Confidence regions for parameters in linear models with additional information

Abstract A standard approach to analysis of case-cohort data involves fitting log-linear models. In this paper, we describe how standard statistical software can be used to fit a broad class of general relative rate models to case-cohort data and derive confidence intervals. We focus on a case-cohort design in which a roster has been assembled and events ascertained but additional information needs to be collected on explanatory variables. The additional information is ascertained just for persons who experience the event of interest and for a sample of the cohort members enumerated at study entry. One appeal of such a case-cohort design is that this sample of the cohort may be used to support analyses of several outcomes. The ability to fit general relative rate models to case-cohort data may allow an investigator to reduce model misspecification in exposure-response analyses, fit models in which some factors have effects that are additive and others multiplicative, and facilitate estimation of relative excess risk due to interaction. We address model fitting for simple random sampling study designs as well as stratified designs. Data on lung cancer among radon-exposed men (Colorado Plateau uranium miners, 1950–1990) are used to illustrate these methods.

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Generalized Log-Linear Models of Housing Choice

Environment and Planning A Economy and Space ◽

10.1068/a200055 ◽

1988 ◽

Vol 20 (1) ◽

pp. 55-69 ◽

Cited By ~ 13

Author(s):

M C Deurloo ◽

F M Dieleman ◽

W A V Clark

Keyword(s):

Linear Models ◽

Nonlinear Effects ◽

Design Matrix ◽

Housing Choice ◽

Ordered Categories ◽

Public And Private ◽

Income Effects ◽

Additional Information ◽

Log Linear

By incorporating the structure of polytomous variables with ordered categories in the design matrix, nonstandard logit models are used to analyze housing choice. The detailed effects of income, age, and type of housing market on choice are examined. The additional information that is incorporated in the modeling leads to a more parsimonious representation of the data. The results confirm the central and substantial role of income; income effects are linear for owners but there are nonlinear effects for public and private renters. There are important age and region interaction effects on choice for households originally in the rental sector, and for former owners the value of the previous dwelling influences choice.

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Sequential confidence regions of generalized linear models with adaptive designs

Journal of Statistical Planning and Inference ◽

10.1016/s0378-3758(00)00200-7 ◽

2001 ◽

Vol 93 (1-2) ◽

pp. 277-293 ◽

Cited By ~ 14

Author(s):

Yuan-chin Ivan Chang

Keyword(s):

Generalized Linear Models ◽

Linear Models ◽

Confidence Regions ◽

Adaptive Designs

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Asymptotic Results for Multinomial Models

Symmetry ◽

10.3390/sym13112173 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2173

Author(s):

Isaac Akoto ◽

João T. Mexia ◽

Filipe J. Marques

Keyword(s):

Linear Models ◽

Confidence Regions ◽

Asymptotic Results ◽

Chi Square ◽

Normal Distributions ◽

Limit Distributions ◽

Multinomial Models ◽

Multidimensional Contingency Table ◽

Log Linear ◽

Key Parameter

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table.

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Best Prediction of the Additive Genomic Variance in Random-Effects Models

10.1101/282343 ◽

2018 ◽

Cited By ~ 2

Author(s):

Nicholas Schreck ◽

Hans-Peter Piepho ◽

Martin Schlather

Keyword(s):

Linkage Disequilibrium ◽

Random Effects ◽

Linear Models ◽

Additive Genetic Variance ◽

Random Variable ◽

Phenotypic Data ◽

Random Effects Models ◽

Additional Information ◽

Genomic Marker ◽

Genomic Variance

ABSTRACTThe additive genomic variance in linear models with random marker effects can be defined as a random variable that is in accordance with classical quantitative genetics theory. Common approaches to estimate the genomic variance in random-effects linear models based on genomic marker data can be regarded as the unconditional (or prior) expectation of this random additive genomic variance, and result in a negligence of the contribution of linkage disequilibrium.We introduce a novel best prediction (BP) approach for the additive genomic variance in both the current and the base population in the framework of genomic prediction using the gBLUP-method. The resulting best predictor is the conditional (or posterior) expectation of the additive genomic variance when using the additional information given by the phenotypic data, and is structurally in accordance with the genomic equivalent of the classical additive genetic variance in random-effects models. In particular, the best predictor includes the contribution of (marker) linkage disequilibrium to the additive genomic variance and eliminates the missing contribution of LD that is caused by the assumptions of statistical frameworks such as the random-effects model. We derive an empirical best predictor (eBP) and compare its performance with common approaches to estimate the additive genomic variance in random-effects models on commonly used genomic datasets.

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Confidence regions and testing statistical hypotheses in reduced linear models

Mathematica Slovaca ◽

10.2478/s12175-012-0044-7 ◽

2012 ◽

Vol 62 (4) ◽

Author(s):

Lubomír Kubáček

Keyword(s):

Linear Model ◽

Linear Models ◽

Confidence Regions ◽

Reduced Model ◽

New Model ◽

Statistical Hypotheses

AbstractLet in a linear model with large number of parameters some parameters be neglected and remaining parameters be changed in such a way (if it is possible) that the new model still corresponds with data. In the new (reduced) model problems of confidence regions and testing statistical linear hypotheses are investigated.

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