A New Rank Test Against Ordered Alternatives in K-Sample Problems

The distribution-free test against ordered alternatives proposed by Jonckheere (1954) is based on the Kendall's rank correlation coefficient τ. A new rank test is proposed and illustrated with a numerical example. The proposed test is based on Spearman's σ and has similar functional structure as the Kruskal-Wallis test. A useful by-product is a test for departure from a trend.     

Dissimilarity for partially ranked data and its application to cover-abundance data

Cover-abundance estimates are commonly employed in phytosociological investigations to record the performance of species. Because the coded values are on an ordinal scale of measure, various authors have suggested that some transformation is necessary before such values can be used for classification and ordination. However, it is not clear that transformation is a sufficient treatment, and it would seem preferable to use ordinal data directly. In this paper we examine such direct use of partial rankings and show that several dissimilarity measures can be defined for this case without invoking any transformations. They include dissimilarity measures associated with various rank correlation measures and with distances between strings; all the measure are variant forms of Hausdorf's interset distance. Certain other kinds of data, such as those employing dominant and subdominant species and the dry-weight-rank estimation of biomass, are also on an ordinal scale and could be analysed using similar techniques.To illustrate the approach, a string dissimilarity measure is used to analyse a set of data from Slovakian grasslands which appear to reflect a simple gradient. The original data were recorded with 10 classes of performance and are analysed using hierarchical and nondeterministic, overlapping, classifications.     

A brief report on the social behavior of the crested mangabey (Cercocebus galeritus galeritus) with a comparison to the sooty mangabey (C. torquatus atys)

A group of 38 free ranging crested mangabeys in the Tana River Primate Reserve was studied over a 6-week period for a total of 209.5 hr and behavioral comparisons made to a captive group of sooty mangabeys. Although quantitative comparisons between these two mangabey species are not possible, the present data suggest that these geographically separated mangabeys share several behavioral similarities. Copulatory behavior in both species involved a pattern of female darting and female vocalizing following the mount by the male. Several similarities in agonistic behavior also existed: 1) The victim often returned or stayed within 1 m of the aggressor following an agonistic episode; 2) retaliation in which the victim first fled or avoided the aggressor, then subsequently, chased or lunged at the aggressor, typically while screaming; and 3) frequent redirection of aggression by the victim following an agonistic episode. A dominance rank reversal occurred between the two adult male crested mangabeys with no severe wounding. The rank reversal seemed to be related to two subsequent behaviors which included infant carriage by the deposed alpha in the presence of the new alpha male and female demonstrations of extreme protectiveness of their infants in the presence of the new alpha male. Both of these behaviors have been reported in the sooty mangabey group.     

Rank and age related feeding strategy observed through field experiments in the Koshima group of Japanese macaques

The feeding process of Japanese monkeys on soy beans which were scattered over a sandy beach on Koshima islet was studied. Younger monkeys were able to pick up more beans when 8 kg of beans were divided and given two times (“two times feeding”) than when the whole amount (8 kg) of beans was given at one time (“one time feeding”). The effect of saturation of the food intake capacity in younger monkeys at the first feeding in “two times feeding” did not appear at the second feeding one hour later. The minutely intake of soy beans (feeding speed) for each age class was analyzed. The decline of feeding speed in adult females after the peak in “one time feeding” was not related to the decline in density of beans on the ground, and this decline was caused by saturation of their food intake capacity. Adult females were divided into four classes according to their dominance rank order: high, lower-high, higher-low, and low classes. The total amount of intake in “one time feeding” was far larger in the high class than in any of the other classes. The total amount of feeding in the first feeding of “two times feeding” increased in accordance with rise in the dominance rank class, and there was no relation to rank and total feeding amount in the second feeding of “two times feeding.” Differences existed in the process of feeding between the rank classes. The feeding speed of the low class was as high as that of the high class on the curve of minutely intake, while the low class stopped feeding much earlier than the high class. The lower-high class displayed a low feeding speed, and stopped feeding the latest. The order of the duration to stay and to feed in the feeding area was lower-high > high > higher-low > low, and this order did not change under the three different feeding conditions, “one time feeding,” and the first and second feedings of “two times feeding.” Adolescent females tended to stay the longest duration in the feeding area among all age classes. Both the lower-high class females and adolescent females had an unstable social status in the Koshima group, and their social status affected their feeding behaviors. The feeding behaviors were similar in attitude depending on social status, and are considered to be maintained for a fairly long time. The feeding strategy of the lower-high class, in staying a longer duration in the artificial feeding area, and departing later, may be effective under the artificial feeding conditions, but it may be a bad strategy in a natural habitat where the food is not so clumped as in artificial feeding, and where choice of other food patches is possible. The above results agree well with previous reports for the Koshima group, indicating that the rank of the lower-high class females was unstable (Mori et al., 1989), and that their reproductive success was low (Watanabe et al., 1992).     

Modeling multivariate survival data by a semiparametric random effects proportional odds model

In this article, the focus is on the analysis of multivariate survival time data with various types of dependence structures. Examples of multivariate survival data include clustered data and repeated measurements from the same subject, such as the interrecurrence times of cancer tumors. A random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model. The distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log-odds function. This class of models, which includes the usual shared random effects model, the additive variance components model, and the dynamic random effects model as special cases, is highly flexible and is capable of modeling a wide range of multivariate survival data. A unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal-likelihood approach. Unlike the fully parametric case, the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects. The marginal likelihood is approximated by the Monte Carlo method. Simulation studies are carried out to investigate the performance of the proposed method. The proposed method is applied to two well-known data sets, including clustered data and recurrent event times data.     

Reproductive Constraints on Dominance Competition in Male Homo Sapiens

Dominance competition among males of the same group is characteristic for most primates including humans, with the outcome—rank—being positively associated with fitness. However, because we do not observe an evolutionary arms race toward hyperdominance in primate social systems, the evolution of ever more dominating behavior characteristics may be checked by increased costs in fitness to top rank. Empirical evidence for such costs, particularly in humans, however, is almost nonexistent. Here, for the first time, we can demonstrate for a cohort of male humans, military officers, all graduates of the class of 1950 of the U.S. Military Academy, constituting a closed and cohesive social group, that competitive qualities leading to top rank may have a negative effect on fitness.     

A Global View on Parametric and Nonparametric Approaches to the Analysis of Ordered Categorical Data

Rank approaches are very common in the analysis of ordered categorical data but can only be interpreted on an experiment‐wise level. Therefore, parametric tests from linear models, although based on metric structures, are used frequently to analyze this type of data. So the questions arise 1. what parametric tests measure in this context and 2. whether the rank approach could be modified to achieve a global level of interpretation. A possible solution to question 2. offers the so called ridit approach, which is based on known reference distributions. In this paper we discuss a global view that shows how rank analysis and ridit analyses are related and how parametric procedures fit into the same framework. The use of the uniform distribution as a reference in the ridit approach gives an explanation to question 1. The asymptotic multivariate normality of the effect estimators is shown and robust test statistics are discussed. Type I and type II error rates are examined in simulation studies and the approach is applied to a toxicological example. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)