An approach to non-linear principal components analysis using radially symmetric kernel functions

An approach to non-linear principal components using radially symmetric kernel basis functions is described. The procedure consists of two steps: a projection of the data set to a reduced dimension using a non-linear transformation whose parameters are determined by the solution of a generalized symmetric eigenvector equation. This is achieved by demanding a maximum variance transformation subject to a normalization condition (Hotelling's approach) and can be related to the homogeneity analysis approach of Gifi through the minimization of a loss function. The transformed variables are the principal components whose values define contours, or more generally hypersurfaces, in the data space. The second stage of the procedure defines the fitting surface, the principal surface, in the data space (again as a weighted sum of kernel basis functions) using the definition of self-consistency of Hastie and Stuetzle. The parameters of this principal surface are determined by a singular value decomposition and crossvalidation is used to obtain the kernel bandwidths. The approach is assessed on four data sets.     

Modeling Fetal Death and Malformation in Developmental Toxicity Studies

We review approaches to dose-response modeling and risk assessment for binary data from developmental toxicity studies. In particular, we focus on jointly modeling fetal death and malformation and use a continuation ratio formulation of the multinomial distribution to provide a model for risk. Generalized estimating equations are used to account for clustering of animals within litters. The fitted model is then used to calculate doses corresponding to a specified level of excess risk. Two methods of arriving at a lower confidence limit or Benchmark dose are illustrated and compared. We also discuss models based on single binary end points and compare our approach to a binary analysis of whether or not the animal was 'affected' (either dead or malformed). The models are illustrated using data from four developmental toxicity studies in EG, DEHP, TGDM, and DYME conducted through the National Toxicology Program.     

Standard statistical tools for the breed allocation problem

Modern technologies are frequently used in order to deal with new genomic problems. For instance, the STRUCTURE software is usually employed for breed assignment based on genetic information. However, standard statistical techniques offer a number of valuable tools which can be successfully used for dealing with most problems. In this paper, we investigated the capability of microsatellite markers for individual identification and their potential use for breed assignment of individuals in seventy Lidia breed lines and breeders. Traditional binomial logistic regression is applied to each line and used to assign one individual to a particular line. In addition, the area under receiver operating curve (AUC) criterion is used to measure the capability of the microsatellite-based models to separate the groups. This method allows us to identify which microsatellite loci are related to each line. Overall, only one subject was misclassified or a 99.94% correct allocation. The minimum observed AUC was 0.986 with an average of 0.997. These results suggest that our method is competitive for animal allocation and has some interpretative advantages and a strong relationship with methods based on SNPs and related techniques.     

Use,of andrews' function plot technique to construct control curves for multivariate process

This paper describes a method for quality control of product when it depends on several characteristics. The proposed procedure is graphical in nature and is based on Andrews' function plot technique. The method is illust¬rated with the help of a small simulated data.     

Bayesian Analysis of a Generalized Poisson Distribution

A generalized form of the Poisson Distribution with two parameters will be estimated by the Bayesian technique. When one of the parameters is known, several important parametric functions will be estimated and a numerical comparison with estimates obtained by the methods of maximum likelihood and unbiased minimum variance will be drawn. The simplicity of the posterior distribution of the unknown parameter enables us to construct exact probability intervals, and to devise a statistic to test the homogeneity of several populations. When the two parameters are unknown, dependent priors are being considered. Although the posterior distributions are sensitive to the choice of the prior, the posterior estimates are very stable and we use the Pearson system of curves to construct approximate posterior confidence limits for the parameters.     

A Single Form for t-Distributions and Symmetric Beta Distributions

A single parametric form is given for the symmetric distributions in the Pearson system with finite variance. In effect, these are Student's t-distributions with ν > 2 and all centered symmetric beta distributions. A different parametrization allows the inclusion of the t-distributions with ν ≤2 at the expense of symmetric beta distributions with a low shape parameter.     

Nonparametric Predictive Multiple Comparisons of Lifetime Data

We consider lifetime experiments to compare units from different groups, where the units’ lifetimes may be right censored. Nonparametric predictive inference for comparison of multiple groups is presented, in particular lower and upper probabilities for the event that a specific group will provide the largest next lifetime. We include the practically relevant consideration that the overall lifetime experiment may be terminated at an early stage, leading to simultaneous right-censoring of all units still in the experiment.     

Approximations to the distribution of weighted combination of independent probabilities

Two simple approximations are proposed for the distribution of the weighted combina-tion of n independent probabilities. The approximations are compared with other avail-able approximations. It is shown that one of the proposed approximations is better than the other approximations.     

Trajectory of quality of mother-child interactions: Prospective links with child socioemotional functioning

Research shows that the quality of mother-child interactions is a robust antecedent of child socioemotional functioning. Yet, relatively little is known about the evolution of this relational quality over time, and even less about how changes in relational quality may bear on child adjustment. This study aimed to describe the trajectory of quality of mother-child interactions between ages 2 and 7 and to investigate associations between individual differences in this trajectory and child socioemotional functioning at age 8. In a sample of 233 mother-child dyads primarily comprised of White French-Canadian mothers, the quality of interactions was assessed during 10-min play sequences when children were aged 2, 4, and 7 years. Child internalizing, externalizing, and prosocial behaviors were reported by a subsample of 171 teachers at age 8. The results showed that on average, quality of mother-child interactions decreased over time. In terms of individual differences, children who experienced a slower decrease in the quality of interactions with their mother from 2 to 7 years showed less internalizing behavior at age 8, over and above initial quality at 2 years. Children involved in higher quality interactions with their mother at 2 years showed more prosocial and less externalizing behavior at age 8, independent of the subsequent decrease in the quality of those interactions. The findings suggest that initial levels and subsequent changes in the quality of mother-child interactions are two distinct indicators of their relationship with potentially different implications for child adjustment.     

A trajectory analysis of body mass index for Finnish children

The aim of this study is to investigate the early development of body mass index (BMI), a standard tool for assessing the body shape and average level of adiposity for children and adults. The main aim of the study is to identify the primary trajectories of BMI development and to investigate the changes of certain growth characteristics over time. Based on our longitudinal data of 4223 Finnish children, we took anthropometric measurements from birth up to 15 years of age for birth years 1974, 1981, 1991 and 1995, but only up to 11 years of age for the birth year 2001. As a statistical method, we utilized trajectory analysis with the methods of nonparametric regression. We identified four main trajectories of BMI growth. Two of these trajectories do not seem to follow the normal growth pattern. The highest growth track appears to yield to a track that may yield to overweight and the low birth BMI track shows that the girls’ track differs that of boys on the same track, and on the normal tracks. The so-called adiposity rebound time decreased over time and started earlier for those on the overweight track. According to our study, this kind of acceleration of growth might be more of a general phenomenon that also relates to the other phases of BMI development. The major change seems to occur especially for those children on high growth tracks.