Score and profile likelihood confidence intervals for contingency table parameters

Lang, Joseph B.

doi:10.1002/sim.3391

Cited by 19 publications

(19 citation statements)

References 42 publications

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“…One measure of association between smoking level and myocardial infarction is a variant of the gamma coefficient introduced in Lang (2008) :…”

Section: Independent Multinomial Modelmentioning

confidence: 99%

“…For the numerically calculated profile likelihood region, we used an approach proposed by Lang (2008). Lang (2008) developed a numerical method to compute score and profile likelihood confidence intervals for a function of parameters g(θ) in a contingency table where the counts had a product multinomial distribution.…”

Section: Independent Multinomial Modelmentioning

confidence: 99%

“…Lang (2008) developed a numerical method to compute score and profile likelihood confidence intervals for a function of parameters g(θ) in a contingency table where the counts had a product multinomial distribution. His approach consists of two parts, computation of the restricted maximum likelihood estimator for g(θ) and, given the restricted maximum likelihood estimator, calculation of the confidence interval for g(θ) using a simple and efficient algorithm(a so called 'sliding quadratic' algorithm).…”

Section: Independent Multinomial Modelmentioning

confidence: 99%

“…His approach consists of two parts, computation of the restricted maximum likelihood estimator for g(θ) and, given the restricted maximum likelihood estimator, calculation of the confidence interval for g(θ) using a simple and efficient algorithm(a so called 'sliding quadratic' algorithm). Note that γ(θ) in (4.1) was one of four examples considered by Lang (2008). Two R-functions(mph.fit and ci.table) for the algorithm are available from Professor J.…”

Section: Independent Multinomial Modelmentioning

confidence: 99%

“…Consider the simulation model discussed in Lang (2008), the two independent multinomial models used in Section 4.2, and follow the simulation set-up there (simulation model, parameters, sample sizes, number of simulations and use of asymptotic critical value in defining a confidence set). We first generated 10,000 samples of size (n 1 , n 2 ) from two independent multinomial models with the cell probabilities p = ((p 1|1 , p 2|1 , p 3|1 ), (p 1|2 , p 2|2 , p 3|2 )).…”

Section: Simulation Studymentioning

confidence: 99%

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Using confidence distribution sampling to visualize confidence sets

Kim¹,

Lindsay²

2011

STAT Sinica

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This paper presents a new sampling-based methodology designed to facilitate the visual analysis of the confidence sets generated by an inference function such as the likelihood. This methodology generates a sample of parameters from a confidence distribution. This distribution is designed so that its probabilities on the parameter space are equal to the asymptotic coverage probabilities of the targeted confidence sets. Plotting these samples provides a picture of the inference function surface around the point estimator optimizing the inference function. Once the sample is created, one can also picture the profile inference function confidence sets for various functions of the parameters, all without further numerical optimization. The result is similar to a Bayesian analysis based on samples from the posterior. One distinction is that we can target the samples to obtain a clearer picture of the confidence set boundary. We illustrate the methodology with four different inference functions.Although this methodology is related to Fisher's concept of fiducial inference, the fiducial-like confidence distribution we create here is chosen for its ability to recover the confidence sets generated by the inference function and for its ease in computation, nothing more. Unlike resampling methods such as the parametric bootstrap, our method uses only the original data set, as in Bayesian inference. We use illustrative examples to compare our sampling-based confidence sets with those based on numerical optimization, and to compare the confidence regions generated by different inference functions.

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“…One measure of association between smoking level and myocardial infarction is a variant of the gamma coefficient introduced in Lang (2008) :…”

Section: Independent Multinomial Modelmentioning

confidence: 99%

Section: Independent Multinomial Modelmentioning

confidence: 99%

Section: Independent Multinomial Modelmentioning

confidence: 99%

Section: Independent Multinomial Modelmentioning

confidence: 99%

Section: Simulation Studymentioning

confidence: 99%

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Using confidence distribution sampling to visualize confidence sets

Kim¹,

Lindsay²

2011

STAT Sinica

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2010

Analysis of Ordinal Categorical Data

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Ordinal Data

Agresti¹

2015

Wiley StatsRef: Statistics Reference Online

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An ordinal variable is one that has a natural ordering of its possible values, but for which the distances between the values are undefined. For simple bivariate analyses, measures of association such as generalizations of Kendall's tau summarize the strength of positive or negative trend in the data by evaluating relative frequencies of concordant and discordant pairs of observations. Log‐linear models with scores for the categories can describe the structure of the joint distribution. Generalizations of the binary logistic regression model describe the dependence of an ordinal response variable on a set of qualitative and/or quantitative explanatory variables. Most commonly used is the cumulative logit model , which applies the logit link function to the set of cumulative probabilities. The proportional odds version of the model assumes the same effect on the logit of each cumulative probability. Extensions of the model apply to correlated multivariate ordinal responses; such extensions often occur in longitudinal studies. These extensions include marginal models , which simultaneously describe effects of explanatory variables on each marginal response, and generalized linear mixed models with random effects .

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Score and profile likelihood confidence intervals for contingency table parameters

Cited by 19 publications

References 42 publications

Using confidence distribution sampling to visualize confidence sets

Using confidence distribution sampling to visualize confidence sets

Bibliography

Ordinal Data

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