Packaging of offspring by nests of the ant,Leptothorax longispinosus: parent-offspring conflict and queen-worker conflict

Models of the packaging of offspring predict that parental fitness is maximized by following a set of rules, including the rule to invest the minimal amount in each offspring. Offspring can maximize their fitness by demanding more resources than the parent is selected to give, leading to parent-offspring conflict over packaging. Social insect nests may also experience queen-worker conflict over packaging. Experiments were conducted, using two populations of the ant Leptothorax longispinosus, in order to determine the role of both parent-offspring conflict and queen-worker conflict in packaging. Parent-offspring conflict over packaging was detected towards males and workers, but not to females. This may be because both parental and offspring fitness are maximized by investing as much in possible in females so both parties benefit by cooperating over packaging of females. Queen-worker conflict over packaging was detected for females, males, and workers. The direction taken by the queen-worker conflict is best explained by asymmetries in genetic relatedness among nestmates.     

Estimation of heritability by parent-offspring regression

Summary The implications of bias due to previous inbreeding of parents and genotype x environmental interaction on narrow sense heritability (h²) estimates by parent-offspring regression are enumerated. To remove the bias caused by genotype x environment interaction, an analysis of covariance model could be used. In special cases, where phenotypic expression is a result of two organisms interacting, such as in symbiotic N₂ fixation, an analysis of covariance model with a test of heterogeneity of slopes is recommended. When host genotype x strain interactions are significant, separate heritability estimates for each strain are suggested to take advantage of genotype x strain interaction, which may be a major factor contributing to the expression of N₂ fixation traits.     

Bias of maximum likelihood estimator of intraclass correlation

Summary A bias correction was derived for the maximum likelihood estimator (MLE) of the intraclass correlation. The bias consisted of two parts: a correction from MLE to the analysis of variance estimator (ANOVA) and the bias of ANOVA. The total possible bias was always negative and depended upon both the degree of correlation and the design size and balance. The first part of the bias was an exact algebraic expression from MLE to ANOVA, and the corrected estimator by this part was ANOVA. It was also shown that the first correction term was equivalent to Fisher's reciprocal bias correction on hisZ scores. The total possible bias of MLE was large for small and moderate samples. Relative biases were larger for small parametric values and vice versa. To ensure a relative bias less than 10% assuming an intraclass correlation of 0.025, which is not unusual in most of the animal genetic studies, the total number of observations (N) should be not less than 500. From a design point of view, minimum bias occurred atn = 2, the minimum family size possible, underN fixed.     

Parameter Estimation for Partially Complete Time and Type of Failure Data

The theory of competing risks has been developed to asses a specific risk in presence of other risk factors. In this paper we consider the parametric estimation of different failure modes under partially complete time and type of failure data using latent failure times and cause specific hazard functions models. Uniformly minimum variance unbiased estimators and maximum likelihood estimators are obtained when latent failure times and cause specific hazard functions are exponentially distributed. We also consider the case when they follow Weibull distributions. One data set is used to illustrate the proposed techniques. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种基于数学期望的亲子与同胞相关系数的估计方法

本文在对亲本平方和、子代同胞间平方和、同胞内平方和与亲子间乘积和求数学期望的基础上,估计亲子与同胞相关系数,导出了两套不同的亲子与同胞相关系数的估计公式,其中之一与Srivastava（1984）提出的完全一致,但估计方法较之具有直接性,推导过程得到了简化．     

Notes on interval estimation of the gamma correlation under stratified random sampling

We have developed four asymptotic interval estimators in closed forms for the gamma correlation under stratified random sampling, including the confidence interval based on the most commonly used weighted‐least‐squares (WLS) approach (CIWLS), the confidence interval calculated from the Mantel‐Haenszel (MH) type estimator with the Fisher‐type transformation (CIMHT), the confidence interval using the fundamental idea of Fieller's Theorem (CIFT) and the confidence interval derived from a monotonic function of the WLS estimator of Agresti's α with the logarithmic transformation (MWLSLR). To evaluate the finite‐sample performance of these four interval estimators and note the possible loss of accuracy in application of both Wald's confidence interval and MWLSLR using pooled data without accounting for stratification, we employ Monte Carlo simulation. We use the data taken from a general social survey studying the association between the income level and job satisfaction with strata formed by genders in black Americans published elsewhere to illustrate the practical use of these interval estimators.     

Small Sample Comparison of Modified Chi‐Square Test Statistics for Survey Data

The problem of categorial data analysis in survey sampling arises because of non‐independence of sample elements of the sample obtained through imposed sampling design. In this article the performance of modified χ² statistic for testing independence of attributes have been evaluated for small sample sizes with the help of log‐linear models with respect to its achieved level of significance for fixed nominal level at 5%, through simulation technique. It hase been observed that the perfiormance of these test statistics depends on average and coefficient of variation of eigen values of design effect matrix. The first order corrected statistic is able to capture the effect of sampling design to a great extent but the performance of second order corrected statistic is much better. Further, these modified χ² test statistics were applied to a real survey data and their performance were evaluated with respect to their achievied level of significance.     

Mixed Moment Estimation in Hermite Distribution and its Comparison with Other Estimation Procedures from Sample Size Considerations

In this paper (1) expressions (correct to n^?2 terms) for biases, variances, and covariances of the estimators a and b of Hermite distribution with probability generating function Exp[a(t–1) + b(t–1)] are obtained for two mixed moment estimates; (2) for the biases and variance-covariances, approximate regions of the parameter space (a>0, b>0) have been outlined where a sample of size 100 can be considered as “safe” in the sense that contribution of second order terms in them is 5% of that from the first order term; (3) comparison of the biases and variance-covariances of these two sets of estimators are made with those for the moment estimators, maximum likelihood estimates and the even point estimators for a sample of size 100 using the terms up to order n^?2; (4) the comparisons based on n^?2 terms in (3) have not only provided information on the estimation procedures included in the Hermite distribution, but also demonstrated the importance of higher order terms in the sampling properties of the various alternative techniques for the Hermite distribution.     

Genetic structure of the Saguenay, 1852-1911: evidence from migration and isonymy matrices

The Saguenay is a region in northeastern Québec populated in the second half of the 19th century through migration from other parts of Québec. The present-day population of nearly 300,000 is the result of both immigration and high rates of intrinsic growth. This population has been of interest to geneticists because of the high incidence of certain hereditary diseases, notably spastic ataxia, tyrosinemia, agenesis of the corpus callosum, vitamin D-dependent rickets, and myotonic dystrophy. Parent-offspring migration and isonymy matrices were used to estimate random kinship using the Malécot model for six 10-year time periods from 1852-1911. Comparisons between two estimates of kinship--one from parent-offspring migration matrices (phi) and the other from isonymy (R)--and geographic distance were made using both product-moment and Mantel correlation. Comparisons of within- and between-subdivision kinship were made using nonparametric and Mantel correlation. Within-subdivision kinship from the phi matrix was also compared with kinship estimated from marriage dispensations for endogamous marriages. The estimates of random kinship from the parent-offspring matrices showed a good fit with geography. However, isonymy did not correlate well with geographic distance; and phi and R showed no correlation until the last two time periods, and the diagonal of phi did not correlate with the marriage dispensations. Examination of scatterplots of phi vs. R suggests that nonrandom migration during the process of settlement formation is responsible for the lack of correlation. While movement across space seems to be highly dependent on distance, nonrandom selection of migrants means that between-subdivision estimates of kinship based on migration are not congruent with those obtained by other methods. On the whole, genetic differentiation seems to have been low due to the high levels of movement between subdivisions and immigration. The weak dependence of genetic structure on geographic distances in the present population is demonstrated by mapping the geographic distribution of cases of three recessively inherited diseases.     

Sample Size Considerations for GEE Analyses of Three‐Level Cluster Randomized Trials

Summary Cluster randomized trials in health care may involve three instead of two levels, for instance, in trials where different interventions to improve quality of care are compared. In such trials, the intervention is implemented in health care units (“clusters”) and aims at changing the behavior of health care professionals working in this unit (“subjects”), while the effects are measured at the patient level (“evaluations”). Within the generalized estimating equations approach, we derive a sample size formula that accounts for two levels of clustering: that of subjects within clusters and that of evaluations within subjects. The formula reveals that sample size is inflated, relative to a design with completely independent evaluations, by a multiplicative term that can be expressed as a product of two variance inflation factors, one that quantifies the impact of within‐subject correlation of evaluations on the variance of subject‐level means and the other that quantifies the impact of the correlation between subject‐level means on the variance of the cluster means. Power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total, when data were analyzed using bias‐corrected estimating equations for the correlation parameters in combination with the model‐based covariance estimator or the sandwich estimator with a finite sample correction.     

Estimation of stature from long bones utilizing the line of organic correlation

Estimation of stature from skeletal measurements is of great interest in some studies, e.g. in forensic anthropology, where victims have to be identified. A problem occurring in practice is that the individual whose stature has to be assessed is in general from an unknown population. Alternatives to ordinary least squares regression are discussed. Application of available information about stature/long bone proportions leads to a general proposal called thethe weighted line of organic correlation, which is fitted to a wide range of populations. The effects of sex and race upon this line are practically negligible. These properties makes it suitable for use not only for forensic purposes, but also for the estimation of stature based on skeletons or skeletal populations from the past.     

Bayesian Estimation in a Generalized Negative Binomial Distribution

A generalized negative binomial (GNB) distribution was introduced by JAIN and CONSUL (1971) and was modified by NELSON (1975). The probability function of the distribution is defined by the function p(x; m, β, θ)= θ^x (1 - θ)^m+βx—x for x=0, 1, …, and zero otherwise, where m>0, 0<θ<1 and β=0 or 1≦β<θ^?1. The Bayes estimators for a number of parametric functions of θ when m and β are known are derived. The prior information on θ may be given by a beta distribution, B(a, b), to which no subjective significance is attached. It has been illustrated that the parameters in the prior distribution can be assigned by a computer. Comparisons are made of the Bayes estimate of P(X=k) to the corresponding ML estimate and the MVU estimate for any given sample to the order n^?1 for different values of k..     

On a restricted occupancy model and its applications

With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould-Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.     

Estimation of the correlation between nutrient intake measures under restricted sampling

Food frequency questionnaires (FFQs) are commonly used to assess dietary intake in epidemiologic research. To evaluate the FFQ reliability, the commonly used approach is to estimate the correlation coefficient between the data given in FFQ and those in food records (for example, 4-day food records [4DFR]) for nutrients of interest. However, in a dietary intervention study, a criterion for eligibility may be to select participants who have baseline FFQ-measured dietary intake of percent energy from fat above a prespecified quantity. Other instruments, such as the 4DFR, may be subsequently administrated only to eligible participants. Under these circumstances, analysis without adjusting for the restricted population will usually lead to biased estimation of correlation coefficients and other parameters of interest. In this paper, we apply likelihood-based and multiple imputation (MI) methods to accommodate such incomplete data obtained as a result of the study design. A simulation study is conducted to examine finite sample performance of various estimators. We note that both the MI estimate and the maximum likelihood (ML) estimate based on a bivariate-normal model are not sensitive to departures from this normality assumption. This led us to investigate robustness properties of the ML estimator analytically. We present some data analyses from a dietary assessment study from the Women's Health Initiative to illustrate the methods.