Standardized residuals as a means for detection of growth alteration in the pathologic human fetus.

This paper introduces and discusses the use of standardized residuals as a technique for comparing the growth of normal and pathologic human fetuses. Anthropometric measures, radiographic measures, and organ weights were regressed on known gestational age of second- and third-trimester fetuses. Standardized residuals were calculated for a group of potentially growth-impaired fetuses. Use of residuals aids in identification of patterns of growth alteration in specific pathologies. Most important, studying the response of developing organ systems to a variety of insults may elucidate mechanisms of growth regulation in the fetus. We emphasize the special quality of the multivariate measures of the core sample of fetuses from the Akron Children's Hospital collection.     

Application of Multiple Test Procedures to the Combination of Multivariate and Univariate Tests with Varying Variable Sets

The positive ascertainment of location differences in a multivariate comparison of two or more groups gives rise to the question for the contribution of the single variables or of subsets of variables to the multivariate difference. In this paper two methods are proposed to accomplish the original multivariate test by tests in variable subsets or in single variables using a closed test procedure and Holm's procedure, respectively. Both control the multiple level of the whole procedure.     

Levene tests of homogeneity of variance for general block and treatment designs

This article develops a weighted least squares version of Levene's test of homogeneity of variance for a general design, available both for univariate and multivariate situations. When the design is balanced, the univariate and two common multivariate test statistics turn out to be proportional to the corresponding ordinary least squares test statistics obtained from an analysis of variance of the absolute values of the standardized mean-based residuals from the original analysis of the data. The constant of proportionality is simply a design-dependent multiplier (which does not necessarily tend to unity). Explicit results are presented for randomized block and Latin square designs and are illustrated for factorial treatment designs and split-plot experiments. The distribution of the univariate test statistic is close to a standard F-distribution, although it can be slightly underdispersed. For a complex design, the test assesses homogeneity of variance across blocks, treatments, or treatment factors and offers an objective interpretation of residual plots.     

Resampling-based methods in single and multiple testing for equality of covariance/correlation matrices

Traditional resampling-based tests for homogeneity in covariance matrices across multiple groups resample residuals, that is, data centered by group means. These residuals do not share the same second moments when the null hypothesis is false, which makes them difficult to use in the setting of multiple testing. An alternative approach is to resample standardized residuals, data centered by group sample means and standardized by group sample covariance matrices. This approach, however, has been observed to inflate type I error when sample size is small or data are generated from heavy-tailed distributions. We propose to improve this approach by using robust estimation for the first and second moments. We discuss two statistics: the Bartlett statistic and a statistic based on eigen-decomposition of sample covariance matrices. Both statistics can be expressed in terms of standardized errors under the null hypothesis. These methods are extended to test homogeneity in correlation matrices. Using simulation studies, we demonstrate that the robust resampling approach provides comparable or superior performance, relative to traditional approaches, for single testing and reasonable performance for multiple testing. The proposed methods are applied to data collected in an HIV vaccine trial to investigate possible determinants, including vaccine status, vaccine-induced immune response level and viral genotype, of unusual correlation pattern between HIV viral load and CD4 count in newly infected patients.     

具有空间自相关残差的回归模型及其应用

提出了具有空间自相关残差的多变量回归问题,这种残差包括单点、局部和区域化三种尺度.文中提出了两种处理空间自相关的方法:把自相关加入残差协方差作参数的改进估计──相邻相关方法和把残差作区域化最优自相关估计──一般空间自相关方法.用森林对舞毒蛾危害敏感性概率的大范围估计为例,比较了传统回归方法和本文方法间的差异,交叉检验结果表明本文的方法明显优于直接回归方法,这说明加入空间自相关对空间回归问题是必要的.     

To some reasonable test procedures in multiple contingency tables to investigate certain epidemiological or medicin-sociological relationships

One of the most important tasks of the application of mathematical-statistical methods consists in giving help in the search for possible relationships, and connected with this, the specification of new hypotheses. The progress of both the special diciplines of sciences and mathematical statistics itself leads to the application of more and more complex, that means multivariate, methods. In medical fields, especially in epidemiological and medicin-sociological studies, this fact means the necessity of analysing multidimensional contingency tables. The above formulated problem is equivalent to the problem of fitting an appropriate mathematical model (for contingency tables is this a log-linear model) to the data in a way which makes the structural relationships clear to us. In this paper it is shown that one is able to get to well-interpretable models of independence with relatively simple means. Two stepwise test procedures are described yielding essentially the same results: a so called reduction procedure which is particularly profitable in sparsely occupied tables and a procedure which uses a combination of hypotheses of conditional pairwise independence.     

Expected Error Rates for Logistic Regression Versus Normal Discriminant Analysis

The expected error rates associated with using the allocation rule based on logistic regression are derived in the context of two multivariate normal populations with a common covariance matrix and compared with the corresponding error rates of the classical rule based on this normality assumption. It is shown in terms of the actual sizes of the asymptotic expected error rates that the performance of the logistic procedure does not fall far short of the normality based method, even for widely separated populations. This latter result is not obvious from previously available work on the asymptotic relative efficiency of the logistic procedure.     

Recursive Residuals for Multivariate Field Processes

Vector recursive residuals are developed for multivariate regression models on a field. A vector response variable is observed at points on a rectangular grid, together with regression variables measured at the same points. Neighbouring values of the response vector may be correlated and simple models are considered using a direct product structure for the variance matrix. Subsequent to obtaining vector recursive residuals principal component analysis is applied to obtain an evaluation of any changes that may be occurring in the regression relationship over the field. The method is then applied to the problem of detecting zones of bush fire damage and recovery from LANDSAT data.     

Robust estimating functions and bias correction for longitudinal data analysis

Robust methods are useful in making reliable statistical inferences when there are small deviations from the model assumptions. The widely used method of the generalized estimating equations can be "robustified" by replacing the standardized residuals with the M-residuals. If the Pearson residuals are assumed to be unbiased from zero, parameter estimators from the robust approach are asymptotically biased when error distributions are not symmetric. We propose a distribution-free method for correcting this bias. Our extensive numerical studies show that the proposed method can reduce the bias substantially. Examples are given for illustration.     

Phylogenetic ANOVA: Group‐clade aggregation,biological challenges,and a refined permutation procedure

Phylogenetic regression is frequently used in macroevolutionary studies, and its statistical properties have been thoroughly investigated. By contrast, phylogenetic ANOVA has received relatively less attention, and the conditions leading to incorrect statistical and biological inferences when comparing multivariate phenotypes among groups remain underexplored. Here, we propose a refined method of randomizing residuals in a permutation procedure (RRPP) for evaluating phenotypic differences among groups while conditioning the data on the phylogeny. We show that RRPP displays appropriate statistical properties for both phylogenetic ANOVA and regression models, and for univariate and multivariate datasets. For ANOVA, we find that RRPP exhibits higher statistical power than methods utilizing phylogenetic simulation. Additionally, we investigate how group dispersion across the phylogeny affects inferences, and reveal that highly aggregated groups generate strong and significant correlations with the phylogeny, which reduce statistical power and subsequently affect biological interpretations. We discuss the broader implications of this phylogenetic group aggregation, and its relation to challenges encountered with other comparative methods where one or a few transitions in discrete traits are observed on the phylogeny. Finally, we recommend that phylogenetic comparative studies of continuous trait data use RRPP for assessing the significance of indicator variables as sources of trait variation.     

Inferences Concerning a Mean Vector when the Variables are Grouped into Subsets

In experiments involving multivariate measurements biological considerations often indicate a grouping of the variables into subsets such that all the variables in a subset are equally important and the subsets may be arranged in a decreasing order of importance (JENSEN, 1972). This paper deals with a method of analysis appropriate in such cases, to solve multivariate problems such as profile analysis, comparison of two mean vectors, or univariate problems such as analysis of SCHEFFÉ'S mixed effects model with interaction (SCHEFFÉ, 1959; MILLER, 1966), usually treated using HOTELLING'S T². An invariance structure underlying this procedure is examined and used to obtain noncentrality parameters of the power function, and derive some of its properties. The multiple comparisons procedure in MUDHOLKAR and SUBBAIAH (1976) is extended and illustrated in terms of the data from a clinical trial.     

Procedure for Detecting Outliers in a Circular Regression Model

A number of circular regression models have been proposed in the literature. In recent years, there is a strong interest shown on the subject of outlier detection in circular regression. An outlier detection procedure can be developed by defining a new statistic in terms of the circular residuals. In this paper, we propose a new measure which transforms the circular residuals into linear measures using a trigonometric function. We then employ the row deletion approach to identify observations that affect the measure the most, a candidate of outlier. The corresponding cut-off points and the performance of the detection procedure when applied on Down and Mardia’s model are studied via simulations. For illustration, we apply the procedure on circadian data.     

Skeletal growth in early and late Neolithic foragers from the Cis‐Baikal region of Eastern Siberia

Skeletal growth is explored between Early Neolithic (EN) (8000 to 6800 BP) and Late Neolithic (LN) (6000 to 5200 BP) foragers from the Cis‐Baikal region of Eastern Siberia. Previous studies suggest that increased systemic stress and smaller adult body size characterize the EN compared to LN. On this basis, greater evidence for stunting and wasting is expected in the EN compared to LN. Skeletal growth parameters assessed here include femoral and tibial lengths, estimated stature and body mass, femoral midshaft cortical thickness, total bone thickness, and medullary width. Forward selection was used to fit polynomial lines to each skeletal growth parameter relative to dental age in the pooled samples, and standardized residuals were compared between groups using t tests. Standardized residuals of body mass and femoral length were significantly lower in the EN compared to LN sample, particularly from late infancy through early adolescence. However, no significant differences in the standardized residuals for cortical thickness, medullary width, total bone thickness, tibial length, or stature were found between the groups. Age ranges for stunting in femoral length and wasting in body mass are consistent with environmental perturbations experienced at the cessation of breast feeding and general resource insecurity in the EN compared to LN sample. Differences in relative femoral but not tibial length may be associated with age‐specific variation in growth‐acceleration for the distal and proximal limb segments. Similarity in cortical bone growth between the two samples may reflect the combined influences of systemic and mechanical factors on this parameter. Am J Phys Anthropol 153:377–386, 2014. © 2013 Wiley Periodicals, Inc.     

Shape Variation in the Dermatocranium of the Greater Short-Horned Lizard <Emphasis Type="Italic">Phrynosoma hernandesi</Emphasis> (Reptilia: Squamata: Phrynosomatidae)

Dermatocranial shape and horn morphology display great disparity among the species of Phrynosoma. Ontogenetic change in dermatocranial shape in a series of 79 specimens of the short-horned Phrynosoma hernandesi (54F: 25M) was examined using geometric morphometric techniques. A multivariate ANCOVA of Procrustes residuals with sex as a factor and ln(centroid size) as the covariate indicated sexual shape dimorphism. Separate multivariate regressions of Procrustes residuals on ln(centroid size) for each sex indicated that allometry accounts for ~52–54% of the total sample shape variance. Comparisons of ontogenetic shape change between sexes indicate that sexual shape dimorphism is minimal and of uncertain biological significance. Groupings of multivariate regression coefficients by magnitude and sign suggest that allometric integration of the dermatocranium is not uniform over the dermatocranium. Principal component analysis of the landmark configurations corrected for sex and allometry yields a first principal component which describes shape variance concentrated in the posterolateral and posterior regions of the dermatocranium, and again is indicative of non-uniform shape variation over the dermatocranium. Our findings for P. hernandesi indicate that the adult shape of the dermatocranium may contribute to a passive defence against predation. We hypothesize that the complexity in dermatocranial shape demonstrated here for P. hernandesi indicates parcellation of shape variance, which may contribute to explanations of the pronounced dermatocranial disparity exhibited by the species of Phrynosoma.     

Model checking in regression via dimension reduction

Lack-of-fit checking for parametric and semiparametric modelsis essential in reducing misspecification. The efficiency ofmost existing model-checking methods drops rapidly as the dimensionof the covariates increases. We propose to check a model byprojecting the fitted residuals along a direction that adaptsto the systematic departure of the residuals from the desiredpattern. Consistency of the method is proved for parametricand semiparametric regression models. A bootstrap implementationis also discussed. Simulation comparisons with several existingmethods are made, suggesting that the proposed methods are moreefficient than the existing methods when the dimension increases.Air pollution data from Chicago are used to illustrate the procedure.     

An adaptive test for a subset of coefficients in a multivariate regression model

An adaptive multivariate test is proposed for a subset of regression coefficients in a linear model. This adaptive method uses the studentized deleted residuals to calculate an appropriate weight for each observation. The weights are then used to compute Wilk's lambda for the weighted model. The adaptive test is performed by permuting the independent variables corresponding to those parameters that are assumed to equal zero in the null hypothesis. The permuted variables are then weighted to obtain a permutation test statistic that is used to estimate the p-value. An example is presented of a multivariate regression that uses systolic and diastolic blood pressure as dependent variables with age and body mass index as independent variables. The simulation results show that the adaptive test maintains its size for the three multivariate error distributions that were used in the study. For normal error models the power of the adaptive test nearly equaled that of the non-adaptive test. For models that used non-normal errors the adaptive test was considerably more powerful than the traditional non-adaptive test.     

Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structurefor multivariate failure-time data. Estimation of some jointquantities can be highly sensitive to the assumed parametricform, and hence model fit is an important issue. This paperlays out a general diagnostic framework for evaluating and selectingfrailty and copula models. The approach is based on the cumulativesum of residuals that are calculated in bivariate time. Theresiduals reflect the difference between the observed and expectedbivariate association structures. The proposed model-checkingprocess is interpretable with a limiting distribution whichcan be approximated using the bootstrap. Simulations and a dataexample illustrate the practical application of the method.     

Spatial Autocorrelation Approaches to Testing Residuals from Least Squares Regression

In geo-statistics, the Durbin-Watson test is frequently employed to detect the presence of residual serial correlation from least squares regression analyses. However, the Durbin-Watson statistic is only suitable for ordered time or spatial series. If the variables comprise cross-sectional data coming from spatial random sampling, the test will be ineffectual because the value of Durbin-Watson’s statistic depends on the sequence of data points. This paper develops two new statistics for testing serial correlation of residuals from least squares regression based on spatial samples. By analogy with the new form of Moran’s index, an autocorrelation coefficient is defined with a standardized residual vector and a normalized spatial weight matrix. Then by analogy with the Durbin-Watson statistic, two types of new serial correlation indices are constructed. As a case study, the two newly presented statistics are applied to a spatial sample of 29 China’s regions. These results show that the new spatial autocorrelation models can be used to test the serial correlation of residuals from regression analysis. In practice, the new statistics can make up for the deficiencies of the Durbin-Watson test.     

大熊猫双胞胎生长发育影响因素的研究

为了研究影响大熊猫Ailuropoda melanoleuca双胞胎生长发育的因素,以2013—2016年成都大熊猫繁育研究基地出生的22对大熊猫双胞胎幼仔及其母兽为研究对象,分析母兽孕期增重、双胞胎个体性别和双胞胎性别类型与大熊猫双胞胎幼仔初生体质量之间的关系,以及双胞胎个体性别和大熊猫幼仔初生体质量与1~12月龄大熊猫幼仔体质量之间的关系。结果显示,不同双胞胎性别类型的大熊猫幼仔初生体质量的差异有统计学意义(P=0.015),但母兽孕期增重、双胞胎个体性别与幼仔初生体质量的差异无统计学意义(P=0.257、P=0.170);双胞胎2只个体的初生体质量不同(χ^2=9.043,P=0.041),且双胞胎性别类型与幼仔初生体质量差异程度呈中等强度相关(Cramer s V=0.492,P=0.030),双雌性双胞胎初生体质量差异为20%~40%(调整后标化残差:2.30),双雄性双胞胎初生体质量差异小于20%(调整后标化残差:2.60);双胞胎个体性别和初生体质量对1~12月龄大熊猫幼仔生长发育的影响无统计学意义(P>0.05)。对大熊猫双胞胎幼仔生长发育影响因素的研究,为大熊猫双胞胎的饲养管理提供理论依据。     

Distribution ofUrtica dioica L. andRubus fruticosus L. (+agg.) in relation to edaphic factors in cultivated poplar woods

Urtica dioica L. andRubus fruticosus L. (+agg.) are widely distributed in Belgian cultivated poplar woods. Using adjusted standardized residuals as an objective measure of preference of a species for ecoparameters, it seems possible to describe the distribution betweenUrtica andRubus as coincidental as regards ecological considerations. Both plant species behave obviously as antagonists.