Numerical Integration in<i>S-PLUS</i>or<i>R</i>: A Survey

Kuonen, Diego

doi:10.18637/jss.v008.i13

Cited by 10 publications

(7 citation statements)

References 22 publications

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“…Alternatively, if g j (·| x j , θ ) does not exist in closed form, numerical integration techniques (e.g., adaptive Gaussian quadrature) could be used to evaluate g j (·| x j , θ ) at

Y_{p_{j}}

and thus facilitate the maximization of . However, it is well known that the computational burden associated with implementing these numerical techniques rapidly increases with the dimension of the integral, making this approach infeasible for c j >2; for further discussion, see . Further, numerical integration techniques, like the adaptive Gaussian quadrature, may perform poorly for peaked‐integrand distribution functions .…”

Section: Methodsmentioning

confidence: 99%

A general framework for the regression analysis of pooled biomarker assessments

2017

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As a cost efficient data collection mechanism, the process of assaying pooled biospecimens is becoming increasingly common in epidemiological research; e.g. pooling has been proposed for the purpose of evaluating the diagnostic efficacy of biological markers (biomarkers). To this end, several authors have proposed techniques that allow for the analysis of continuous pooled biomarker assessments. Regretfully, most of these techniques proceed under restrictive assumptions, are unable to account for the effects of measurement error, and fail to control for confounding variables. These limitations are understandably attributable to the complex structure that is inherent to measurements taken on pooled specimens. Consequently, in order to provide practitioners with the tools necessary to accurately and efficiently analyze pooled biomarker assessments, herein a general Monte Carlo maximum likelihood based procedure is presented. The proposed approach allows for the regression analysis of pooled data under practically all parametric models and can be used to directly account for the effects of measurement error. Through simulation, it is shown that the proposed approach can accurately and efficiently estimate all unknown parameters and is more computational efficient than existing techniques. This new methodology is further illustrated using monocyte chemotactic protein-1 data collected by the Collaborative Perinatal Project in an effort to assess the relationship between this chemokine and the risk of miscarriage.

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“…Alternatively, if g j (·| x j , θ ) does not exist in closed form, numerical integration techniques (e.g., adaptive Gaussian quadrature) could be used to evaluate g j (·| x j , θ ) at

Y_{p_{j}}

Section: Methodsmentioning

confidence: 99%

A general framework for the regression analysis of pooled biomarker assessments

2017

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“…Since there is no analytical solution available for them, a numerical integration was used to obtain these values. The numerical integration was carried out by adaptive quadrature [10] of functions implemented in the function ‘ quadinf ’ of an R package pracma . In order to optimize Equation (5), the R function ‘ nlminb ’ was used for optimization.…”

Section: Methodsmentioning

confidence: 99%

Sample size determination for logistic regression on a logit-normal distribution

Kim

Heath

Heilbrun

2015

Stat Methods Med Res

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Although the sample size for simple logistic regression can be readily determined using currently available methods, the sample size calculation for multiple logistic regression requires some additional information, such as the coefficient of determination (Rcov2) of a covariate of interest with other covariates, which is often unavailable in practice. The response variable of logistic regression follows a logit-normal (LN) distribution which can be generated from a logistic transformation of a normal distribution. Using this property of logistic regression, we propose new methods of determining the sample size for simple and multiple logistic regressions using a normal transformation of outcome measures. Simulation studies and a motivating example show several advantages of the proposed methods over the existing methods: (i) no need for Rcov2 for multiple logistic regression, (ii) available interim or group-sequential designs, and (iii) much smaller required sample size.

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“…These results provide further evidence that the functions given here are correct, and in fact are superior to numerical integration in obtaining moments, since it only requires a simple evaluation of a polynomial with integer coefficients. Numerical integration using adaptive methods was also implemented but worked poorly for higher dimensions (Kuonen 2003).…”

Section: R Functions To Compute Normal Multivariate Momentsmentioning

confidence: 99%

RFunctions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution

Phillips¹

2010

J. Stat. Soft.

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The central moments of the multivariate normal distribution are functions of its n × n variance-covariance matrix Σ. These moments can be expressed symbolically as linear combinations of products of powers of the elements of Σ. A formula for these moments derived by differentiating the characteristic function is developed. The formula requires searching integer matrices for matrices whose n successive row and column sums equal the n exponents of the moment. This formula is implemented in R, with R functions to display moments in L A T E X and to evaluate moments at specified variance-covariance matrices included.

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Numerical Integration inS-PLUSorR: A Survey

Cited by 10 publications

References 22 publications

A general framework for the regression analysis of pooled biomarker assessments

A general framework for the regression analysis of pooled biomarker assessments

Sample size determination for logistic regression on a logit-normal distribution

RFunctions to Symbolically Compute the Central Moments of the Multivariate Normal Distribution

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