Penalized Likelihood for General Semi-Parametric Regression Models

Green, Peter J.

doi:10.2307/1403404

Cited by 237 publications

(173 citation statements)

References 25 publications

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“…Similarly, the estimated medians and coefficients of variation are summarized by M and S curves over the age range, respectively. Penalized likelihood estimation finds the L, M, and S curves as cubic smoothing splines, 15 and the degree of smoothing is indicated in terms of equivalent degrees of freedom (edf). Using LMS Chartmaker 2.4, 16 we created a set of percentile curves (third, 10th, 25th, 50th, 75th, 90th, and 97th) for weight, height, head circumference, and BMI according to gender.…”

Section: Methods and Measurementsmentioning

confidence: 99%

Growth Charts for Non-Growth Hormone Treated Prader-Willi Syndrome

2014

PEDIATRICS

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OBJECTIVE: The goal of this study was to generate and report standardized growth curves for weight, height, head circumference, and BMI for non-growth hormone-treated white male and female US subjects with Prader-Willi syndrome (PWS) between 3 and 18 years of age and develop standardized growth charts. METHODS:Anthropometric measures (N = 133) were obtained according to standard methods from 120 non-growth hormone-treated white subjects (63 males and 57 females) with PWS between 3 and 18 years of age. Standardized growth curves were developed for the third, 10th, 25th, 50th, 75th, 90th, and 97th percentiles by using the LMS method for weight, height, head circumference, and BMI for PWS subjects along with the normative third, 50th, and 97th percentiles from national and international growth data. The LMS smoothing procedure summarized the distribution of the anthropometric variables at each age using three parameters: power of the Box-Cox transformation l (L), median m (M) and coefficient of variation d (S).RESULTS: Weight, height, head circumference, and BMI standardized growth charts representing 7 percentile ranges were developed from 120 non-growth hormone-treated white male and female US subjects with PWS (age range: 3-18 years) and normative third, 50th, and 97th percentiles from national and international data. CONCLUSIONS:We encourage the use of syndrome-specific growth standards to examine and evaluate subjects with PWS when monitoring growth patterns and determining nutritional and obesity status. These variables can be influenced by culture, individual medical care, diet intervention, and physical activity plans.

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Section: Methods and Measurementsmentioning

confidence: 99%

Growth Charts for Non-Growth Hormone Treated Prader-Willi Syndrome

2014

PEDIATRICS

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Section: Penalized Maximum-likelihood Estimationmentioning

confidence: 99%

“…Let logLðuÞ denote the log-likelihood in a standard, unpenalized maximum-likelihood (or REML) analysis and u denote the vector of parameters, composed of the distinct elements of S G and S E or the equivalent. The penalized likelihood is then (Green 1987) logL P ðuÞ ¼ logLðuÞ 2 1 2 cPðuÞwith the penalty PðuÞ a nonnegative function of the parameters to be estimated and u the so-called tuning factor that modulates the strength of penalization (the factor of 1/2 is used for algebraic consistency and could be omitted).The penalty can be derived by assuming a suitable prior distribution for the parameters u (or functions thereof) as minus the logarithmic value of the pertaining probability density. As in Bayesian estimation, the choice of the prior is often somewhat ad hoc or driven by aspects of convenience (such as conjugacy of the priors) and computational feasibility.…”

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confidence: 99%

Simple Penalties on Maximum-Likelihood Estimates of Genetic Parameters to Reduce Sampling Variation

Meyer

2016

Genetics

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Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum-likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved by maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty-derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated-rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented, demonstrating that such penalties can yield very worthwhile reductions in loss, i.e., the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude to computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined.KEYWORDS genetic parameters; improved estimates; regularization; maximum likelihood; penalty E STIMATION of genetic parameters, i.e., partitioning of phenotypic variation into its causal components, is one of the fundamental tasks in quantitative genetics. For multiple characteristics of interest, this involves estimation of covariance matrices due to genetic, residual, and possibly other random effects. It is well known that such estimates can be subject to substantial sampling variation. This holds especially for analyses comprising more than a few traits, as the number of parameters to be estimated increases quadratically with the number of traits considered, unless the covariance matrices of interest have a special structure and can be modeled more parsimoniously. Indeed, a sobering but realistic view is that "Few datasets, whether from livestock, laboratory or natural populations, are of sufficient size to obtain useful estimates of many genetic parameters" (Hill 2010, p. 75). This not only emphasizes the importance of appropriate data, but also implies that a judicious choice of methodology for estimation-which makes the most of limited and precious records available-is paramount.A measure of the quality of an estimator is its "loss," i.e., the deviation of the estimate from the true value. This is an aggregate of bias and sampling variation. We speak of improving an estimator if we can modify it so that the expected loss is lessened. In most cases, this involves reducing sampling variance at the expense of some bias-if the additional bias is small and the reduction in variance sufficiently large, the loss is reduced. In statistical parlance "regularization" refers to the use of some kind of additional ...

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“…(14) and Eq. (15) via Fisher scoring algorithm (Green, 1987) can be expressed as the iterative solution of the system:…”

Section: Parameter Estimationmentioning

confidence: 99%

Penalized composite link models for aggregated spatial count data: A mixed model approach

et al. 2016

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Mortality data provide valuable information for the study of the spatial distribution of mortality risk, in disciplines such as spatial epidemiology and public health. However, they are frequently available in an aggregated form over irregular geographical units, hindering the visualization of the underlying mortality risk. Also, it can be of interest to obtain mortality risk estimates on a finer spatial resolution, such that they can be linked to potential risk factors that are usually measured in a different spatial resolution. In this paper, we propose the use of the penalized composite link model and its mixed model representation. This model considers the nature of mortality rates by incorporating the population size at the finest resolution, and allows the creation of mortality maps at a finer scale, thus reducing the visual bias resulting from the spatial aggregation within original units. We also extend the model by considering individual random effects at the aggregated scale, in order to take into account the overdispersion. We illustrate our novel proposal using two datasets: female deaths by lung cancer in Indiana, USA, and male lip cancer incidence in Scotland counties. We also compare the performance of our proposal with the area-to-point Poisson kriging approach.

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Penalized Likelihood for General Semi-Parametric Regression Models

Cited by 237 publications

References 25 publications

Growth Charts for Non-Growth Hormone Treated Prader-Willi Syndrome

Growth Charts for Non-Growth Hormone Treated Prader-Willi Syndrome

Simple Penalties on Maximum-Likelihood Estimates of Genetic Parameters to Reduce Sampling Variation

Penalized composite link models for aggregated spatial count data: A mixed model approach

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