Two meanings of “if”? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

Two meanings of "if"? Individual differences in the interpretation of conditionals

This work investigates the nature of two distinct response patterns in a probabilistic truth table evaluation task, in which people estimate the probability of a conditional on the basis of frequencies of the truth table cases. The conditional-probability pattern reflects an interpretation of conditionals as expressing a conditional probability. The conjunctive pattern suggests that some people treat conditionals as conjunctions, in line with a prediction of the mental-model theory. Experiments 1 and 2 rule out two alternative explanations of the conjunctive pattern. It does not arise from people believing that at least one case matching the conjunction of antecedent and consequent must exist for a conditional to be true, and it does not arise from people adding the converse to the given conditional. Experiment 3 establishes that people's response patterns in the probabilistic truth table task are very consistent across different conditionals, and that the two response patterns generalize to conditionals with negated antecedents and consequents. Individual differences in rating the probability of a conditional were loosely correlated with corresponding response patterns in a classical truth table evaluation task, but there was little association with people's evaluation of deductive inferences from conditionals as premises. A theoretical framework is proposed that integrates elements from the conditional-probability view with the theory of mental models.     

认知诊断中基于条件期望的距离判别方法

分类是认知诊断评估的一个核心问题。基于观察反应模式与理想反应模式之间的距离的判别方法, 以确定性的理想反应模式为类中心, 而这没有考虑误差, 故未充分利用总体分布信息。为了更充分地利用总体分布信息、提高诊断分类效果和拓展诊断评估的适用性, 本研究提出给定知识状态条件下项目反应模式的条件期望向量为类中心的欧氏距离判别方法, 同时提出认知诊断模型下项目反应函数估计方法以获得这个条件期望向量。模拟研究表明：认知诊断模型下的项目反应函数估计方法得到的条件期望向量返真性较高, 获得的分布信息较准确; 在观察反应模式与理想反应模式差异大的情形下, 基于条件期望向量为类中心的欧氏距离判别方法优于基于理想反应模式为类中心的分类方法(广义距离方法和非参数方法）。研究可为认知诊断分类和等值方法提供一个参考。     

基于作答数据的模型参数和Q矩阵联合估计

Q矩阵在认知诊断的模型参数估计和诊断分类中起着重要作用。本文通过研究Liu等人的方法, 设计了同时估计项目参数和Q矩阵的联合估计算法。在DINA模型下, 对项目参数未知时开展模拟研究。研究假设项目为20个, 考察的属性个数分别是3、4和5, 初始Q矩阵中分别存在3、4和5个属性界定错误的项目。结果表明, 联合估计算法能在错误的初始Q矩阵基础上以很高的概率得到正确的Q矩阵。另外, 当专家认定测验的属性个数存在错误时, 该方法推导的Q矩阵和模型参数能提供很好的鉴别Q矩阵错误的信息。     

Accurate step-hold tracking of smoothly varying periodic and aperiodic probability

Subjects observing many samples from a Bernoulli distribution are able to perceive an estimate of the generating parameter. A question of fundamental importance is how the current percept—what we think the probability now is—depends on the sequence of observed samples. Answers to this question are strongly constrained by the manner in which the current percept changes in response to changes in the hidden parameter. Subjects do not update their percept trial-by-trial when the hidden probability undergoes unpredictable and unsignaled step changes; instead, they update it only intermittently in a step-hold pattern. It could be that the step-hold pattern is not essential to the perception of probability and is only an artifact of step changes in the hidden parameter. However, we now report that the step-hold pattern obtains even when the parameter varies slowly and smoothly. It obtains even when the smooth variation is periodic (sinusoidal) and perceived as such. We elaborate on a previously published theory that accounts for: (i) the quantitative properties of the step-hold update pattern; (ii) subjects’ quick and accurate reporting of changes; (iii) subjects’ second thoughts about previously reported changes; (iv) subjects’ detection of higher-order structure in patterns of change. We also call attention to the challenges these results pose for trial-by-trial updating theories.     

Operant conditioning of behavioral variability using a percentile reinforcement schedule.

The present investigation developed and tested a new percentile reinforcement schedule suited to study pattern variability, whose main feature was the relative dissociation it provided between the variability requirement defining criterional responses and overall probability of reinforcement. In a discrete-trials procedure, pigeons produced patterns of four pecks on two response keys. If the pattern emitted on the current trial differed from the N preceding patterns, reinforcement was delivered with probability mu. The schedule continuously adjusted the criterion N such that the probability of a criterional response, estimated from the subject's recent behavior, was always constant. In these circumstances, the criterion corresponded to an invariant percentile in the distribution of recent responses. Using a between-subjects design, Experiment 1 manipulated the variability requirement--the percentile--while keeping overall reinforcement probability constant. The degree of variability varied directly with the requirement. In addition, an inverse relationship existed between the requirement and within-group variance. Experiment 2 manipulated probability of reinforcement while maintaining the variability requirement constant. No consistent relationship was found between variability and reinforcement probability. A tentative hypothesis was advanced ascribing the operant conditioning of behavioral variability to a process of probability-dependent selection.     

On Holland's Dutch identity conjecture

The manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory. Under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear, Holland (1990a) gives a quadratic form for the log-manifest probabilities by using the Dutch Identity. Further, Holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity. The purpose of this paper is to give three counterexamples to demonstrate that Holland's Dutch Identity conjecture does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving sets of such strong conditions are given.     

Probability-of-coverage tolerance intervals for the beta binomial

True score tolerance intervals, which are designed to cover a chosen proportion of the conditional distribution of true scores given an observed score, are suggested as alternatives to true score confidence intervals. Using large sample theory, a tolerance interval estimator for the beta binomial is derived. An example indicates that with moderate sample sizes, tolerance intervals with high probability of coverage will not be much wider than when the two beta true score parameters are known.The author acknowledges valuable comments from Richard Sawyer.Most work was completed while the author was at the American College Testing Program.     

Two unlike patterns of random-ratio responding associated with different eating habits in rhesus monkeys

Four rhesus monkeys were exposed to an identical series of schedules that specified a uniform probability of reinforcement for every response. As probability was lowered slowly in 10 steps of 20 sessions each from 1.0 through 0.01, two distinct patterns of responding emerged. Two subjects showed high, pause-free response rates that increased with each successive reduction in reinforcement probability. The other two showed consistent post-reinforcement pausing at all probabilities, including 1.0, and substantially lower response rates that peaked at the moderate probability values of 0.04 and 0.03. This low-rate pattern was found to be correlated with a pre-experimental preference in the two subjects for mouthing and chewing food pellets one at a time, while the former high-rate, pause-free pattern was linked to a long-standing habit of “pouch feeding” in the other monkeys. These idiosyncratic collateral behaviors that differentiated the schedule performances appeared neither superstitious in origin, nor useful in the case of the low-rate monkeys.     

Aggregate and individual replication probability within an explicit model of the research process

We study a model of the research process in which the true effect size, the replication jitter due to changes in experimental procedure, and the statistical error of effect size measurement are all normally distributed random variables. Within this model, we analyze the probability of successfully replicating an initial experimental result by obtaining either a statistically significant result in the same direction or any effect in that direction. We analyze both the probability of successfully replicating a particular experimental effect (i.e., the individual replication probability) and the average probability of successful replication across different studies within some research context (i.e., the aggregate replication probability), and we identify the conditions under which the latter can be approximated using the formulas of Killeen (2005a, 2007). We show how both of these probabilities depend on parameters of the research context that would rarely be known in practice. In addition, we show that the statistical uncertainty associated with the size of an initial observed effect would often prevent accurate estimation of the desired individual replication probability even if these research context parameters were known exactly. We conclude that accurate estimates of replication probability are generally unattainable.     

基于等级反应模型的属性层级方法

给出基于等级反应模型的属性层级方法（Attribute Hierarchy Method, AHM）,并简记为GRM-AHM,提出了相应的确定GRM-AHM的期望项目反应模式全集的方法和一种新的归类法LL。用蒙特卡洛模拟实验比较GRM-AHM的几种归类法的归准率（属性模式归准率和单个属性的平均判准率）。结果发现,新归类法的归准率与AHM中的方法A差不多,但比方法B高很多;随着被试作答失误率的提高,它们的归准率都有所下降。在归类精度和简单性方面,GRM-AHM都比Bolt等(2004)提出的多级评分融合模型（Fusion Model）好     

The smart potential behind probability matching

Probability matching is a classic choice anomaly that has been studied extensively. While many approaches assume that it is a cognitive shortcut driven by cognitive limitations, recent literature suggests that it is not a strategy per se, but rather another outcome of people’s well-documented misperception of randomness. People search for patterns even in random sequences, which results in probability matching at the outcome level. Previous studies have supported this by the finding that distracting people with a secondary verbal working memory task presumably prevents the pattern search, resulting in more maximizing behavior that is considered more rational. The current paper demonstrates with two experiments that there is actually truth in both accounts. For some participants, probability matching indeed seems to be the result of a cognitive shortcut, a simple “win-stay, lose-shift” strategy, and in one experiment identified these as participants low in working memory capacity. For others, however, a potentially smart pattern search strategy underlies probability matching. These probability matchers (who still look irrational in the absence of patterns) actually have a higher chance of finding a pattern if one exists. Contrary to the almost uniformly negative perception of probability matching, we therefore conclude that there can be a potentially smart strategy behind probability matching.     

Indicative conditionals,conditional probabilities,and the “defective truth-table”: A request for more experiments

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ? entails conditional-free ψ, “if ? then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional.     

Gamma oscillations distinguish true from false memories

ABSTRACT— To test whether distinct patterns of electrophysiological activity prior to a response can distinguish true from false memories, we analyzed intracranial electroencephalographic recordings while 52 patients undergoing treatment for epilepsy performed a verbal free-recall task. These analyses revealed that the same pattern of gamma-band (28–100 Hz) oscillatory activity that predicts successful memory formation at item encoding—increased gamma power in the hippocampus, prefrontal cortex, and left temporal lobe—reemerges at retrieval to distinguish correct from incorrect responses. The timing of these oscillatory effects suggests that self-cued memory retrieval begins in the hippocampus and then spreads to the cortex. Thus, retrieval of true, as compared with false, memories induces a distinct pattern of gamma oscillations, possibly reflecting recollection of contextual information associated with past experience.     

Coping patterns in shock anticipation and in everyday stress

Abstract.— GSR patterns were studied in 30 subjects anticipating and receiving electric shocks with high but not definitive probability. Although the majority of subjects showed anticipatory responses, six subjects displayed low or no response during anticipation but very high responses to shocks. As these subjects also reported that during anticipation they tended to deny the possibility of receiving a shock, their response pattern was interpreted as indicating denial of threat, and consequently, little preparation for stress. Self reports about behavior in everyday stress revealed a similar kind of behavior.     

Recall termination in free recall

Although much is known about the dynamics of memory search in the free recall task, relatively little is known about the factors related to recall termination. Reanalyzing individual trial data from 14 prior studies (1,079 participants in 28,015 trials) and defining termination as occurring when a final response is followed by a long nonresponse interval, we observed that termination probability increased throughout the recall period and that retrieval was more likely to terminate following an error than following a correct response. Among errors, termination probability was higher following prior-list intrusions and repetitions than following extralist intrusions. To verify that this pattern of results can be seen in a single study, we report a new experiment in which 80 participants contributed recall data from a total of 9,122 trials. This experiment replicated the pattern observed in the aggregate analysis of the prior studies.     

Choice as a function of local versus molar reinforcement contingencies.

Rats were trained on a discrete-trial probability learning task. In Experiment 1, the molar reinforcement probabilities for the two response alternatives were equal, and the local contingencies of reinforcement differentially reinforced a win-stay, lose-shift response pattern. The win-stay portion was learned substantially more easily and appeared from the outset of training, suggesting that its occurrence did not depend upon discrimination of the local contingencies but rather only upon simple strengthening effects of individual reinforcements. Control by both types of local contingencies decreased with increases in the intertrial interval, although some control remained with intertrial intervals as long as 30 s. In Experiment 2, the local contingencies always favored win-shift and lose-shift response patterns but were asymmetrical for the two responses, causing the molar reinforcement rates for the two responses to differ. Some learning of the alternation pattern occurred with short intertrial intervals, although win-stay behavior occurred for some subjects. The local reinforcement contingencies were discriminated poorly with longer intertrial intervals. In the absence of control by the local contingencies, choice proportion was determined by the molar contingencies, as indicated by high exponent values for the generalized matching law with long intertrial intervals, and lower values with short intertrial intervals. The results show that when molar contingencies of reinforcement and local contingencies are in opposition, both may have independent roles. Control by molar contingencies cannot generally be explained by local contingencies.     

Neural activity during encoding predicts false memories created by misinformation

False memories are often demonstrated using the misinformation paradigm, in which a person's recollection of a witnessed event is altered after exposure to misinformation about the event. The neural basis of this phenomenon, however, remains unknown. We used fMRI to investigate encoding processes during the viewing of an event and misinformation to see whether neural activity during either encoding phase could predict what would be remembered. fMRI data were collected as participants studied eight vignettes (Original Event phase). Shortly afterward, participants studied the same vignettes during scanning, but with changes to several details, serving as the misinformation (Misinformation phase). Two days later, their memories for the Original Event were assessed. Activity that subsequently led to true and false memories was examined during both encoding phases. Two interaction patterns between encoding phase (Original Event and Misinformation) and type of memory (true and false) were observed in MTL and PFC regions. In the left hippocampus tail and perirhinal cortex, a predictive item-encoding pattern was observed. During the Original Event phase, activity was greater for true than false memories, whereas during the Misinformation phase, activity was greater for false than true memories. In other regions, a pattern suggestive of source encoding was observed, in which activity for false memories was greater during the Original Event phase than the Misinformation phase. Together, these results suggest that encoding processes play a critical role in determining true and false memory outcome in misinformation paradigms.     

Modeling patterns of probability calibration with random support theory: Diagnosing case-based judgment

We describe four broad characterizations of subjective probability calibration (overconfidence, conservatism, ecologically perfect calibration, and case-based judgment) and show how Random Support Theory (RST) can serve as a tool for representing, evaluating, and discriminating between these perspectives. We present five studies of probability judgment in a simulated stock market setting and analyse the calibration data in terms of RST parameters. The observed pattern of calibration varies with the outcome base rate and cue value diagnosticity, as predicted by case-based judgment. A similar pattern of calibration is found in real-world judgments of experts in various domains. Case-based RST—defined as RST with stable parameter values—provides a parsimonious account of the substantial changes in calibration performance observed across different judgment environments.     

基于等级反应模型的规则空间方法

本研究基于Tatsuoka的规则空间方法, 对理想反应模式与异常反应指标进行了扩展, 推导了多级评分项目下规则空间方法的算法公式。在4种属性层级结构(发散型、收敛型、线型与无结构型)×4种“失误”作答概率(2%、5%、10%与15%)测验情境下, 以属性模式判准率、被试属性判准率、敏感性与特异性为指标, 检验了多级评分项目下规则空间方法的分类准确性。结果表明：(1) 基于多级评分项目构建的异常反应指标, 能有效地对被试进行分类与解释, 且0-1评分项目下异常反应指标及其性质都是多级评分下的特例; (2) 随着“失误”作答概率的增加, 4种属性层级结构的分类准确性都会降低; (3) 线型和收敛型的分类准确性明显好于发散型与无结构型; (4) 纯规则点的分布对规则空间方法的分类准确性有显著影响。