Bootstrap confidence intervals for principal covariates regression

Principal covariate regression (PCOVR) is a method for regressing a set of criterion variables with respect to a set of predictor variables when the latter are many in number and/or collinear. This is done by extracting a limited number of components that simultaneously synthesize the predictor variables and predict the criterion ones. So far, no procedure has been offered for estimating statistical uncertainties of the obtained PCOVR parameter estimates. The present paper shows how this goal can be achieved, conditionally on the model specification, by means of the bootstrap approach. Four strategies for estimating bootstrap confidence intervals are derived and their statistical behaviour in terms of coverage is assessed by means of a simulation experiment. Such strategies are distinguished by the use of the varimax and quartimin procedures and by the use of Procrustes rotations of bootstrap solutions towards the sample solution. In general, the four strategies showed appropriate statistical behaviour, with coverage tending to the desired level for increasing sample sizes. The main exception involved strategies based on the quartimin procedure in cases characterized by complex underlying structures of the components. The appropriateness of the statistical behaviour was higher when the proper number of components were extracted.     

Unconscious reward cues increase invested effort,but do not change speed–accuracy tradeoffs

While both conscious and unconscious reward cues enhance effort to work on a task, previous research also suggests that conscious rewards may additionally affect speed–accuracy tradeoffs. Based on this idea, two experiments explored whether reward cues that are presented above (supraliminal) or below (subliminal) the threshold of conscious awareness affect such tradeoffs differently. In a speed–accuracy paradigm, participants had to solve an arithmetic problem to attain a supraliminally or subliminally presented high-value or low-value coin. Subliminal high (vs. low) rewards made participants more eager (i.e., faster, but equally accurate). In contrast, supraliminal high (vs. low) rewards caused participants to become more cautious (i.e., slower, but more accurate). However, the effects of supraliminal rewards mimicked those of subliminal rewards when the tendency to make speed–accuracy tradeoffs was reduced. These findings suggest that reward cues initially boost effort regardless of whether or not people are aware of them, but affect speed–accuracy tradeoffs only when the reward information is accessible to consciousness.     

How do people react to negative procedures? On the moderating role of authority’s biased attitudes

The authors focus on the effects an authority’s apparent inconsistency between persons on judgments of relational treatment and procedural justice following negative procedures (i.e., procedures that people commonly regard as unfair). In Experiment 1, participants responded most negatively following a procedure that denied them, but granted another participant, an opportunity to voice an opinion when the intergroup context raised suspicions of bias (i.e., when both the experimenter and another participant were outgroup members). In Experiment 2, participants responded most negatively when the experimenter had expressed biased attitudes in favor of another participant, but this effect occurred only following procedures that denied participants a voice opportunity. We conclude that authority’s biased attitudes help people to make sense of negative procedure information.     

Properties of and Algorithms for Fitting Three-Way Component Models with Offset Terms

Prior to a three-way component analysis of a three-way data set, it is customary to preprocess the data by centering and/or rescaling them. Harshman and Lundy (1984) considered that three-way data actually consist of a three-way model part, which in fact pertains to ratio scale measurements, as well as additive “offset” terms that turn the ratio scale measurements into interval scale measurements. They mentioned that such offset terms might be estimated by incorporating additional components in the model, but discarded this idea in favor of an approach to remove such terms from the model by means of centering. Then estimates for the three-way component model parameters are obtained by analyzing the centered data. In the present paper, the possibility of actually estimating the offset terms is taken up again. First, it is mentioned in which cases such offset terms can be estimated uniquely. Next, procedures are offered for estimating model parameters and offset parameters simultaneously, as well as successively (i.e., providing offset term estimates after the three-way model parameters have been estimated in the traditional way on the basis of the centered data). These procedures are provided for both the CANDECOMP/PARAFAC model and the Tucker3 model extended with offset terms. The successive and the simultaneous approaches for estimating model and offset parameters have been compared on the basis of simulated data. It was found that both procedures perform well when the fitted model captures at least all offset terms actually underlying the data. The simultaneous procedures performed slightly better than the successive procedures. If fewer offset terms are fitted than there are underlying the model, the results are considerably poorer, but in these cases the successive procedures performed better than the simultaneous ones. All in all, it can be concluded that the traditional approach for estimating model parameters can hardly be improved upon, and that offset terms can sufficiently well be estimated by the proposed successive approach, which is a simple extension of the traditional approach. The author is obliged to Jos M.F. ten Berge and Marieke Timmerman for helpful comments on an earlier version of this paper. The author is obliged to Iven van Mechelen for making available the data set used in Section 6.     

On growth curves and mixture models

The multilevel model of change and the latent growth model are flexible means to describe all sorts of population heterogeneity with respect to growth and development, including the presence of sub‐populations. The growth mixture model is a natural extension of these models. It comes at hand when information about sub‐populations is missing and researchers nevertheless want to retrieve developmental trajectories from sub‐populations. We argue that researchers have to make rather strong assumptions about the sub‐populations or latent trajectory classes in order to retrieve existing population differences. A simulated example is discussed, showing that a sample of repeated measures drawn from two sub‐populations easily leads to the mistaken inference of three sub‐populations, when assumptions are not met. The merits of methodological advises on this issue are discussed. It is concluded that growth mixture models should be used with understanding, and offer no free way to growth patterns in unknown sub‐populations. Copyright © 2006 John Wiley & Sons, Ltd.     

Heart work after errors: Behavioral adjustment following error commission involves cardiac effort

Posterror slowing (PES) is the observation that people respond slower on trials subsequent to error commissions than on trials subsequent to correct responses. Different accounts have been proposed to explain PES. On the one hand, it has been suggested that PES arises from an adaptive increase in cognitive control following error commission, thereby making people more cautious after making an error. On the other hand, PES has been attributed to an orienting response, indicating that attention is shifted toward the error. In the present study we tested these accounts by investigating the effects of error commission in both flanker and switch tasks on two task-evoked cardiac measures: the interbeat interval—that is, the interval between two consecutive R peaks—and the RZ interval—that is, the interval between the R peak and the Z point—as measured using electro- and impedance cardiography, respectively. These measures allowed us to measure cardiac deceleration (autonomic orienting) and cardiac effort mobilization, respectively. Our results revealed a shorter RZ interval during posterror trials, indicating increased effort mobilization following errors. In addition, we replicated earlier studies that have shown cardiac slowing during error trials. However, multilevel analyses showed that only the posterror decrease in RZ interval predicted posterror reaction times, whereas there was no positive relationship between error-related cardiac deceleration and posterror reaction times. Our results suggest that PES is related to increased cardiac effort, supporting a cognitive-control account of PES.     

Maintenance of semantic information in capacity-limited item short-term memory

We report a semantic effect in immediate free recall, which is localized at recency and is preserved under articulatory suppression but is highly reduced when recall is delayed after an intervening distractor task. These results are explained by a neurocomputational model based on a limited-capacity short-term memory (STM) store, consisting ofactivated long-term memory representations. The model makes additional predictions about serial position functions in semantically cued recall, indicating capacity limitations caused by a displacement type mechanism, which are confirmed in a second experiment. This suggests that in addition to the phonological component in verbal STM, there is an activation/ item-limited component with semantically sensitive representations.     

Once the money is in sight: Distinctive effects of conscious and unconscious rewards on task performance

Monetary rewards facilitate performance on behavioral and cognitive tasks, even when these rewards are perceived without conscious awareness. Also, recent research suggests that consciously (vs. unconsciously) perceived rewards may prompt people to more strongly concentrate on task stimuli and details. Here we propose that the latter is sometimes dysfunctional, in that it prevents improvements in task performance. We used an Attentional Blink paradigm, in which such enhanced concentration on task stimuli is detrimental to performance. Participants were consciously (supraliminally) or unconsciously (subliminally) exposed to a high-value or low-value coin that they could earn by performing well on an Attentional Blink trial. As hypothesized, high-value rewards increased performance when they were presented subliminally, while this performance benefit vanished when high-value rewards were presented consciously. We discuss this finding in the context of recent research on unconscious goal pursuit.