: In this paper, the problem of selecting the model and coefficients for a spline regression curve with normal errors is considered, where the locations of all possible knots are assumed to be known; which subset of these is the set of actual knots is unknown.
Abstract: SUMMARY The problem of selecting the model and coefficients for a spline regression curve with normal errors is considered. The locations of all possible knots are assumed to be known; which subset of these is the set of actual knots is unknown. Each subset forms a model. Priors of the form of a marginal distribution on the index of the model and a conditional distribution for each model on the coefficients and variance are allowed. The posterior distribution is explicitly derived for natural conjugate and vague priors. The optimal predictor is derived for a loss function which is a generalization of that appearing in Lindley (1968). All that is required of the opinion is the marginal distribution for the model and the mean vector for the coefficients.
16 citations
01 Dec 1973
TL;DR: In this paper, the authors consider input forcing function selection for discriminating among alternative structural models and for estimating parameters of functional models, where model outputs are corrupted by an additive noise source, which represents the so-called breath-to-breath variation in the observation of a ventilation response to an end-tidal CO2-O2 forcing function input.
Abstract: This paper considers input forcing function selection for discriminating among alternative structural models and for estimating parameters of functional models. The model outputs are corrupted by an additive noise source, which represents the so-called breath-to-breath variation in the observation of a ventilation response to an end-tidal CO2-O2 forcing function input. The problem of forcing function selection for model discrimination is formulated around minimizing the probability of error in model selection while the problem of forcing function selection for model parameter estimation is formulated around minimizing the parameter estimation error variance. Forcing function selection is illustrated by considering end-tidal CO2 inputs that enhance parameter estimation for a functional model that summarizes normoxic respiratory controller behavior.
5 citations
01 Feb 1973
TL;DR: A computer program is described that performs a statistical multiple-decision procedure called chain pooling that uses a number of mean squares assigned to error variance that is conditioned on the relative magnitudes of the mean squares.
Abstract: A computer program is described that performs a statistical multiple-decision procedure called chain pooling. It uses a number of mean squares assigned to error variance that is conditioned on the relative magnitudes of the mean squares. The model selection is done according to user-specified levels of type 1 or type 2 error probabilities.
2 citations