Defining the linear portion of a sigmoid‐shaped curve: bend points

Formulae are provided that define the ‘bend points’, the beginning and end of the essentially linear dose–response region, for the four‐parameter logistic model. The formulae are expressed in both response and dose units. The derivation of the formulae is shown in order to illustrate the general nature of the methodology. Examples are given that describe how the formulae may be used while planning and conducting bioassays. Copyright © 2003 John Wiley & Sons, Ltd.     

A Numerical Solution to the Nonhomogeneous Two-Stage MVK Model of Cancer

In this article, we describe a straightforward method for solving the probability of at least one malignant cell by time t, and the associated hazard function, in the general (i.e., nonhomogeneous) two-stage Moolgavkar-Venzon-Knudson (MVK) model of cancer. The method consists of solving four coupled ordinary differential equations derived from the Kolmogorov backward equations for this process. The relationship of this method to previously proposed solutions is discussed.     

Joint Attention,Self‐Recognition,and Neurocognitive Function in Toddlers

Recent studies have attempted to understand the processes involved in joint attention because of its relevance to both atypical and normal development. Data from a recent study of young children with autism suggests that performance on a delay nonmatch to sample (DNMS) task associated with ventromedial prefrontal functions, but not an A‐not‐B/delayed response task associated with dorsolateral prefrontal cortex, was related to joint attention skills (Dawson et al., 2002). Recent research also suggests that joint attention is associated with dorsalmedial brain systems linked to self‐monitoring (Mundy, 2003). This study investigated the relations among joint attention, DNMS, and self‐recognition performance in a longitudinal study of 39 normally developing toddlers from 14 to 18 months. The results indicated that development on the DNMS and self‐recognition tasks, but not a means end task, predicted joint attention at 18 months. Further analysis showed that the model was only significant for initiating joint attention (IJA). The implications of these results for the neuro‐development of IJA are discussed.     

A comparison of indicators for evaluating x-11-arima seasonal adjustment

Summary The evaluation of the performance of seasonal adjustment procedures is an issue of practical importance in view of the unobservable nature of the components. Looking at just one indicator when judging the overall quality of a procedure may be misleading, even though this is common practice when many series are involved. The main purpose of this paper is to compare the information content of different synthetic indicators with reference to the X-11-ARIMA procedure. Sixty-six different types of monthly seasonal series are generated and the seasonal component then extracted by carrying out X-11-ARIMA with standard options. The correlation between the pseudo-true error for each series and various synthetic indicators allows us to compare the latter's reliability, under both the hypotheses of minimum and maximum variance of the pseudo-true seasonal component. We show that the overall quality indexQ-the indicator most commonly adopted by users of the X-11-ARIMA-is always outperformed by the simpler diagnostics based on the stability of the estimates. In particular, the “sliding-spans” indicator, proposed by Findley et al. (1990) and included in the diagnostics of the new X-12 procedure, shows a much stronger correlation with the pseudo-true error in the seasonal adjustment. We also show that the total forecasting errors in the one-year-ahead extrapolation of the seasonal component have a good informative power and perform almost as well as the “sliding-spans” indicator.     

Improving on truncated linear estimates of exponential and gamma scale parameters

We consider the problem of estimating the scale parameter of an exponential or a gamma distribution under squared error loss when the scale parameter θ is known to be greater than some fixed value θ₀. Natural estimators in this setting include truncated linear functions of the sufficient statistic. Such estimators are typically inadmissible, but explicit improvements seem difficult to find. Some are presented here. A particularly interesting finding is that estimators which are admissible in the untruncated problem which take values only in the interior of the truncated parameter space are found to be inadmissible for the truncated problem.     

Exploring structure-effectiveness relationships in nonprofit arts organizations

The authors examined nineteen nonprofit performing arts organizations, investigating the distribution of influence among organizational members, the grouping of volunteers and staff in organizational structures, and the effectiveness of the organizations. The organizations' effectiveness was assessed using multiple performance indicators. The analysis revealed five groupings or configurations of influence, which correlated to the organizations exhibiting the highest and lowest levels of organizational effectiveness. The authors conclude that a variety of structures are associated with good performance but structural dysfunctions are associated with organizational failure, and that members' commitment to an organization's structure is an important element of success.     

Leslie matrix models

A review of the Leslie matrix model theory and its literature 1941-1987 is presented. The point of view is that of a mathematician who focuses on the parts of the theory which are relevant to demography. Works of a decidedly applied nature are not dealt with.     

The impact of social networks on the occupational status of migrants

This paper postulates that there is a continuous exchange of information and knowledge between those who share the common bond of having migrated to the US. The individual components of this information exchange constitute social networks. The 2 hypotheses tested are 1) immediate social networks and people known in the US facilitate the flow of information both to new migrants and between established migrants, thus promoting upward social mobility; and 2) access to broader network ties, organization membership, extra-ethnic friendships, and familiarity with established institutions smooths the transition process, resulting in increased social position. The data used comes from a study conducted in 1982-1983 in 4 Mexican sending communities (2 rural, 2 urban), for a total of 440 migrants. Results show that migrants in every socioeconomic bracket reported access to some or all social network characteristics. There was contact with either a family member or acquaintances from the migrants' town of origin. Over 50% of migrants reported knowing many fellow townspeople. Twice as many migrants belong to a sports club as to a social or religious organization. Very few rural migrants report knowing no townspeople, while 32% of urban migrants claim no knowledge of fellow migrants from their town of origin. Urban origin migrants report more contacts with those of other ethnicity than rural migrants. Those employed in agriculture are least acquainted with social information and contacts, while those in skilled and service sectors are well acquainted with them. The results of fact and analysis show that 1) access to personal US networks results in an average 4.4 point advantage in occupational prestige scores over no access, and 2) utilizing institutional US networks combined with any cumulative US experience gives a migrant a 5 point advantage over a fellow migrant with identical experience level but no institutional network contacts. This is also true for institutional Mexican networks. Thus success or failure in migrating is partly due to migrants' societal infrastructure and the fact that available information and social networks are accessed and utilized differently by different migrants.     

Policies over time and pareto optimality

This paper is concerned with sequences of policies that occur over time in voting models and planning procedures. The framework for our analysis includes assumptions that are satisfied by models in the corresponding literatures, together with other standard assumptions for microeconomic analysis that involve time. The starting point for our analyses is the prespective that results from combining the following (widely held) views: 1) certain voting models and planning procedures can be interpreted as being non-tatonnement or sequential processes (where each policy in the sequence that is generated is actually experienced by voters or consumers) and 2) an alternative being Pareto optimal in any given period (temporal Pareto optimality) is the appropriate efficiency criterion only if the alternative is the final outcome from a tatonnement process-and that, otherwise, one should examine the efficiency of the entire path (using intertemporal Pareto optimality). Our first observation about the planning literature is that is has (by and large) neglected the efficiency criterion that is appropriate for the discrete-time procedures that can be interpreted as non-tatonnement or sequential processes-and that, what's more, such trajectories will (in general) fail to meet this criterion. Our second observation identifies some results that can be used to establish that some of these trajectories will at least be ultimately intertemporally Pareto optimal. In our discussion of voting theory, we review Buchanan's opposition to requiring (social) choice consistency for voting procedures-and his argument for this position on (Pareto) efficiency grounds. We then consider voting procedures that can be interpreted as non-tatonnement or sequential processes and arrive at the conclusion that, in these cases, (i) majority rule cycles are intertemporally Pareto inefficient and (ii) achieving intertemporal Pareto optimality requires choice consistency. We then go on to show that related observations apply to Kramer's normative conclusions about his dynamical model of political equilibrium — and identify some further references where similar observations apply. In the final part of our discussion of voting models, we arrive at the further conclusion that, in the most relevant cases, a trajectory that stays in the temporal Pareto set is not necessarily more desirable (on efficiency grounds) than one that doesn't.This paper has been improved by helpful comments and suggestions that have been provided by Kenneth Arrow, an anonymous referee, and the editor who handled the paper.Peter Coughlin gratefully acknowledges financial support provided by (i) National Science Foundation Grant No. SES-8409352, and (ii) the Center for Advanced Study in the Behavioral Sciences at Stanford (with support from National Science Foundation Grant No. BNS-8700864 and the Alfred P. Sloan Foundation).     

Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a multi-profile context. Harsanyi was contented with showing that if the individuals' utilities u _i are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u _i. We provide a related conclusion by considering u as functionally dependent on the u _i, through a suitably restricted social welfare functional (u ₁,...,u _n)u=f(u ₁,...,u _n). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's single-profile theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the u _i discussed by Fishburn as a corollary to harsanyi's theorem.The authors are indebted to L. Haddad, A. Sen and two anonymous referees for useful written comments. They also benefited from stimulating remarks in seminars and helpful conversations with their colleagues. The usual caveat of course applies. One of the authors acknowledges partial financial support from the ARI Communication of the C.N.R.S., Paris.