等效性检验——结构方程模型评价和测量不变性分析的新视角

常用的结构方程模型拟合指数存在一定局限, 如χ ²以传统零假设为目标假设, 无法验证模型, 而RMSEA和CFI等描述性的拟合指数不具备推断统计性质, 等效性检验有效弥补了这些问题。首先说明等效性检验如何评价单个模型的拟合, 并解释其与零假设检验的不同, 然后介绍等效性检验如何分析测量不变性, 接着用实证数据展示了等效性检验在单个模型评价和测量不变性检验中的效果, 并与传统模型评价方法比较。     

Equivalence classes with requirements for short response latencies

Five adult humans were tested for emergent conditional discriminations under rapid-responding contingencies. During four-comparison matching-to-sample baseline training (AB and AC), limited-hold contingencies for responding to samples and comparisons were gradually restricted to the shortest duration consistent with at least 95% accuracy and no more than 5% failures to respond. The final limited-hold values were 0.4-0.5 s for samples and 1.2-1.3 s for comparisons; mean response latencies were 0.15-0.28 s for samples and 0.59-0.73 s for comparisons; inter-trial intervals were 0.4 s. With these fast-responding requirements, test blocks presented 72 probe trials interspersed among 72 baseline trials, all without programmed differential consequences. Four equivalence test blocks (BC and CB probes, which tested simultaneously for both symmetry and transitivity) were followed by four symmetry (BA and CA probes) test blocks. Three subjects' results documented emergent performances indicative of equivalence classes despite fast-responding requirements that severely limited the time available for mediating vocal or subvocal responses. For these three subjects, mean latencies were slightly shorter in baseline trials than in probes, and shorter on symmetry than on equivalence probes. These differences, however, were usually less than the differences among mean latencies on the different types of trials within the baseline and probed performances.     

Medical Decision-Making: An Argument for Narrative and Metaphor

This study examines the processes ofdecision-making used by intensive care(critical care) specialists. Ninety-ninespecialists completed a questionnaire involvingthree clinical cases, using a novel methodologyinvestigating the role of uncertainty andtemporal-related factors, and exploring a rangeof ethical issues. Validation and triangulationof the results was done via a comparison studywith a medically lay, but highly informed groupof 37 law students. For both study groups,constructing reasons for a decision was largelyan interpretative and imaginative exercise thatwent beyond the data (as presented), commonlyresulting in different reasons supporting thesame conclusions and similar reasons supportingopposite conclusions. The skills of ethicalimagination and interpretation were related toan individual's prior lived experience,construed in the broadest sense. Application ofthese skills of ethical imagination andinterpretation always occurred, to some degree,in a state of uncertainty and almost alwaysinvolved temporal relationships.Using these results, a theory of ethicaldecision-making is proffered. Three levels ortypes of reasoning processes may be present.Type I decision-making involves the applicationof rules, usually in a deductive fashion. TypeII decision-making is characterised by aprocess where a plurality of reasons arebalanced, weighed and sifted with each other.Type III decision-making is intimately linkedwith respondents lived experiences and `crafts'the content of type I and II reasoningprocesses, via the application of ethicalimagination and interpretation. Relationshipsbetween these three types of reasoningprocesses, and with narrative ethics, are alsodiscussed.     

The formation of linked perceptual classes

Multiple-exemplar training with stimuli in four domains induced two new fill-based (A1' and A2') and satellite-image-based (B1' and B2') perceptual classes. Conditional discriminations were established between the endpoints of the A1' and B1' classes as well as the A2' and B2' classes. The emergence of linked perceptual classes was evaluated by the performances occasioned by nine cross-class probes that contained fill variants as samples and satellite variants as comparisons, along with nine other cross-class probes that consisted of satellite variants as samples and fill variants as comparisons. The 18 probes were first presented serially and then concurrently. Class-consistent responding indicated the emergence of linked perceptual classes. Of the linked perceptual classes, 70% emerged during the initial serial test. An additional 20% of the linked perceptual classes emerged during the subsequently presented concurrent test block. Thus, linked perceptual classes emerged on an immediate or delayed basis. Linked perceptual classes, then, share structural and fuctional similarities with equivalence classes, generalized equivalence classes, cross-modal classes, and complex maturally occurring categories, and may clarify processes such as intersensory perception.     

A functional-analytic model of analogy: a relational frame analysis

The aim of this study was to explore a behavior-analytic model of analogical reasoning, defined as the discrimination of formal similarity via equivalence-equivalence responding. In Experiment 1, adult humans were trained and tested for the formation of four three-member equivalence relations: A1-B1-C1, A2-B2-C2, A3-B3-C3, and A4-B4-C4. The B and C stimuli were three-letter nonsense syllables, and the A stimulus was a colored shape. Subjects were then successfully tested for equivalence-equivalence responding (e.g., matching B1/C1 to B2/C2 rather than B3/C4). These tasks were designed such that equivalence-equivalence responding might allow subjects to discriminate a physical similarity between the relations involved. Some participants (color subjects) received only equivalence-equivalence tasks in which they might discriminate a color relation, whereas others (shape subjects) were given tasks in which they might discriminate a shape relation. A control group received both types of task. In a subsequent test for the discrimination of formal similarity, color subjects matched according to color, shape subjects matched according to shape, and the control group showed no consistent matching pattern. In Experiment 2, adult humans showed a transformation of the functions of a block-sorting task via this basic model of analogy. Empirical and conceptual issues related to these results are discussed.     

The development of emergent differential sample behavior in pigeons

Three experiments attempted to replicate Manabe, Kawashima, and Staddon's (1995) finding of emergent differential sample behavior in budgerigars that has been interpreted as evidence of functional equivalence class formation. In Experiments 1 and 2, pigeons initially learned two-sample/ two-alternative matching to sample in which comparison presentation was contingent on pecking one sample on a differential-reinforcement-of-low-rate (DRL) schedule and the other on a fixed-ratio (FR) schedule. Later, two new samples were added to the task. Comparison presentation on these trials occurred after the first sample peck following a predetermined interval (Experiment 1) or after completion of either the DRL or FR requirement, whichever occurred first (Experiment 2). Experiment 1 found no evidence for emergent spaced versus rapid responding to the new samples as they established conditional control over the familiar choices. By contrast, differential responding did emerge for some pigeons in Experiment 2, with responding to each new sample coinciding with the pattern explicitly conditioned to the original sample occasioning the same comparison choice. This emergent effect, however, disappeared for most pigeons with continued training. Experiment 3 systematically replicated Experiment 2 using differential peck location as the sample behavior. Differential location pecking emerged to the new samples for most pigeons and remained intact throughout training. Our findings demonstrate a viable pigeon analogue to the budgerigar emergent calling paradigm and are discussed in terms of equivalence- and non-equivalence-based processes.     

Naturalism Need Not Be "Made Safe": A Response to William Rottschaefer's Misunderstandings

In this article, I respond to William Rottschaefer's analysis of my writings on religion and science, especially my Religion, Science and Naturalism (1996). I show that I am not trying "to make naturalism safe," as Rottschaefer contends, but rather attempting to explore options available when one endorses naturalistic approaches. I also explain why I object to the label "supernaturalistic naturalism" used by Rottschaefer. Possible limitations to naturalistic projects are discussed, not as limitations imposed but rather as features uncovered.     

Discerning the Limits of Religious Naturalism

In response to my "How to Make Naturalism Safe for Supernaturalism: An Evaluation of Willem Drees's Supernaturalistic Naturalism" (Rottschaefer 2001), Willem Drees maintains that I have misunderstood his purpose and views and have failed to make the case against his view that naturalism is intrinsically limited. In this response, I comment on these concerns.