Statistical bias in maximum likelihood estimators of item parameters

Asymptotic formulas are derived for the bias in the maximum likelihood estimators of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission.     

Improved Fisher z estimators for univariate random‐effects meta‐analysis of correlations

Several authors have studied or used the following estimation strategy for meta‐analysing correlations: obtain a point estimate or confidence interval for the mean Fisher z correlation, and transform this estimate to the Pearson r metric. Using the relationship between Fisher z and Pearson r random variables, I demonstrate the potential discrepancy induced by directly z‐to‐r transforming a mean correlation parameter. Point and interval estimators based on an alternative integral z‐to‐r transformation are proposed. Analytic expressions for the expectation and variance of certain meta‐analytic point estimators are also provided, as are selected moments of correlation parameters; numerical examples are included. In an application of these analytic results, the proposed point estimator outperformed its usual direct z‐to‐r counterpart and compared favourably with an estimator based on Pearson r correlations. Practical implications, extensions of the proposed estimators, and uses for the analytic results are discussed.     

Random‐effects meta‐analysis of correlations: Monte Carlo evaluation of mean estimators

Several authors have cautioned against using Fisher's z‐transformation in random‐effects meta‐analysis of correlations, which seems to perform poorly in some situations, especially with substantial inter‐study heterogeneity. Attributing this performance largely to the direct z‐to‐r transformation (DZRT) of Fisher z results (e.g. point estimate of mean correlation), in a previous paper Hafdahl (2009) proposed point and interval estimators of the mean Pearson r correlation that instead use an integral z‐to‐r transformation (IZRT). The present Monte Carlo study of these IZRT Fisher z estimators includes comparisons with their DZRT counterparts and with estimators based on Pearson r correlations. The IZRT point estimator was usually more accurate and efficient than its DZRT counterpart and comparable to the two Pearson r point estimators – better in some conditions but worse in others. Coverage probability for the IZRT confidence intervals (CIs) was often near nominal, much better than for the DZRT CIs, and comparable to coverage for the Pearson r CIs; every approach's CI fell markedly below nominal in some conditions. The IZRT estimators contradict warnings about Fisher z estimators' poor performance. Recommendations for practising research synthesists are offered, and an Appendix provides computing code to implement the IZRT as in the real‐data example.     

Subclinical delusional ideation and a self‐reference bias in everyday reasoning

Previous studies (e.g. Moller & Husby, 2000 ; Blackwood et al., 2004 ) have revealed that delusional thinking is accompanied by an exaggerated focus upon the self and upon stimuli that are perceived to be related to the self. The objective was to examine whether those high in subclinical delusional ideation exhibit a heightened tendency for self‐reference. Using a mixed design, healthy individuals, classified into high‐ and low‐scoring groups on the Peters et al. Delusions Inventory ( Peters, Day, & Garety, 1996 ), were compared on everyday reasoning tasks across three experiments. High‐PDI scorers, in contrast to the low‐PDI group, rated self‐referent objections to everyday arguments as stronger than other‐referent objections and formulated more self‐referent assertion‐based objections to everyday arguments. The findings support the notion that subclinical delusional ideation is linked to a self‐reference bias, which is evident in the sort of everyday thinking that people engage in when forming or evaluating their beliefs and which may contribute to delusion formation.     

A parametric characterization of mean–variance efficient solutions for general feasible action sets

In this paper we show how the mean–variance efficient solution problem may be converted to a parametric efficient solution problem with objective functions affine in the mean and second moment of the random variable of concern. Some potential uses are considered, the relationship with some other work is examined and two potential applications are given. © 1998 John Wiley & Sons, Ltd.     

Separating response‐execution bias from decision bias: Arguments for an additional parameter in Ratcliff's diffusion model

Diffusion model data analysis permits the disentangling of different processes underlying the effects of experimental manipulations. Estimates can be provided for the speed of information accumulation, for the amount of information used to draw conclusions, and for a decision bias. One parameter describes the duration of non‐decisional processes including the duration of motor‐response execution. In the default diffusion model, it is implicitly assumed that both responses are executed with the same speed. In some applications of the diffusion model, this assumption will be violated. This will lead to biased parameter estimates. Consequently, we suggest accounting explicitly for differences in the speed of response execution for both responses. Results from a simulation study illustrate that parameter estimates from the default model are biased if the speed of response execution differs between responses. A second simulation study shows that large trial numbers (N>1,000) are needed to detect whether differences in response‐execution times are based on different execution times.     

Asymptotic expansion of the distributions of the estimators in factor analysis under non‐normality

Equations for the Edgeworth expansion of the distributions of the estimators in exploratory factor analysis and structural equation modeling are given. The equations cover the cases of non‐normal data, as well as normal ones with and without known first‐order asymptotic standard errors. When the standard errors are unknown, the distributions of the Studentized statistics are expanded. Methods of constructing confidence intervals of population parameters with arbitrary asymptotic confidence coefficients are given using the Cornish‐Fisher expansion. Simulations are performed to see the usefulness of the asymptotic expansions in exploratory factor analysis with rotated solutions and confirmatory factor analysis. The results show that asymptotic expansion gives substantial improvement of approximation to the exact distribution constructed by simulations over the usual normal approximation.     

The development of subjective group dynamics: When in‐group bias gets specific

Children aged 6–7 years and 10–11 years evaluated an in‐group or out‐group summer school and judged in‐group or out‐group members whose attitudes towards the summer schools were either normative or anti‐normative. According to a subjective group dynamics model of intergroup processes, intergroup differentiation and intragroup differentiation co‐occur to bolster the validity of in‐group norms. The hypothesis that this process develops later than simple in‐group bias was confirmed. All children expressed global in‐group bias, but differential reactions to in‐group and outgroup deviants were stronger among older children. Moreover, the increasing relationship, with age, between in‐group bias and evaluative preferences for in‐group and out‐group members that provide relative support to in‐group norms, is mediated by the degree of perceptual differentiation among group members.     

On belief bias in syllogistic reasoning

A multinomial model is used to disentangle the respective contributions of reasoning processes and response bias in conclusion-acceptance data that exhibit belief bias. A model-based meta-analysis of 22 studies reveals that such data are structurally too sparse to allow discrimination of different accounts of belief bias. Four experiments are conducted to obtain richer data, allowing deeper tests through the use of the multinomial model. None of the current accounts of belief bias is consistent with the complex pattern of results. A new theory of belief bias is proposed that assumes that most reasoners construct only one mental model representing the premises as well as the conclusion or, in the case of an unbelievable conclusion, its logical negation. New predictions derived from the theory are confirmed in 4 additional studies.     

On Value‐Attributions: Semantics and Beyond

This paper is driven by the idea that the contextualism‐relativism debate regarding the semantics of value‐attributions turns on certain extra‐semantic assumptions that are unwarranted. One is the assumption that the many‐place predicate of truth, deployed by compositional semantics, cannot be directly appealed to in theorizing about people's assessments of truth value but must be supplemented (if not replaced) by a different truth‐predicate, obtained through certain “postsemantic” principles. Another is the assumption that semantics assigns to sentences not only truth values (as a function of various parameters, such as contexts, worlds and times), but also semantic contents, and that what context‐sensitive expressions contribute to content are contextually determined elements. My first aim in this paper will be to show how the two assumptions have shaped two ways of understanding the debate between contextualism and relativism. My second aim will be to show that both assumptions belong outside semantics and are, moreover, questionable.     

Self‐Handicapping: On the Self‐Perpetuating Nature of Defensive Behavior

The term self‐handicapping was introduced by Jones and Berglas (1978 ) to refer to the creation of barriers to successful performance for the purpose of controlling attributions about the self. In the event of failure, attributions to lack of ability are diminished or discounted because of the handicap and, in the event of success, attributions to ability are enhanced or augmented because of the handicap. This article reviews over 25 years of research on self‐handicapping. A process model is presented in which individual differences in goals and concerns dynamically interact with situational threats to elicit self‐handicapping behavior which produces consequences that perpetuate the use of the behavior in future situations.     

Nearly unbiased estimators for the three‐parameter Weibull distribution with greater efficiency than the iterative likelihood method

The maximum likelihood estimation (MLE) method is the most commonly used method to estimate the parameters of the three‐parameter Weibull distribution. However, it returns biased estimates. In this paper, we show how to calculate weights which cancel the biases contained in the MLE equations. The exact weights can be computed when the population parameters are known and the expected weights when they are not. Two of the three weights' expected values are dependent only on the sample size, whereas the third also depends on the population shape parameters. Monte Carlo simulations demonstrate the practicability of the weighted MLE method. When compared with the iterative MLE technique, the bias is reduced by a factor of 7 (irrespective of the sample size) and the variability of the parameter estimates is also reduced by a factor of 7 for very small sample sizes, but this gain disappears for large sample sizes.     

Ethnic in‐group bias among minority and majority early adolescents: The perception of negative peer behaviour

Using social identity theory (SIT) as a framework, this study investigates in‐group bias in the context of negative social behaviour among Dutch and Turkish children (10–13 years of age) living in the Netherlands. Using stories about peer behaviour in which ethnicity was an available dimension, the children were asked to evaluate the perpetrator and to explain the negative behaviour. Explanations were analysed in terms of the locus of explanation and the level of linguistic abstraction at which the perpetrator's behaviour was explained. Hence, there were three measures of in‐group bias. In addition, ethnic identification, perceived multicultural education and participants' experiences with ethnic victimization were considered as predictor variables. The results revealed a small degree of in‐group bias for the evaluation and the locus of explanation, but not for linguistic abstraction. Furthermore, for both ethnic groups, it was found that stronger ethnic identification was related to a less negative evaluation of an in‐group perpetrator. A higher degree of ethnic victimization was related to a less negative perception of the perpetrator. In addition, a higher degree of perceived exposure to multicultural education was associated with a more negative perception of the perpetrator, particularly among the Dutch participants. It was concluded that the study of ethnic attitudes among children should focus more on the perceptions of actual ethnic conflicts and on specific settings such as schools. Furthermore, it is important to use explicit and implicit measures and to include both majority and minority group children.     

On the Rationality of Vow‐making

I offer a philosophical account of vowing and the rationality of vow‐making. I argue that vows are most productively understood as exceptionless resolutions that do not have any excusing conditions. I then articulate an apparent problem for exceptionless vow‐making: how can it be rational to bind yourself unconditionally, when circumstances might change unexpectedly and make it the case that vow‐keeping no longer makes sense for you? As a solution, I propose that vows can be rational to make only if they are implicitly conditional on a personal identification or social role that is itself escapable.