Data compression and regression based on local principal curves.

Frequently the predictor space of a multivariate regression problem of the type y = m(x_1, …, x_p ) + ε is intrinsically one-dimensional, or at least of far lower dimension than p. Usual modeling attempts such as the additive model y = m_1(x_1) + … + m_p (x_p ) + ε, which try to reduce the complexity of the regression problem by making additional structural assumptions, are then inefficient as they ignore the inherent structure of the predictor space and involve complicated model and variable selection stages. In a fundamentally different approach, one may consider first approximating the predictor space by a (usually nonlinear) curve passing through it, and then regressing the response only against the one-dimensional projections onto this curve. This entails the reduction from a p- to a one-dimensional regression problem. As a tool for the compression of the predictor space we apply local principal curves. Taking things on from the results presented in Einbeck et al. (Classification – The Ubiquitous Challenge. Springer, Heidelberg, 2005, pp. 256–263), we show how local principal curves can be parametrized and how the projections are obtained. The regression step can then be carried out using any nonparametric smoother. We illustrate the technique using data from the physical sciences

A diagnostic plot for assessing model fit incount data models

Whilst many numeric methods, such as AIC and deviance, exist for assessing model fit, diagrammatic methods are few. We present here a diagnostic plot, to which we refer as ‘Christmas tree plot’ due its characteristic shape, that may be used to visually assess the suitability of a given count data model

On statistical testing and mean parameter estimation for zero–modification in count data regression

For the problem of testing for zero–modification in Poisson regression, a simple and intuitive test can be constructed by computing directly confidence intervals for the number of 0’s under the Poisson assumption. This requires the ability of estimating the mean function accurately even if the data are in fact zero–inflated or deflated. A novel hybrid estimator is introduced for this purpose, which is of interest beyond the scope of the motivating test problem

Gradient test for generalised linear models with random effects.

This work develops the gradient test for parameter selection in generalised linear models with random effects. Asymptotically, the test statistic has a chi-squared distribution and the statistic has a compelling feature: it does not require computation of the Fisher information matrix. Performance of the test is verified through Monte Carlo simulations of size and power, and also compared to the likelihood ratio, Wald and Rao tests. The gradient test provides the best results overall when compared to the traditional tests, especially for smaller sample sizes

Implementation of a local principal curves algorithm for neutrino interaction reconstruction in a liquid argon volume

A local principal curve algorithm has been implemented in three dimensions for automated track and shower reconstruction of neutrino interactions in a liquid argon time projection chamber. We present details of the algorithm and characterise its performance on simulated data sets.Comment: 14 pages, 17 figures; typing correction to Eq 5, the definition of the local covariance matri

Effects of maternal mental health on prenatal movement profiles in twins and singletons

Aim: Prenatal experiences, including maternal stress, depression and anxiety, form crucial building blocks affecting the maturation of the fetal central nervous system. Previous research has examined fetal movements without considering effects of maternal mental health factors critical for healthy fetal development. The aim of this research is to assess the effects of maternal mental health factors on fetal twin compared with singleton movement profiles. Method: We coded fetal touch and head movements in 56 ultrasound scans, from a prospective opportunity sample of 30 mothers with a healthy pregnancy (mean gestational age 27.8 weeks for singleton and 27.2 for twins). At the ultrasound scan appointment, participants completed questionnaires assessing their stress, depression and anxiety. Results: Maternal depression increased fetal self-touch significantly. In fetal twins maternal stress significantly decreased and maternal depression significantly increased other twin touch. Maternal mental health factors affected the head movements of twins significantly more than singletons, with maternal depression decreasing head movement frequency for twins significantly. Conclusion: These results indicate that maternal mental health might have an impact on types of body schemata formed in utero, in twin compared with singleton pregnancies. Future research needs to examine whether these prenatal effects affect postnatal differences in body awareness

Local Smoothing with Robustness against Outlying Predictors

Outlying pollutant concentration data are frequently observed in time series studies conducted to investigate the effects of atmospheric pollution and mortality/morbidity. These outliers may severely affect the estimation procedures and even generate unexpected results like a protective effect of pollution. Although robust methods have been proposed to downweight the effect of outliers in the response variable distribution, little has been done to handle outlying explanatory variable values. We consider a robust local polynomial smoothing technique which may be useful for such purposes. It is based on downweighting points with a small design density and may also be used as a diagnostic tool to identify outliers. Using data from a study conducted in São Paulo, Brazil, we show how an unexpected form of the relative risk curve of mortality attributable to pollution by SO_2 obtained via nonrobust methods may be completely reversed when the proposed technique is employed

A diagnostic plot for assessing model fit in count data models

Whilst many numeric methods, such as AIC and deviance, exist for assessing model fit, diagrammatic methods are few. We present here a diagnostic plot, to which we refer as `Christmas tree plot' due its characteristic shape, that may be used to visually assess the suitability of a given count data model