Perturbation Selection and Local Influence Analysis for Nonlinear Structural Equation Model

Local influence analysis is an important statistical method for studying the sensitivity of a proposed model to model inputs. One of its important issues is related to the appropriate choice of a perturbation vector. In this paper, we develop a general method to select an appropriate perturbation vector and a second-order local influence measure to address this issue in the context of latent variable models. An application to nonlinear structural equation models is considered. Six perturbation schemes are investigated, including three schemes under which simultaneous perturbations are made on components of latent vectors to assess the influence of these components and pinpoint the influential ones. The proposed procedure is illustrated by artificial examples and a simulation study as well as a real example.     

Naive Analysis of Food Web Dynamics: A Study of Causal Judgment About Complex Physical Systems

When people make judgments about the effects of a perturbation on populations of species in a food web, their judgments exhibit the dissipation effect: a tendency to judge that effects of the perturbation weaken or dissipate as they spread out through the food web from the locus of the perturbation. In the present research evidence for two more phenomena is reported. Terminal locations are points in the food web with just a single connection to the rest of the web. Judged changes tended to be higher for species at terminal locations than for species the same distance from the perturbation but at nonterminal locations. Branches are points in the web where a route splits into two or more routes. Judged changes tended to be lower for species following branching points than for species the same distance from the perturbation but not following branching points. It is proposed that the findings can be explained as effects of a mental model employing concepts of influence and resistance. Under this model a perturbation is a change in energy level at a point in the system that acts as an influence affecting the rest of the system. The basic concepts in this model are domain‐general and on that basis it is predicted that the dissipation effect should be found in judgments of any physical system to which notions of influence and resistance can be applied.     

Effect of body configuration at step contact on balance recovery from sideways perturbations

Compensatory stepping is an important protective mechanism to prevent falling. To recover from sideways perturbations side steps are generally more advantageous than cross-over steps. However, there is lack of understanding of the characteristics of compensatory side steps following sideways perturbations that separate successful recoveries (i.e., no falls) from falls, the most clinically relevant outcome following a balance perturbation. We aimed to identify the critical determinants for successful side stepping after large sideways balance perturbations. Twelve healthy young adults were subjected to large leftward perturbations at varying intensities on a translating sheet. For recovery attempts started with a side step, we determined body configuration variables (frontal-plane leg and trunk angle) at first step contact, as well as spatiotemporal step variables (onset, length, duration, velocity). A logistic regression analysis was conducted to determine the predictive ability of body configuration and spatiotemporal variables on the probability of success (no fall vs. fall); perturbation intensity (peak jerk of translating sheet) and a random effect for individual were also included in the model. In the final model, leg angle and peak jerk were retained as predictors of successful balance recovery and these variables correctly classified the recovery outcome in 86% of the trials. This final ‘body configuration’ model yielded a −2 log likelihood of −36.3, whereas the best fitting model with only spatiotemporal variables yielded a −2 log likelihood of −45.8 (indicating a poorer fit). The leg angle at a given perturbation intensity appears to be a valid measure of reactive side step quality. The relative ease of measuring this leg angle at step contact makes it a candidate outcome for reactive stepping assessments in clinical practice.     

The DINA model as a constrained general diagnostic model: Two variants of a model equivalency

The ‘deterministic‐input noisy‐AND’ (DINA) model is one of the more frequently applied diagnostic classification models for binary observed responses and binary latent variables. The purpose of this paper is to show that the model is equivalent to a special case of a more general compensatory family of diagnostic models. Two equivalencies are presented. Both project the original DINA skill space and design Q ‐matrix using mappings into a transformed skill space as well as a transformed Q ‐matrix space. Both variants of the equivalency produce a compensatory model that is mathematically equivalent to the (conjunctive) DINA model. This equivalency holds for all DINA models with any type of Q ‐matrix, not only for trivial (simple‐structure) cases. The two versions of the equivalency presented in this paper are not implied by the recently suggested log‐linear cognitive diagnosis model or the generalized DINA approach. The equivalencies presented here exist independent of these recently derived models since they solely require a linear – compensatory – general diagnostic model without any skill interaction terms. Whenever it can be shown that one model can be viewed as a special case of another more general one, conclusions derived from any particular model‐based estimates are drawn into question. It is widely known that multidimensional models can often be specified in multiple ways while the model‐based probabilities of observed variables stay the same. This paper goes beyond this type of equivalency by showing that a conjunctive diagnostic classification model can be expressed as a constrained special case of a general compensatory diagnostic modelling framework.     

Decomposing the reaction time distribution: Pure insertion and selective influence revisited

This paper investigates the consequences of extending the assumptions of pure insertion and selective influence (popular in RT theorizing) to the level of the distribution. In the case of pure insertion and under the additional assumption that the additive random variable is exponentially distributed, a solution is obtained which not only allows estimation of the exponential-rate parameter but also provides a test of the assumptions. The result is shown to be applicable not only when processing is serial but also for certain parallel models. In addition, discrimination between self-terminating and exhaustive search strategies is provided, and in the case of either, both parameter estimation and tests of the model are possible. Extensions to nonexponential models are investigated and a general method of moments solution is outlined. In the case of selective influence a general nonparametric alternative to Sternberg's additive factor method is developed. The problem of empirical estimation and application is then considered. Simulations which place bounds on the type I and II error are reported. Finally the first theorem is provided an illustrative application with data from a memory scanning experiment. The results provide some support for the double assumption of pure insertion and that the additive random variable is distributed exponentially.     

Defining the boundary of childhood amnesia

When adults are asked to recall their earliest autobiographical memories most can recall nothing about their infancy and early childhood, a phenomenon commonly referred to as childhood amnesia. There is general consensus regarding the existence of childhood amnesia, but there remains considerable debate over its boundary. Most researchers have argued that the boundary of childhood amnesia occurs between the ages of 3 and 4 years, but in 1993 Usher and Neisser published a highly influential paper, which has subsequently been used to argue that the boundary may be as low as 2 years. In the present experiment we examined how changes in scoring criteria influence our estimates of the age of adults' earliest memories. We conclude that some coding criteria are more valid than others and that the best estimates of childhood amnesia will include measures of free recall in addition to the specific questions that have dominated prior research in this area.     

Local influence analysis of nonlinear structural equation models

By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis are computed via observations of the latent variables generated by the Metropolis-Hastings algorithm, while the diagnostic measures are obtained via the conformal normal curvature. Seven perturbation schemes, including some perturbation schemes on latent vectors, are investigated. The proposed procedure is illustrated by a simulation study and a real example. Acknowledgment: This research is fully supported by a grant (CUHK 4243/02H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are indebted to ICPSR and the relevant funding agency for allowing use of their data, and to the Editor and reviewers for their valuable comments for improving the paper.     

Defining the boundary of childhood amnesia

When adults are asked to recall their earliest autobiographical memories most can recall nothing about their infancy and early childhood, a phenomenon commonly referred to as childhood amnesia. There is general consensus regarding the existence of childhood amnesia, but there remains considerable debate over its boundary. Most researchers have argued that the boundary of childhood amnesia occurs between the ages of 3 and 4 years, but in 1993 Usher and Neisser published a highly influential paper, which has subsequently been used to argue that the boundary may be as low as 2 years. In the present experiment we examined how changes in scoring criteria influence our estimates of the age of adults’ earliest memories. We conclude that some coding criteria are more valid than others and that the best estimates of childhood amnesia will include measures of free recall in addition to the specific questions that have dominated prior research in this area.     

Two-Stage maximum likelihood estimation in the misspecified restricted latent class model

The maximum likelihood classification rule is a standard method to classify examinee attribute profiles in cognitive diagnosis models (CDMs). Its asymptotic behaviour is well understood when the model is assumed to be correct, but has not been explored in the case of misspecified latent class models. This paper investigates the asymptotic behaviour of a two-stage maximum likelihood classifier under a misspecified CDM. The analysis is conducted in a general restricted latent class model framework addressing all types of CDMs. Sufficient conditions are proposed under which a consistent classification can be obtained by using a misspecified model. Discussions are also provided on the inconsistency of classification under certain model misspecification scenarios. Simulation studies and a real data application are conducted to illustrate these results. Our findings can provide some guidelines as to when a misspecified simple model or a general model can be used to provide a good classification result.     

温度与攻击的研究回顾与展望

从人类攻击的一般理论模型出发,着重介绍了与温度有关的注意不足模型、社会公平模型、负面情绪矫正模型,阐述了热假说的有关研究和成果。最后分析了该研究领域存在的主要问题：(1)研究结果常相互矛盾,有的支持高温增加攻击行为,有的支持高温减少攻击行为。(2)实验室中的攻击与现实生活中的攻击有很大区别。(3)现场研究的数据中热效应与冷效应缺少对称。(4)目前学者的解释和研究未全面考察影响攻击行为的因素,因此需要综合探讨各种影响因素及它们的交互作用,并采用多种方法进行研究。     

Influence analysis for the factor analysis model with ranking data

Influence analysis is an important component of data analysis, and the local influence approach has been widely applied to many statistical models to identify influential observations and assess minor model perturbations since the pioneering work of Cook (1986) . The approach is often adopted to develop influence analysis procedures for factor analysis models with ranking data. However, as this well‐known approach is based on the observed data likelihood, which involves multidimensional integrals, directly applying it to develop influence analysis procedures for the factor analysis models with ranking data is difficult. To address this difficulty, a Monte Carlo expectation and maximization algorithm (MCEM) is used to obtain the maximum‐likelihood estimate of the model parameters, and measures for influence analysis on the basis of the conditional expectation of the complete data log likelihood at the E‐step of the MCEM algorithm are then obtained. Very little additional computation is needed to compute the influence measures, because it is possible to make use of the by‐products of the estimation procedure. Influence measures that are based on several typical perturbation schemes are discussed in detail, and the proposed method is illustrated with two real examples and an artificial example.     

Gender Effects in Couples' Sexual Decision Making and Contraceptive Use

Previous research has demonstrated that men tend to be more influential than women in mixed-sex dyads. The current study was an examination of sex differences in influence among dating couples making two different kinds of sexual decisions. In a laboratory decision-making task, male and female partners wrote their opinions about premarital sex and contraception independently, and then worked together as a couple to write a joint opinion. The results replicated previous findings in that the male partners' responses were more similar to the couples' responses than were the females'. An examination of gender influence in the couples' contraceptive behavior , however, indicated that the female partners were more influential than the males in this arena. Thus the data suggest that while men in general may be more influential than women in couples' decision making, there are specific decision domains in which women have considerable influence. Factors that influence gender effects in sexual decision making are discussed.     

Oscillations in Motor Priming: Positive Rebound Follows the Inhibitory Phase in the Masked Prime Paradigm

From among the diverse meanings of stability, the one the author adopts here is that the effects of a perturbation are opposed, and therefore small effects remain small. Except in linear systems, however, instability need not lead to unbounded motion and may actually be desirable when maneuverability is important. Moreover, properties of nerves, muscles, and tendons present serious challenges to stabilization. A review of observations from the motor control literature reveals that responses to perturbations in many common situations assist rather than resist the perturbation and are therefore presumably destabilizing. The observations encompass situations of position maintenance as well as impending or ongoing movement. The author proposes that the motor control system responds to a sudden perturbation by a pattern of muscle activity that mimics an accustomed voluntary movement, oblivious of stability considerations. What prevents runaway motion in the face of short-term instability appears to be voluntary intervention.     

The Individuality of Species: Some Reflections on the Debate

The thesis that species are individuals, and not classes as the traditional view had it, has been influential in the last 25 years. In this paper David Hull's arguments for the thesis are surveyed, as well as some counterarguments presented by Philip Kitcher. It is claimed that though species can be conceptualized as individuals, we are not compelled to view them in that way. The importance of the issue seems to have been somewhat exaggerated. However, it might happen that empirical findings concerning species selection would strengthen the case for the thesis, thereby rendering it straightforwardly empirical. The applicability of teleological explanation is suggested as a criterion for biological individuality. This revised version was published online in June 2006 with corrections to the Cover Date.     

Level of instigation and model similarity as determinants of aggressive behavior

A study was conducted to replicate and extend a finding by Wheeler and Levine [1967] indicating that a dissimilar model was more effective in inducing the contagion of aggression than a similar model. On the basis of recent findings suggesting the circumstances under which dissimilar others are more influential than similar others, the following predictions were derived: When subjects are highly instigated, dissimilar models can influence subjects to be more aggressive than can similar models; when subjects are under a low degree of instigation similar models will influence subjects to be more aggressive. Subjects presented their point of view on a case study in a three-person group discussion setting. Then subjects heard the second person (instigator) attack their position in a highly abusive or slightly abusive manner (High vs Low Instigation). Next subjects heard a third person, whom they had been led to believe was similar or dissimilar to themselves, attack the instigator (Similar vs Dissimilar Model). Finally subjects had an opportunity to express their feelings to the instigator. The results supported the predictions.     

Predicting Individual Score Elevation in an Applicant Setting: The Influence of Individual Differences and Situational Perceptions

Previous research has indicated that applicants can increase their scores on non‐cognitive measures by half of 1 standard deviation (e.g., Rosse, Stecher, Miller, & Levin, 1998 ; Viswesvaran & Ones, 1999 ). Two influential factors have been proposed to influence this elevation: individual differences and situational influences (e.g., Douglas, McDaniel, & Snell, 1996 ). The current study examined how individual differences and motivation (expectancy theory) predicted individual response elevation from a general to a job applicant context using a conscientiousness measure. Results indicated that elevation was primarily predicted by emotional stability, instrumentality, and the interaction between expectancy and instrumentality. Practical implications and future research directions are discussed.     

Multidimensional vector model of stimulus-response compatibility

The present study proposes and examines the multidimensional vector (MDV) model framework as a modeling schema for choice response times. MDV extends the Thurstonian model, as well as signal detection theory, to classification tasks by taking into account the influence of response properties on stimulus discrimination. It is capable of accounting for stimulus-response compatibility, which is known to be an influential task variable determining choice-reaction performance but has not been considered in previous mathematical modeling efforts. Specific MDV models were developed for 5 experiments using the Simon task, for which stimulus location is task irrelevant, to examine the validity of model assumptions and illustrate characteristic behaviors of model parameters. The MDV models accounted for the experimental data to a remarkable degree, demonstrating the adequacy of the framework as a general schema for modeling the latency of choice performance. Some modeling issues involved in the MDV model framework are discussed.     

Can Persistence be a Matter of Convention?

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories—having to do with reference, persistence conditions, how they relate, and the epistemology of persistence—are revealed.     

I like it, but I'm not sure why: can evaluative conditioning occur without conscious awareness?

There is good evidence that, in general, autonomic conditioning in humans occurs only when subjects can verbalize the contingencies of conditioning. However, one form of conditioning, evaluative conditioning (EC), seems exceptional in that a growing body of evidence suggests that it can occur without conscious contingency awareness. As such, EC offers a unique insight into what role contingency awareness might play in associative learning. Despite this evidence, there are reasons to doubt that evaluative conditioning can occur without conscious awareness. This paper aims to critically review the EC literature and to draw some parallels to what is known about autonomic conditioning. In doing so, some important general issues about measuring contingency awareness are raised. These issues are illustrated with a brief report of an experiment in which a sensitive measure of contingency awareness is compared against a commonly used measure.     

On local influence analysis of full information item factor models

The full information item factor (FIIF) model is very useful for analyzing relations of dichotomous variables. In this article, we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the FIIF model. The development is based on a Q-displacement function which is closely related with the Monte Carlo EM algorithm in the ML estimation. In the E-step of this algorithm, the conditional expectations are approximated by sample means of observations simulated by the Gibbs sampler from the appropriate conditional distributions. It turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures. The diagnoses are based on the conformal normal curvature that can be computed easily. A number of interesting perturbation schemes are considered. The methodology is illustrated with two real examples.The research is fully supported by a grant (CUHK 4356/00H) from the Research Grant Council of the Hong Kong Special Administration Region. The authors are thankful to the Editor, Associate Editor, anonymous reviewers, and W.Y. Poon for valuable comments for improving the paper, and to ICPSR and the relevant founding agency for allowing us to use of their data. The assistance of Michael Leung and Esther Tam is gratefully acknowledged.