The psychology of moderate prediction : II. Leniency and uncertainty

In this paper we demonstrate that intuitive numerical predictions can be somewhat regressive. This moderation of predictions is asymmetric: predictions are more regressive at low than at high values of the predictor. This pattern is analyzed in terms of the operation of multiple heuristics. The representativeness heuristic is responsible for predictions in which extremity of the predicted variable is matched to extremity of the predictor. Matching is modified by a variety of intuitions that promote moderation per se; we lump these together under the heading of weak regressiveness. Third is leniency, a heuristic suggesting that the higher the uncertainty, the more positive should be the predictions. The first experiment demonstrates leniency in isolation from the other heuristics: in multivariate prediction, inconsistent predictors yield more positive predictions. Experiment 2 demonstrates asymmetric regression in a situation where all three heuristics are assumed to have effects. The third experiment exhibits leniency in the context of explanation of regression phenomena (rather than in numerical prediction). The final experiment explores the relation between the three heuristics and experience with multiple determination (Ganzach & Krantz, in press). It demonstrates increased moderation of predictions when subjects are required to generate a predicted value of an intermediate variable, for example, when the prediction of GPA from Intelligence is made subsequent to a prediction of Motivation.     

Asymptotic bias of normal-distribution-based maximum likelihood estimates of moderation effects with data missing at random

Moderation analysis is useful for addressing interesting research questions in social sciences and behavioural research. In practice, moderated multiple regression (MMR) models have been most widely used. However, missing data pose a challenge, mainly because the interaction term is a product of two or more variables and thus is a non-linear function of the involved variables. Normal-distribution-based maximum likelihood (NML) has been proposed and applied for estimating MMR models with incomplete data. When data are missing completely at random, moderation effect estimates are consistent. However, simulation results have found that when data in the predictor are missing at random (MAR), NML can yield inaccurate estimates of moderation effects when the moderation effects are non-null. Simulation studies are subject to the limitation of confounding systematic bias with sampling errors. Thus, the purpose of this paper is to analytically derive asymptotic bias of NML estimates of moderation effects with MAR data. Results show that when the moderation effect is zero, there is no asymptotic bias in moderation effect estimates with either normal or non-normal data. When the moderation effect is non-zero, however, asymptotic bias may exist and is determined by factors such as the moderation effect size, missing-data proportion, and type of missingness dependence. Our analytical results suggest that researchers should apply NML to MMR models with caution when missing data exist. Suggestions are given regarding moderation analysis with missing data.     

Robust Methods for Moderation Analysis with a Two-Level Regression Model

Moderation analysis has many applications in social sciences. Most widely used estimation methods for moderation analysis assume that errors are normally distributed and homoscedastic. When these assumptions are not met, the results from a classical moderation analysis can be misleading. For more reliable moderation analysis, this article proposes two robust methods with a two-level regression model when the predictors do not contain measurement error. One method is based on maximum likelihood with Student's t distribution and the other is based on M-estimators with Huber-type weights. An algorithm for obtaining the robust estimators is developed. Consistent estimates of standard errors of the robust estimators are provided. The robust approaches are compared against normal-distribution-based maximum likelihood (NML) with respect to power and accuracy of parameter estimates through a simulation study. Results show that the robust approaches outperform NML under various distributional conditions. Application of the robust methods is illustrated through a real data example. An R program is developed and documented to facilitate the application of the robust methods.     

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

Moderators of the relation between substance use level and problems: test of a self-regulation model in middle adolescence

The authors tested predictions, derived from a self-regulation model, about variables moderating the relationship between level of substance use (tobacco, alcohol, and marijuana) and problems associated with use. Data were from two independent studies of adolescents, with mean ages of 15.4 and 15.5 years (Ns = 1,699 and 1,225). Factor analysis indicated correlated dimensions of control problems and conduct problems. Protective moderation was found for variables indexing good self-control; risk-enhancing moderation was found for variables indexing poor self-control. These effects were generally independent of deviance-prone attitudes and externalizing symptomatology. Multiple-group structural modeling indicated moderation occurred for paths from life stress and coping motives and for paths from level to control and conduct problems. Moderation effects were also found for parental variables, peer variables, and academic competence.     

Moderation Analysis Using a Two-Level Regression Model

Moderation analysis is widely used in social and behavioral research. The most commonly used model for moderation analysis is moderated multiple regression (MMR) in which the explanatory variables of the regression model include product terms, and the model is typically estimated by least squares (LS). This paper argues for a two-level regression model in which the regression coefficients of a criterion variable on predictors are further regressed on moderator variables. An algorithm for estimating the parameters of the two-level model by normal-distribution-based maximum likelihood (NML) is developed. Formulas for the standard errors (SEs) of the parameter estimates are provided and studied. Results indicate that, when heteroscedasticity exists, NML with the two-level model gives more efficient and more accurate parameter estimates than the LS analysis of the MMR model. When error variances are homoscedastic, NML with the two-level model leads to essentially the same results as LS with the MMR model. Most importantly, the two-level regression model permits estimating the percentage of variance of each regression coefficient that is due to moderator variables. When applied to data from General Social Surveys 1991, NML with the two-level model identified a significant moderation effect of race on the regression of job prestige on years of education while LS with the MMR model did not. An R package is also developed and documented to facilitate the application of the two-level model.     

基于多元回归的调节效应分析

在心理学和其他社科研究领域,大量实证研究建立调节模型,以分析自变量对因变量关系的影响机制,但在基于多元回归的调节效应分析实践中仍存在不足。我们回顾了均值中心化在基于多元回归的调节效应分析中的作用,均值中心化不影响乘积项(即调节效应)的检验,仅对一阶项(即主效应)的检验有影响。讨论了简单斜率的检验方法,建议在调节变量为连续变量时,使用Johnson-Neyman法进行简单斜率检验;在调节变量为类别变量或研究者对某个调节变量值感兴趣时,使用选点法。并用一个实际例子演示如何进行调节效应分析。随后展望了调节效应检验的拓展方向。     

基于两水平回归模型的调节效应分析及其效应量

使用多元回归法进行调节效应分析在社科领域已常有应用。简述了目前多元回归法的调节效应分析存在的不足, 包括人为变换检验模型、自变量和调节变量区分不足、误差方差齐性的假设难以满足、调节效应量指标ΔR²没有直接测量调节变量对自变量与因变量关系的调节程度。比较好的方法是用两水平回归模型进行调节效应分析并使用相应的效应量指标。在介绍新方法和新效应量后, 总结出一套调节效应的分析流程, 通过一个例子来演示如何用Mplus软件进行两水平回归模型的调节效应及其效应量分析。最后讨论了两水平回归模型的调节效应分析的发展, 包括稳健的调节效应分析、潜变量的调节效应分析、有调节的中介效应分析和有中介的调节效应分析等。     

Unconditional respect for persons and the prediction of intergroup action tendencies

Unconditional respect for persons is an orientation that rests on the assumption that all people have intrinsic worth and deserve respect simply by their being human. This paper reports three cross‐sectional studies concerning unconditional respect in intergroup relations in three very different contexts. In all three studies, unconditional respect was positively related to positive action tendencies, and negatively related to negative action tendencies, toward other groups. Regression analyses showed that respect was a significant predictor of negative action tendencies even when attitude to the other group, social dominance orientation, empathy, and the quality and quantity of intergroup contact were statistically controlled. Moderation analyses showed that respect was particularly important under conditions of high threat. The implications of unconditional respect for intergroup relations are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Cognitive distortions as mediators between life stress and depression in adolescents

This research examined the possibility that cognitive distortions mediate between life stress and depression in an adolescent population. Measures of cognitive distortion, life stress, and depressive tendencies were administered to 103 ninth- to twelfth-grade high school students. It was predicted that measures of cognitive distortion would be better predictors of depressive tendencies than measures of life stress. It was also predicted that cognitive distortions would affect the perceived stressfulness of life events. In addition, it was predicted that three measures of cognitive distortion would be correlated and that the measure of immediate negative thinking would be a better predictor of depressive tendencies than the measures of dysfunctional attitudes and irrational beliefs. Findings from correlation and regression analyses were consistent with the predictions.     

Intuitive prediction: ecological validity versus representativeness

Insufficiently regressive intuitive predictions have been attributed to mistaken reliance on the representativeness heuristic. In contrast, we suggest that intuitive predictions stem from a conceptualization of ‘goodness of prediction’ that differs from the accepted statistical definition in terms of error minimization, namely, ecological validity—that is, representation of the substantive characteristics of the predicted variable Y and its distribution as well as of the relationship between Y and the predictor X—rather than minimization of prediction errors. Simultaneous satisfaction of the above representation requirements is achieved by multivalued prediction: The prediction of different Y′ values for the same X value, resulting in conditional distributions Y′|X for at least some X values. Empirical results supporting this hypothesis are presented and discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Stability and level of self-esteem as predictors of anger arousal and hostility

We examined stability of self-esteem and level of self-esteem as predictors of dispositional tendencies to experience anger and hostility. We reasoned that individuals with unstable high self-esteem would report especially high tendencies to experience anger and hostility, and that individuals with stable high self-esteem would report particularly low tendencies. We expected individuals with stable and unstable low self-esteem to fall between these two extremes. These predictions were derived from an analysis of anger and hostility that emphasized the instigating role of threats to self-esteem. Stability of self-esteem was assessed through multiple assessments of global self-esteem in naturalistic settings. Results revealed the predicted pattern for the tendency to experience anger and a "motor" component of hostility. The importance of considering both stability and level of self-esteem in analyses of anger and hostility is discussed.     

The role of alternative hypotheses in the integration of evidence that disconfirms an acquired belief

Two experiments examined the role of alternative hypotheses in the recognition of belief-incongruent evidence and the consequent attribution of probative value to that evidence. Using a contingency judgement and prediction task, subjects monitored multiple predictor-outcome contingencies. In a subset of three of these contingencies the evidence strongly endorsed a positive contingency in a first phase but strongly endorsed a negative contingency in a second phase. In Experiment 1 the negative evidence was presented, in part, in terms of an alternative contingency involving a new predictor or a new outcome, or in terms of no alternatives. The presence of alternative hypotheses did not influence the recognition of the negative evidence but significantly reduced the subjects' persistence in predicting the outcome in the presence of the predictor. Using the same positive-negative contingencies, Experiment 2 replicated this effect but also demonstrated that error in the feedback during the negative phase strengthened the perseverance in outcome predictions even when subjects acknowledged the negative nature of the evidence. Results from these two experiments indicate that prior beliefs do not bias the recognition of belief-incongruent evidence but the integration of that evidence is determined by the nature of the alternative hypotheses available to the reasoner.     

Two-Part Predictors in Regression Models

Researchers often build regression models to relate a response to a set of predictor variables. In some cases, there are predictors that apply to some participants, or to some measurement occasions, but not others. For example, a romantic partner's substance use may be a key predictor of one's own substance use. However, not all participants have a partner, and in a longitudinal study, participants may have a partner during only some occasions. This could be viewed as missing data, but of a very distinctive type: the values are not just unknown but also undefined. In this paper, we present a simple method to accommodate this situation, along with a motivating example, the algebraic justification, a simulation study, and examples on how to carry out the technique.     

Improving metacognitive accuracy: How failing to retrieve practice items reduces overconfidence

People often exhibit inaccurate metacognitive monitoring. For example, overconfidence occurs when people judge that they will remember more information on a future test then they actually do. The present experiments examined whether a small number of retrieval practice opportunities would improve participants’ metacognitive accuracy by reducing overconfidence. Participants studied Lithuanian–English paired associates and predicted their performance on an upcoming memory test. Then they attempted to retrieve one or more practice items (or none in the control condition) and made a second prediction. Experiment 1 showed that failing to retrieve a single practice item lead to improved subsequent performance predictions – participants became less overconfident. Experiment 2 directly manipulated retrieval failure and showed that again failure to retrieve a single practice item significantly improved subsequent predictions, relative to when participants successfully retrieved the practice item. Finally, Experiment 3 showed that additional retrieval practice opportunities reduced overconfidence and improved prediction accuracy.     

Category size and judgments of variability: The effects of seeing the trees in the forest1

Abstract: Competing predictions about the effects of category size on judgments of category variability were examined in two studies involving the presentation of exemplars of two artificial social groups. In contrast to predictions of some exemplar-based models, Experiment 1 demonstrated that a numerically smaller group was perceived to be more variable than a larger group on the standard deviation measure of frequency distribution estimates. The result was interpreted to be an effect of differential information load. Experiment 2 revealed that variability judgments were influenced by prior expectations about the central tendencies as well as by practice in retrieving information about category exemplars. When frequency distribution estimates were made subsequent to abstract tasks, expectations about the numerical majority reduced perceived variability, while this influence was mitigated when memory measures preceded the frequency estimates.     

Self-Efficacy and the Prediction of Domain-Specific Cognitive Abilities

ABSTRACT We evaluated predictors of performance in 4 specific cognitive ability domains: verbal, numerical, spatial, and mechanical. The predictors were individual differences in self-efficacy beliefs, self-enhancement tendencies, and cross-domain abilities. Our university students' beliefs about their verbal, numerical, and spatial capabilities correlated well with their actual performance on standardized tests (verbal r =.33, numerical r =.27, spatial r =.36). In contrast, the students' self-efficacy for mechanical tasks did relatively poorly in predicting mechanical test performance ( r =.10). Most interesting were two other findings: (a) The best predictor of domain performance was level of cross-domain performance by far, even for mechanical tasks, and (b) self-enhancement tendencies added to cross-domain abilities and self-efficacy beliefs in the prediction of performance. The results are discussed in terms of possible mechanisms explaining how one's score on a maximal performance task can be affected by self-efficacy beliefs and self-enhancement tendencies.     

The “Black Sheep Effect”: Extremity of judgments towards ingroup members as a function of group identification

The present study proposes an extension to the phenomenon of ingroup favouritism, based on the hypothesis that judgments about ingroup members may be more positive or more negative than judgments about similar outgroup members. It contrasts predictions issued from the complexity-extremity hypothesis (Linville, 1982; Linville and Jones, 1980), from the ingroup favouritism hypothesis (Tajfel, 1982) and from Tesser's (1978; Millar and Tesser, 1986) attitude polarization model. Our main prediction, based on Social Identity Theory, is that judgments about both likeable and unlikeable ingroup members are more extreme than judgments about outgroup members. This phenomenon, coined the Black Sheep Effect, is viewed as due to the relevance that ingroup members'behaviour, as compared to that of outgroup members, has for the subjects' social identity. Three experiments supported our predictions. Experiment I additionally showed that inter-trait correlations were stronger for the ingroup than for the outgroup. Experiment 2 showed that the black sheep effect occurs only when the judgmental cues are relevant for the subjects' social identity, and Experiment 3 showed that levels of information about the target of the judgment were ineffective in generating judgmental extremity. Results are discussed in light of a cognitive-motivational alternative explanation to a purely cognitive interpretation of outgroup homogeneity.     

Output and retrieval interference in the missing-number task

Three experiments are reported that represent a reexamination of the missing-number method (Buschke, 1963b) of estimating short-term memory span. The missing-number task involved presenting a random sequence of all but one of the numbers of a known reference set and asking subjects to identify the missing number. Experiment 1 introduced a modified missing-number task that included two missing items and two choices made by the subject. With a large decline in performance for the second choice relative to the first, it is possible that only the second choice was subject to output or retrieval interference. An alternative explanation is that subjects output the number with the weakest memory representation as their first response. By postcuing subjects to report their two choices in a forward or backward sequence, Experiment 2 provided evidence against the importance of output interference and support either for the importance of retrieval interference or for the "weakest-first" hypothesis. However, with a paradigm that replaced only correctly identified missing numbers, a prediction that subjects would select the number with the weakest memory representation as their first response was not confirmed in Experiment 3. Instead, retrieval interference was implicated to explain the first-choice superiority found in Experiments 1 and 3. The results were interpreted in terms of the TODAM model of Murdock (1982, 1987, in press).     

Response-based strengthening in task shifting: evidence from shift effects produced by errors

The hypothesis is introduced that 1 source of shift costs is the strengthening of task-related associations occurring whenever an overt response is produced. The authors tested this account by examining shift effects following errors and error compensation processes. The authors predicted that following a specific type of error, called task confusion, shift benefits instead of shift costs should result. A series of 3 experiments confirmed this prediction showing that task confusions produce shift benefits in subsequent trials (Experiment 1), even when the error is detected (Experiment 2). Moreover, only posterror processes that imply an error correction response produce shift costs (Experiment 3). These results additionally suggest that error detection cannot prevent errors from affecting subsequent performance.