Bayesian estimation of log odds ratios fromR × Cand 2 × 2 × Kcontingency tables

Demirhan, Haydar; Hamurkaroğlu, Canan

doi:10.1111/j.1467-9574.2008.00387.x

Cited by 9 publications

(14 citation statements)

References 11 publications

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“…We use the approach given by Chen and Dunson [7] to decompose the covariance matrix, and reflect the degree of belief in prior knowledge using the decomposed elements by the approach of Demirhan and Hamurkaroglu [11]. The approach of Demirhan and Hamurkaroglu [11] is outlined for log odds ratios. We reformulate the latter approach for scores and model parameters.…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Chen and Dunson [7] give a reparameterization that is based on the Cholesky decomposition of the covariance matrix of parameters corresponding to the random part of a linear model. Demirhan and Hamurkaroglu [11] propose an approach for the representation of the degree of belief in prior knowledge concerning the log odds ratios using the decomposed elements. We use the approach given by Chen and Dunson [7] to decompose the covariance matrix, and reflect the degree of belief in prior knowledge using the decomposed elements by the approach of Demirhan and Hamurkaroglu [11].…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Demirhan and Hamurkaroglu [11] propose an approach for the representation of the degree of belief in prior knowledge concerning the log odds ratios using the decomposed elements. We use the approach given by Chen and Dunson [7] to decompose the covariance matrix, and reflect the degree of belief in prior knowledge using the decomposed elements by the approach of Demirhan and Hamurkaroglu [11]. The approach of Demirhan and Hamurkaroglu [11] is outlined for log odds ratios.…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Setting the values of all ϕ i(t) parameters to arbitrary numbers has no effect on the results. Demirhan and Hamurkaroglu [11] induce the following uniform prior on each ρ i(ts) :…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Let σ i(ts) denote the (t, s)th element of i . Then, σ i(tt) and σ i(ts) are obtained as follows [10,7,11]:…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

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Bayesian estimation of order-restricted and unrestricted association models

Demirhan

2013

Journal of Multivariate Analysis

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a b s t r a c tAssociation models include score parameters to multiplicatively represent the hierarchy between the levels of the considered ordinal factor. If order restrictions are placed on the scores, an estimation problem becomes a non-linear and restricted estimation, which is somewhat problematic with respect to the classical approaches. In this article, we consider the Bayesian estimation of the scores and other parameters of an association model both with and without order restrictions. We propose the use of a previously introduced multivariate prior in the unrestricted case and an order statistics approach in the order-restricted case. The advantages of using these prior structures are that we are able to consider the correlation patterns arising from the hierarchy between the levels of ordinal factors, there is no violation of the exchangeability assumption, the approaches are general for any size of contingency table, and the posterior inferences are easily derived. The proposed approaches are applied to both a previously analyzed popular two-way contingency table and a threeway contingency table. Smaller standard deviations than those of previous analyses are obtained, and a new best-fitting model is identified for the two-way table.

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Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Setting the values of all ϕ i(t) parameters to arbitrary numbers has no effect on the results. Demirhan and Hamurkaroglu [11] induce the following uniform prior on each ρ i(ts) :…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

“…Let σ i(ts) denote the (t, s)th element of i . Then, σ i(tt) and σ i(ts) are obtained as follows [10,7,11]:…”

Section: Exchangeability Assumption and Determination Of Hyper-priorsmentioning

confidence: 99%

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