Ordinal consistency and ordinal true scores

This paper argues that test data are ordinal, that latent trait scores are only determined ordinally, and that test data are used largely for ordinal purposes. Therefore it is desirable to develop a test theory based only on ordinal assumptions. A set of ordinal assumptions is presented, including an ordinal version of local independence. From these assumptions it is first shown that the gamma-correlation between two tests is the product of their gamma-correlations with the true latent order. The theory is generalized to allow for heterogeneous tests by defining a weighted average local independence. The tau-correlations between total score and the latent order can be found in both homogeneous and heterogeneous cases, and a system of differential item weighting to maximize the tau-correlation between weighted items and the latent order is provided. Thus a purely ordinal test theory seems possible.Part of this work was done while the author was a Visiting Fellow at Macquarrie University. The paper has benefitted from discussions with Professors Thomas J. Reynolds and Roderick P. McDonald and from the comments of several anonymous reviewers.     

Sequential effects in dimensional contrast

Two experiments examined pigeons' response rates during short trials signaled by stimuli closely spaced along a wavelength continuum. In Experiment 1 separate halves of the continuum were correlated with different reinforcement schedules. In Experiment 2, the middle stimulus was accompanied by a lower probability of reinforcement than were the remaining wavelengths. Both procedures resulted in dimensional contrast “shoulders,” seen as relatively enhanced or depressed response rates in the presence of stimuli between the extreme of the continuum and the border separating the positive and negative stimuli. Sequential analyses addressed possible contributions of the following interactions: (a) local contrast, seen when rate during a given schedule depends on the schedule in the just-preceding trial; (b) modification of local contrast by the similarity of the signaling stimuli (P. Blough, 1983); and (c) schedule-independent rate contrast, seen when rate in a given trial depends on the rate controlled by the stimulus that accompanied the just-preceding trial (Malone & Rowe, 1981). Dimensional contrast functions were similar when isolated according to the schedule, to the similarity of the signaling stimulus, and to the response rate of the just-preceding trial. The interactions noted above do not appear to make important contributions to this effect.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

Transfer effects from language processing to visual attention dynamics: The impact of orthographic transparency

The consistency between letters and sounds varies across languages. These differences have been proposed to be associated with different reading mechanisms (lexical vs. phonological), processing grain sizes (coarse vs. fine) and attentional windows (whole words vs. individual letters). This study aimed to extend this idea to writing to dictation. For that purpose, we evaluated whether the use of different types of processing has a differential impact on local windowing attention: phonological (local) processing in a transparent language (Spanish) and lexical (global) processing of an opaque language (English). Spanish and English monolinguals (Experiment 1) and Spanish–English bilinguals (Experiment 2) performed a writing to dictation task followed by a global–local task. The first key performance showed a critical dissociation between languages: the response times (RTs) from the Spanish writing to dictation task was modulated by word length, whereas the RTs from the English writing to dictation task was modulated by word frequency and age of acquisition, as evidence that language transparency biases processing towards phonological or lexical strategies. In addition, after a Spanish task, participants more efficiently processed local information, which resulted in both the benefit of global congruent information and the reduced cost of incongruent global information. Additionally, the results showed that bilinguals adapt their attentional processing depending on the orthographic transparency.     

儿童运动视觉表象操作水平的发展及影响因素

采用计算机软件控制实验,以暴露运动一段行程后进入遮蔽的光点为刺激物,光点以三种不同运动速度、三种不同运动行距组合呈现,要求儿童判断光点到达目标位置时按键反应。结果表明：5—19岁儿童运动视觉表象操作水平的发展存在5一8岁、11—14岁两个加速期;客体运动速度对运动视觉表象操作绩效有显著影响,5、8、11岁组快速较中速下．5．8岁组中速较慢速下操作准确性均有显著降低;客体运动行距对运动视觉表象操作绩效也有显著的影响．5、8、11岁组右目标位置下较中目标位置下操作准确性显著降低;性别对运动视觉表象操作水平无显著影响。     

Effects of component length and of the transitions among components in multiple schedules

Pigeons received equal variable-interval reinforcement during presentations of two line-orientation stimuli while five other orientations appeared in extinction. Component duration was 30 seconds for all orientations and the sequence was arranged so that each orientation preceded itself and each other orientation equally often. The duration of one component (0°) was shortened to 10 seconds and the other (90°) was lengthened to 50 seconds. All animals showed large increases in response rate in the shortened component and this increase was recoverable after an interpolated condition in which all components were again 30 seconds in duration. This effect was replicated in a second experiment in which component duration was changed from 150 seconds to 50 seconds and 250 seconds. An examination of local contrast effects during the first experiment showed that the shortened component produced local contrast during subsequent presentations of the lengthened component, just as would a component associated with more frequent reinforcement. When the presentation sequence was changed so that the lengthened component was always followed by the shortened component, response rates generally increased during the lengthened component. When the sequence was arranged so that the shortened component always preceded the longer component, response rate decreased in the former. These effects, as well as the increases in response rate following change in component length, seem not to be the product of local contrast effects among components.     

Local contrast and maintained generalization.

Pigeons received variable-interval reinforcement for key pecking during presentations of horizontal and vertical line-orientation stimuli, while pecks during five intermediate orientations were extinguished. Lowest peck rates were observed during presentations of negative stimuli adjacent to the positive orientations while peck rate during 45 degrees (the intermediate negative orientation) was relatively high, i.e., there were negative contrast shoulders. When peck rates were manipulated in the positive orientations, peck rate in neithboring orientations changed in the opposite direction. Contrast shoulders faded after prolonged training. A second type of contrast, local contrast, was correlated with similarity of preceding stimulus and different average peck rates during different stages of the discrimination process. The data suggest that sequential local contrast accompanying the formation of a discrimination contributes to the form of generalization gradients. Blough's model of stimulus control predicts the changes in gradient form described here, but may not accurately depict the underlying process responsible for gradient form.     

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.     

Essential independence and likelihood-based ability estimation for polytomous items

A definition ofessential independence is proposed for sequences of polytomous items. For items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability, we develop a theory ofessential unidimensionality which closely parallels that of Stout. Essentially unidimensional item sequences can be shown to have a unique (up to change-of-scale) dominant underlying trait, which can be consistently estimated by a monotone transformation of the sum of the item scores. In more general polytomous-response latent trait models (with or without ordered responses), anM-estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity/identifiability conditions. A rigorous proof of this fact is given, and the standard error of the estimator is explored. These results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence, but standard errors may vary greatly from what is usually expected, depending on the degree of departure from local independence. An index of departure from local independence is also proposed.This work was supported in part by Office of Naval Research Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556. The author is grateful to William F. Stout for many helpful comments, and to an anonymous reviewer for raising the questions addressed in section 2. A preliminary version of section 6 appeared in the author's Ph.D. thesis.     

A note on the investigation of local and global identifiability

In general, nonlinear models such as those commonly employed for the analysis of covariance structures, are not globally identifiable. Any investigation of local identifiability must either yield a mapping of identifiability onto the entire parameter space, which will rarely be feasible in any applications of interest, or confine itself to the neighbourhood of such points of special interest as the maximum likelihood point.The author would like to thank J. Jack McArdle and Colin Fraser for their comments on this paper.