Investigation of the within- and between-sample colour pattern differentiation in Hydropsyche contubernalis (Trichoptera)

The caddisfly Hydropsyche contubernalis (Trichoptera; Hydropsychidae) occurs in rivers and large streams throughout Europe. The aquatic larvae of this species are highly variable in their head capsule colour patterns. This paper describes the differentiation of such a pattern within and between 13 samples from three different West European river basins. The main aim is to investigate whether differences in colour pattern exist between river basins. Because the head capsule colour patterns of H. contubernalis do not have clear detectable morphs, an image analysis technique is presented to quantify the pattern in the form of mean colour curves expressed as grey levels. These curves are described by mathematical spline functions, and the differences between these functions, which formalize the original data set of colour curves, are analysed by multivariate Between-Group Principal Component Analysis. Our results show that distinct head capsule colour patterns occur in the Loire and Rhône, individuals of the Rhône being darker than individuals of the Loire. However these results also suggest that important differences in such a colour pattern can be detected at smaller scales: along the whole length of the Loire; within a 10km stretch of the Doubs, and also within a single site on the Loire (Amboise). Temporal differences at the same site between different H. contubernalis generations were also recorded. The mechanisms responsible for such differentiation patterns are discussed but still remain unclear. The overall statistical procedure detailed in this paper could potentially be used in numerous other fields of evolutionary biology.     

Quadratic inference functions for varying-coefficient models with longitudinal data

Nonparametric smoothing methods are used to model longitudinal data, but the challenge remains to incorporate correlation into nonparametric estimation procedures. In this article, we propose an efficient estimation procedure for varying-coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models. The proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified. For varying-coefficient models, it is often of interest to test whether coefficient functions are time varying or time invariant. We propose a unified and efficient nonparametric hypothesis testing procedure, and further demonstrate that the resulting test statistics have an asymptotic chi-squared distribution. In addition, the goodness-of-fit test is applied to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome (AIDS) data set.     

A partial linear model in the outcome-dependent sampling setting to evaluate the effect of prenatal PCB exposure on cognitive function in children

Outcome-dependent sampling (ODS) has been widely used in biomedical studies because it is a cost-effective way to improve study efficiency. However, in the setting of a continuous outcome, the representation of the exposure variable has been limited to the framework of linear models, due to the challenge in terms of both theory and computation. Partial linear models (PLM) are a powerful inference tool to nonparametrically model the relation between an outcome and the exposure variable. In this article, we consider a case study of a PLM for data from an ODS design. We propose a semiparametric maximum likelihood method to make inferences with a PLM. We develop the asymptotic properties and conduct simulation studies to show that the proposed ODS estimator can produce a more efficient estimate than that from a traditional simple random sampling design with the same sample size. Using this newly developed method, we were able to explore an open question in epidemiology: whether in utero exposure to background levels of polychlorinated biphenyls (PCBs) is associated with children's intellectual impairment. Our model provides further insights into the relation between low-level PCB exposure and children's cognitive function. The results shed new light on a body of inconsistent epidemiologic findings.     

Bayesian Inference in Semiparametric Mixed Models for Longitudinal Data

Summary .  We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within-subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.     

Geographic phenetic variation of two eastern-Mediterranean non-commensal mouse species, Mus macedonicus and M. cypriacus (Rodentia: Muridae) based on traditional and geometric approaches to morphometrics

We tested the hypothesis that skull shape within the genus Mus may vary with geographic location by assessing the extent and spatial distribution of phenotypic skull variation within and among two wild mouse species, M. macedonicus and M. cypriacus, using traditional and geometric morphometrics including a rather novel application of sliding semilandmarks. Shape was shown to be significantly correlated both with longitude and latitude in M. macedonicus, yet the correlation between morphometric and geographic distances was not significant, and morphometric differences between Asian and European populations were not higher than those within the particular continents. The phylogenetic signal was found to be stronger in dental characters than in cranial ones, however, overall concordance between the pattern of morphometric variation and the presumed history of M. macedonicus was rather weak. In both species, the dorsal and ventral sides of the skull were shown to covary in many aspects though there were also some differences between them, making the functional interpretation of these differences difficult. Discrimination between M. cypriacus and M. macedonicus as well as discrimination between two M. macedonicus subspecies was highly reliable using both traditional and geometric morphometric tools to analyze skull measurements.     

Extensions of the Penalized Spline of Propensity Prediction Method of Imputation

Summary .  Little and An (2004,  Statistica Sinica   14, 949–968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covariate. The predicted unconditional mean of the missing variable has a double robustness (DR) property under misspecification of the imputation model. We show that a simplified version of PSPP, which does not center other regressors prior to including them in the prediction model, also has the DR property. We also propose two extensions of PSPP, namely, stratified PSPP and bivariate PSPP, that extend the DR property to inferences about conditional means. These extended PSPP methods are compared with the PSPP method and simple alternatives in a simulation study and applied to an online weight loss study conducted by Kaiser Permanente.     

Evidence for Morphometric Differentiation of Wild and Captively Reared Adult Coho Salmon: A Geometric Analysis

As part of a comprehensive genetic evaluation of reproduction in naturally spawning coho salmon, Oncorhynchus kisutch, we examined morphometric variation in captively reared and wild adults from Hood Canal, Washington (U.S.A.) for evidence of differentiation between these groups. We collected captively reared fish as parr from two stocks and reared to adulthood at a freshwater hatchery, maturing in 1995 and 1996; we sampled closely size-matched wild fish as they returned to a neighboring stream in both years. Multivariate analysis of shape variation by Procrustes coordinates, visualized by thin-plate splines, indicated that the captively reared adults were differentiated from the wild fish by sharply reduced sexual dimorphism as well as smaller heads and less hooked snouts, increased trunk depth, larger caudal peduncles, shorter dorsal fins, larger hindbodies and a reduction in body streamlining. The differences between the captively reared and wild fish were similar to but more pronounced than some differences previously reported between hatchery and wild coho salmon. The magnitude and pattern of differences suggested that at least some of them were environmentally induced. Shape variation showed an allometric relationship with variation in body (measured as centroid) size. Morphometric variation was a poor correlate of most spawning behaviors. Nevertheless, our results suggest that the morphometric consequences of captive rearing for mate selection and reproductive activity of spawning fish may limit its effectiveness as a restorative tool.