Multiplicatively interacting factors selectively influencing parameters in multiple response class processing and rate trees

Evidence in many experiments indicates that the processes involved in producing responses are arranged in a tree structure. Evidence often indicates further that an experimental factor, such as item similarity, changes a single parameter, leaving others invariant. In typical studies, a few tree structures are hypothesized a priori, and tested by goodness of fit. With the method of Tree Inference, a tree is constructed by examining the data to see if patterns occur that are predicted when two factors selectively influence different processes (Schweickert & Chen, 2008). The patterns can reveal, for example, whether selectively influenced processes are executed in order, and what the order is. If the patterns do not occur, one can conclude that no tree is possible in which the factors selectively influence processes. In earlier work, three restrictions were imposed on the trees considered: There were two classes of responses; parameters were probabilities, bounded above by 1; and factors were assumed to change parameters associated with children of a single vertex. More general results are derived here, removing these restrictions. Results on representation, uniqueness of parameters, uniqueness of tree structure, and mixtures of trees are presented.     

Cognitive psychometrics: assessing storage and retrieval deficits in special populations with multinomial processing tree models

This article demonstrates how multinomial processing tree models can be used as assessment tools to measure cognitive deficits in clinical populations. This is illustrated with a model developed by W. H. Batchelder and D. M. Riefer (1980) that separately measures storage and retrieval processes in memory. The validity of the model is tested in 2 experiments, which show that presentation rate affects the storage of items (Experiment 1) and part-list cuing hurts item retrieval (Experiment 2). Experiments 3 and 4 examine 2 clinical populations: schizophrenics and alcoholics with organic brain damage. The model reveals that each group exhibits deficits in storage and retrieval, with the retrieval deficits being stronger and occurring more consistently over trials. Also, the alcoholics with organic brain damage show no improvement in retrieval over trials, although their storage improves at the same rate as a control group.     

Additive factors and stages of mental processes in task networks

To perform a task a subject executes mental processes. An experimental manipulation, such as a change in stimulus intensity, is said to selectively influence a process if it changes the duration of that process leaving other process durations unchanged. For random process durations a definition of a factor selectively influencing a process by increments is given in terms of stochastic dominance (also called “the usual stochastic order”). A technique for analyzing reaction times, Sternberg’s Additive Factor Method, assumes all the processes are in series. When all processes are in series, each process is called a stage. With the Additive Factor Method, if two experimental factors selectively influence two different stages by increments, the factors will have additive effects on reaction time. An assumption of the Additive Factor Method is that if two experimental factors interact, then they influence the same stage. We consider sets of processes in which some pairs of processes are sequential and some are concurrent (i.e., the processes are partially ordered). We propose a natural definition of a stage for such sets of processes. For partially ordered processes, with our definition of a stage, if two experimental factors selectively influence two different processes by increments, each within a different stage, then the factors have additive effects. If each process selectively influenced by increments is in the same stage, then an interaction is possible, although not inevitable.     

The statistical analysis of general processing tree models with the EM algorithm

Multinomial processing tree models assume that an observed behavior category can arise from one or more processing sequences represented as branches in a tree. These models form a subclass of parametric, multinomial models, and they provide a substantively motivated alternative to loglinear models. We consider the usual case where branch probabilities are products of nonnegative integer powers in the parameters, 0_s1, and their complements, 1 - _s. A version of the EM algorithm is constructed that has very strong properties. First, the E-step and the M-step are both analytic and computationally easy; therefore, a fast PC program can be constructed for obtaining MLEs for large numbers of parameters. Second, a closed form expression for the observed Fisher information matrix is obtained for the entire class. Third, it is proved that the algorithm necessarily converges to a local maximum, and this is a stronger result than for the exponential family as a whole. Fourth, we show how the algorithm can handle quite general hypothesis tests concerning restrictions on the model parameters. Fifth, we extend the algorithm to handle the Read and Cressie power divergence family of goodness-of-fit statistics. The paper includes an example to illustrate some of these results.This research was supported by National Science Foundation Grant BNS-8910552 to William H. Batchelder and David M. Riefer. We are grateful to David Riefer for his useful comments, and to the Institute for Mathematical Behavior Sciences for its support.     

多项式加工树模型次序约束的量化分析及其应用

多项式加工树（MPT）模型是一种认知测量模型,能够对潜在认知过程进行测量和检验。已有研究探讨了二链MPT模型次序约束的重新参数化问题,本研究探讨了MPT模型次序约束的量化分析方法并从二链推广到多链,同时归纳出MPT模型参数向量内和参数向量间两参数次序约束量化分析的结论。数据分析结果表明该方法不仅在MPT模型框架下验证了潜在参数次序关系,而且给出了约束的量化指标,为潜在认知测量提供更有意义的解释。     

学习次数对记忆源检测图片偏向的影响

人们总是会根据他们对记忆工作模式的原有假设或图式来进行源检测, 这使得图片—文字源检测测验中出现图片偏向, 即人们更多倾向于将以文字方式呈现的项目错误归源于视觉图像形式呈现, 而不是将图像形式呈现的项目归于文字形式呈现。实验采用标准的源检测范式, 考察了学习次数对记忆源检测图片偏向的影响。结果发现随着学习次数的增加, 记忆源检测的图片偏向越发明显。     

Selective Influence and Response Time Cumulative Distribution Functions in Serial-Parallel Task Networks

We analyze sets of mental processes, some of which are concurrent and some of which are sequential, under the assumption that the processes are partially ordered, that is, arranged in a directed acyclic network. Information about the process arrangement can be discovered by examining the effects on response time of selectively influencing process durations. Previous work has mainly focused on analyses of mean response times. Here we consider analyses based on cumulative distribution functions, for one of the major classes of directed acyclic networks, serial-parallel networks. When two processes are selectively influenced, patterns in the cumulative distribution functions can be used to test whether the processes are sequential or concurrent and whether the task network has AND gates or OR gates. Cumulative distribution functions are potentially more informative than means, and some previous results for means are shown to follow from our results for cumulative distribution functions. Copyright 2000 Academic Press.     

Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach

Multinomial processing tree models are widely used in many areas of psychology. Their application relies on the assumption of parameter homogeneity, that is, on the assumption that participants do not differ in their parameter values. Tests for parameter homogeneity are proposed that can be routinely used as part of multinomial model analyses to defend the assumption. If parameter homogeneity is found to be violated, a new family of models, termed latent-class multinomial processing tree models, can be applied that accommodates parameter heterogeneity and correlated parameters, yet preserves most of the advantages of the traditional multinomial method. Estimation, goodness-of-fit tests, and tests of other hypotheses of interest are considered for the new family of models. The author thanks Bill Batchelder, Edgar Erdfelder, Thorsten Meiser, and Christoph Stahl for helpful comments on a previous version of this paper. The author is also grateful to Edgar Erdfelder for making available the data set analyzed in this paper.     

Evaluation of six multinomial models of conscious and unconscious processes with the recall-recognition paradigm

Six multinomial processing-tree models (W. H. Batchelder & D. M. Riefer, 1999), which include parameters representing conscious and unconscious memory processes, were tested using the recall-recognition paradigm. Data from 2 experiments were fit equally well by 3 of the 6 models. One model recognition was an extension of the generate-recognize model (L. L. Jacoby, 1998), and another was an extension of the non-high-threshold model (D. M. McBride & B. A. Dosher, 1999). The 3rd model was the source evaluation model (D. M. McBride & B. A. Dosher, 1999). Values of the parameters of 2 of these 3 models, excepting the non-high-threshold model, responded to experimental manipulations in accordance with the meaning of the parameters. The equivalence of models with regard to goodness-of-fit tests is discussed as is how experiments can be designed to demonstrate the superiority of one model over another. The potential usefulness of these models in the study of amnesia is considered.     

A multinomial processing tree model for degradation and redintegration in immediate recall

When items are presented for immediate recall, a verbal trace is formed and degrades quickly, becoming useless after about 2 sec. The span for items such as digits equals the number of items that canbe pronounced in the available time. The length of the items affects span by affecting pronunciation rate. Other properties, such as phonological similarity and lexicality, can affect span without affecting pronunciation rate. These properties change the trace's useful lifetime by affecting redintegration. An analogy is drawn between trace reconstruction and repair of errors in speech. When a trace is degraded, one process attempts to form a phoneme string, and another process attempts to form a word. The two processes are autonomous and can be selectively influenced by lexicality and phonological similarity. The resulting processing tree models make simple predictions that depend on whether or not the influenced processes are sequential. The results are illustrated with data from experiments by Besner and Davelaar (1982).     

Separate modifiability, mental modules, and the use of pure and composite measures to reveal them

How can we divide a complex mental process into meaningful parts? In this paper, I explore an approach in which processes are divided into parts that are modular in the sense of being separately modifiable. Evidence for separate modifiability is provided by an instance of selective influence: two factors F and G (usually experimental manipulations) such that part A is influenced by F but invariant with respect to G, while part B is influenced by G but invariant with respect to F. Such evidence also indicates that the modules are functionally distinct. If we have pure measures MA and MB, each of which reflects only one of the parts, we need to show that MA is influenced by F but not G, while MB is influenced by G but not F. If we have only a composite measure MAB of the entire process, we usually also need to confirm a combination rule for how the parts contribute to MAB. I present a taxonomy of separate-modifiability methods, discuss their inferential logic, and describe several examples in each category. The three categories involve measures that are derived pure (based on different transformations of the same data; example: separation of sensory and decision processes by signal detection theory), direct pure (based on different data; example: selective effects of adaptation on spatial-frequency thresholds), and composite (examples: the multiplicative-factor method for the analysis of response rate; the additive-factor method for the analysis of reaction time). Six of the examples concern behavioral measures and functional processes, while four concern brain measures and neural processes. They have been chosen for their interest and importance; their diversity of measures, species, and combination rules; their illustration of different ways of thinking about data; the questions they suggest about possibilities and limitations of the separate-modifiability approach; and the case they make for the fruitfulness of searching for mental modules.     

The advantages of mathematical modeling over traditional methods in the analysis of category clustering

A mathematical model for the analysis of category clustering is developed and testd. The model, which can be applied to categories of any size, is an extension of a two-item statistical model developed by Batchelder and Riefer (Psychological Review, 1980, 87, 375–397), and is equivalent to their model when categories consist of two items. The model is based on a current theory of clustering which postulates that the learning of a list of category items occurs on different hierarchical levels. Two category list-learning experiments are presented, and the data from these experiments are analyzed using the general statistical model. The first experiment reveals that the probabilities of storing and retrieving a cluster increase with category size, while the learning of items as singletons decreases. The effects of within-category spacing indicate that the storage of clusters decreases while cluster retrievability increases with an increase in input spacing. In the second experiment, the storage and retrieval of clusters are shown to be unaffected by whether the presentation of items is uncued or cued with the name of the category. However, the association of items decreases and the learning of items as singletons increases with uncued presentation. In the final sections, the general statistical model is compared to other methods for the measurement of category clustering. The model is shown to be superior to numerical indices of clustering, since these measures are not based on any theory of clustering, and because unitary measures cannot capture the multiprocess nature of categorized recall. The model is also argued to have certain advantages over other mathematical models that have been applied to category clustering, since these models cannot account for situations in which a portion of the items are clustered while others are learned singularly.     

A general model of relationship commitment: Evidence from same‐sex partners

A model of relationship commitment previously validated with data from both partners from dating heterosexual couples was tested with survey data obtained from both partners from 304 same‐sex couples cohabiting in the United States. The model posits that commitment is influenced by factors that are ordered along a proximal–distal continuum. From most distal to most proximal, these factors are personality traits, support for the relationship from family members and friends, effective arguing, and dependence on the relationship. Of the 25 predicted effects, 23 were significant (p < .05). Findings support the use of the model for understanding commitment processes for diverse types of dyadic relationships.     

From exemplar to grammar: a probabilistic analogy-based model of language learning

While rules and exemplars are usually viewed as opposites, this paper argues that they form end points of the same distribution. By representing both rules and exemplars as (partial) trees, we can take into account the fluid middle ground between the two extremes. This insight is the starting point for a new theory of language learning that is based on the following idea: If a language learner does not know which phrase-structure trees should be assigned to initial sentences, s/he allows (implicitly) for all possible trees and lets linguistic experience decide which is the "best" tree for each sentence. The best tree is obtained by maximizing "structural analogy" between a sentence and previous sentences, which is formalized by the most probable shortest combination of subtrees from all trees of previous sentences. Corpus-based experiments with this model on the Penn Treebank and the Childes database indicate that it can learn both exemplar-based and rule-based aspects of language, ranging from phrasal verbs to auxiliary fronting. By having learned the syntactic structures of sentences, we have also learned the grammar implicit in these structures, which can in turn be used to produce new sentences. We show that our model mimicks children's language development from item-based constructions to abstract constructions, and that the model can simulate some of the errors made by children in producing complex questions.     

Memory for common and bizarre stimuli: A storage-retrieval analysis

We tested the hypothesis that common stimuli are stored in memory better than bizarre stimuli are. Subjects memorized a series of noun pairs embedded within 20 common or bizarre sentences. By using a between-list design, free and cued recall, and intentional-learning instructions, we were able to obtain a commonness effect (i.e., a recall advantage for the common sentences). Riefer and Rouder’s (1992) multinomial processing-tree model for measuring storage and retrieval was applied to the data, which revealed that the recall advantage for common sentences was due to storage and not retrieval processes. We propose a two-factor theory: that common items are stored better in memory, but that bizarre items are retrieved better from memory. This storage-retrieval explanation does a good job of accounting for a number of findings associated with the bizarreness effect.     

Additive similarity trees

Similarity data can be represented by additive trees. In this model, objects are represented by the external nodes of a tree, and the dissimilarity between objects is the length of the path joining them. The additive tree is less restrictive than the ultrametric tree, commonly known as the hierarchical clustering scheme. The two representations are characterized and compared. A computer program, ADDTREE, for the construction of additive trees is described and applied to several sets of data. A comparison of these results to the results of multidimensional scaling illustrates some empirical and theoretical advantages of tree representations over spatial representations of proximity data.We thank Nancy Henley and Vered Kraus for providing us with data, and Jan deLeeuw for calling our attention to relevant literature. The work of the first author was supported in part by the Psychology Unit of the Israel Defense Forces.     

TreeBUGS: An R package for hierarchical multinomial-processing-tree modeling

Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes. Traditionally, data are aggregated across participants and analyzed under the assumption of independently and identically distributed observations. Hierarchical Bayesian extensions of MPT models explicitly account for participant heterogeneity by assuming that the individual parameters follow a continuous hierarchical distribution. We provide an accessible introduction to hierarchical MPT modeling and present the user-friendly and comprehensive R package TreeBUGS, which implements the two most important hierarchical MPT approaches for participant heterogeneity—the beta-MPT approach (Smith & Batchelder, Journal of Mathematical Psychology 54:167-183, 2010) and the latent-trait MPT approach (Klauer, Psychometrika 75:70-98, 2010). TreeBUGS reads standard MPT model files and obtains Markov-chain Monte Carlo samples that approximate the posterior distribution. The functionality and output are tailored to the specific needs of MPT modelers and provide tests for the homogeneity of items and participants, individual and group parameter estimates, fit statistics, and within- and between-subjects comparisons, as well as goodness-of-fit and summary plots. We also propose and implement novel statistical extensions to include continuous and discrete predictors (as either fixed or random effects) in the latent-trait MPT model.     

Topological Aspects of Branching-Time Semantics

The aim of this paper is to present a new perspective under which branching-time semantics can be viewed. The set of histories (maximal linearly ordered sets) in a tree structure can be endowed in a natural way with a topological structure. Properties of trees and of bundled trees can be expressed in topological terms. In particular, we can consider the new notion of topological validity for Ockhamist temporal formulae. It will be proved that this notion of validity is equivalent to validity with respect to bundled trees.     

Logic-based XML data integration: a semi-materializing approach

We first describe the approach to XML data integration in the XPathLog/LoPiX project that uses a warehouse strategy. We show that the DOM model and the XML Query Data Model are not suitable for this task since the integrated database is not necessarily a tree, but a set of overlapping (original and integrated) trees. The problem is solved by using a node-labeled graph-based data model, called XTreeGraph, for the internal XML database that represents multiple, overlapping XML trees, or tree views.In the second part, we return to the standard XML data model—by still keeping the overlapping tree idea by “simulating” it: The data is internally represented by XML where the “overlayed” resulting tree is represented by XLink elements that refer to the original sources. By using a logical, transparent data model for XLinks as investigated in [May, in: 11th WWW Conference, 2002], all queries behave as stated against the XTreeGraph. The use of links for partial materialization also turns the approach from a warehouse approach into a mixed approach that combines the advantages of the warehouse approach and of the virtual approach. The approach is again illustrated by using XPathLog as data integration language.     

Mental architectures with selectively influenced but stochastically interdependent components

The way external factors influence distribution functions for the overall time required to perform a mental task (such as responding to a stimulus, or solving a problem) may be informative as to the underlying mental architecture, the hypothetical network of interconnected processes some of which are selectively influenced by some of the external factors. Under the assumption that all processes contributing to the overall performance time are stochastically independent, several basic results have been previously established. These results relate patterns of response time distribution functions produced by manipulating external factors to such questions as whether the hypothetical constituent processes in the mental architecture enter AND gates or OR gates, and whether pairs of processes are sequential or concurrent. The present study shows that all these results are also valid for stochastically interdependent component times, provided the selective dependence of these components upon external factors is understood within the framework of a recently proposed theory of selective influence. According to this theory each component is representable as a function of three arguments: the factor set selectively influencing it, a component-specific source of randomness, and a source of randomness shared by all the components.