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The Theoretical Status of Latent Variables
 Psychological Review
, 2003
"... This article examines the theoretical status of latent variables as used in modern test theory models. First, it is argued that a consistent interpretation of such models requires a realist ontology for latent variables. Second, the relation between latent variables and their indicators is discussed ..."
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This article examines the theoretical status of latent variables as used in modern test theory models. First, it is argued that a consistent interpretation of such models requires a realist ontology for latent variables. Second, the relation between latent variables and their indicators is discussed. It is maintained that this relation can be interpreted as a causal one but that in measurement models for interindividual differences the relation does not apply to the level of the individual person. To substantiate intraindividual causal conclusions, one must explicitly represent individual level processes in the measurement model. Several research strategies that may be useful in this respect are discussed, and a typology of constructs is proposed on the basis of this analysis. The need to link individual processes to latent variable models for interindividual differences is emphasized. Consider the following sentence: “Einstein would not have been able to come up with his e � mc 2 had he not possessed such an extraordinary intelligence. ” What does this sentence express? It relates observable behavior (Einstein’s writing e � mc 2)toan unobservable attribute (his extraordinary intelligence), and it does so by assigning to the unobservable attribute a causal role in
On Reichenbach's common cause principle and Reichenbach's notion of common cause
"... It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlation ..."
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It is shown that, given any finite set of pairs of random events in a Boolean algebra which are correlated with respect to a fixed probability measure on the algebra, the algebra can be extended in such a way that the extension contains events that can be regarded as common causes of the correlations in the sense of Reichenbach's definition of common cause. It is shown, further, that, given any quantum probability space and any set of commuting events in it which are correlated with respect to a fixed quantum state, the quantum probability space can be extended in such a way that the extension contains common causes of all the selected correlations, where common cause is again taken in the sense of Reichenbach's definition. It is argued that these results very strongly restrict the possible ways of disproving Reichenbach's Common Cause Principle.
Conditional association, essential independence and monotone unidimensional item response models
 Annals of Statistics
, 1993
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Selective influence through conditional independence
 Psychometrika
, 2003
"... Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own ” fact ..."
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Cited by 18 (7 self)
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Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own ” factor set? The answer proposed and elaborated in this paper is: One can say this if and only if one can find a factorindependent random vector given whose value the vectors in question are conditionally independent, with their conditional distributions selectively influenced by the corresponding factor sets. Equivalently, the random vectors should be representable as deterministic functions of “their ” factor sets and of some mutually independent and factorindependent random variables, some of which may be shared by several of the functions. Key words: selective influence, conditional independence, marginal selectivity, processing architectures, Thurstonian modeling. 1. Problem This paper presents a generalization and improvement for the definition proposed in Dzhafarov (2001a) for selectiveness in the dependence of several random variables upon several (sets of) external factors. This generalization links the notion of selective influence with that of
Nonparametric item response theory in action: An overview of the special issue
 Applied Psychological Measurement
, 2001
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Generalized measurement models
, 2004
"... document without permission of its author may be prohibited by law. ..."
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Cited by 7 (4 self)
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document without permission of its author may be prohibited by law.
Bayesian Estimation of Discrete Multivariate Latent Structure Models with Structural Zeros
 Journal of Computational and Graphical Statistics
, 2014
"... In multivariate categorical data, models based on conditional independence assumptions, such as latent class models, offer efficient estimation of complex dependencies. However, Bayesian versions of latent structure models for categorical data typically do not appropriately handle impossible combin ..."
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In multivariate categorical data, models based on conditional independence assumptions, such as latent class models, offer efficient estimation of complex dependencies. However, Bayesian versions of latent structure models for categorical data typically do not appropriately handle impossible combinations of variables, also known as structural zeros. Allowing nonzero probability for impossible combinations results in inaccurate estimates of joint and conditional probabilities, even for feasible combinations. We present an approach for estimating posterior distributions in Bayesian latent structure models with potentially many structural zeros. The basic idea is to treat the observed data as a truncated sample from an augmented dataset, thereby allowing us to exploit the conditional independence assumptions for computational expediency. As part of the approach, we develop an algorithm for collapsing a large set of structural zero combinations into a much smaller set of disjoint marginal conditions, which greatly speeds computation. We apply the approach to sample from a semiparametric version of the latent class model with structural zeros in the context of a key issue faced by national statistical agencies seeking to disseminate confidential data to the public: estimating the number of records in a sample that are unique in the population on a
1 Causal Markov, Robustness and the Quantum Correlations
"... It is still a matter of controversy whether the Principle of the Common Cause (PCC) can be used as a basis for sound causal inference. It is thus to be expected that its application to quantum mechanics should be a correspondingly controversial issue. Indeed the early 90’s saw a flurry of papers add ..."
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It is still a matter of controversy whether the Principle of the Common Cause (PCC) can be used as a basis for sound causal inference. It is thus to be expected that its application to quantum mechanics should be a correspondingly controversial issue. Indeed the early 90’s saw a flurry of papers addressing just this issue in connection with the EPR correlations. Yet, that debate does not seem to have caught up with the most recent literature on causal inference generally, which has moved on to consider the virtues of a generalised PCCinspired condition, the socalled Causal Markov Condition (CMC). In this paper we argue that the CMC is an appropriate benchmark for debating possible causal explanations of the EPR correlations. But we go on to take issue with some pronouncements
Entanglement, Upper Probabilities and Decoherence in Quantum Mechanics
"... Abstract Computation of decay time for entangled quantum systems is an important aspect of decoherence theories. Here we explore this topic from the standpoint of computing the decay time to the existence of a joint probability distribution of the entangled particles – atoms, in our case. We also ..."
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Abstract Computation of decay time for entangled quantum systems is an important aspect of decoherence theories. Here we explore this topic from the standpoint of computing the decay time to the existence of a joint probability distribution of the entangled particles – atoms, in our case. We also analyze the problem from the viewpoint of the decay of an improper upper probability distribution, for the entangled particles and its continuous decay into a proper probability distribution. A standard quantum decoherence model and the upperprobability model have, it turns out, the same expected decay time for a familiar example of a system with a Bell state. Quantum mechanical entangled configurations of particles that do not satisfy Bell’s inequalities, or equivalently, do not have a joint probability distribution, are familiar in the foundational literature of quantum mechanics. Nonexistence of a joint probability measure for the correlations predicted by quantum mechanics is itself equivalent to the nonexistence of local hidden variables that account for the correlations (for a proof of this equivalence, see Suppes and Zanotti, 1981).