What Carries a Mediation Process? Configural Analysis of Mediation

Mediation is a process that links a predictor and a criterion via a mediator variable. Mediation can be full or partial. This well-established definition operates at the level of variables even if they are categorical. In this article, two new approaches to the analysis of mediation are proposed. Both of these approaches focus on the analysis of categorical variables. The first involves mediation analysis at the level of configurations instead of variables. Thus, mediation can be incorporated into the arsenal of methods of analysis for person-oriented research. Second, it is proposed that Configural Frequency Analysis (CFA) can be used for both exploration and confirmation of mediation relationships among categorical variables. The implications of using CFA are first that mediation hypotheses can be tested at the level of individual configurations instead of variables. Second, this approach leaves the door open for different types of mediation processes to exist within the same set. Using a data example, it is illustrated that aggregate-level analysis can overlook mediation processes that operate at the level of individual configurations.     

"The" interpretation(s) of conditionals

Recent studies indicate that a vast majority of people judge the probability of a conditional as equivalent to the conditional probability of . This means that in evaluating the applicability of a conditional people do not seem to take into account situations in which the antecedent is false. This has been taken as evidence against the model theory of Johnson-Laird and Byrne (2002). This theory, however, claims that the conditional interpretation in which false-antecedent cases are relevant is only one of many possible interpretations of "if." We present new evidence that confirms this flexibility of the interpretive system. When people are primed by thinking (1) about truth and the difference between the and or (2) are invited to judge which situations are consistent with the conditional, they are more likely to select a probability estimate that takes into account the false-antecedent cases.     

The use of configural frequency analysis for explorative data analysis

Configural frequency analysis (CFA) is a widely used method of explorative data analysis. It tries to detect patterns in the data that occur significantly more or significantly less often than expected by chance. Patterns which occur more often than expected by chance are called CFA types, while those which occur less often than expected by chance are called CFA antitypes. The patterns detected are used to generate knowledge about the mechanisms underlying the data. We investigate the ability of CFA to detect adequate types and antitypes in a number of simulation studies. The basic idea of these studies is to predefine sets of types and antitypes and a mechanism which uses them to create a simulated data set. This simulated data set is then analysed with CFA and the detected types and antitypes are compared to the predefined ones. The predefined types and antitypes together with the method to generate the data are called a data generation model. The results of the simulation studies show that CFA can be used in quite different research contexts to detect structural dependencies in observed data. In addition, we can learn from these simulation studies how much data is necessary to enable CFA to reconstruct the predefined types and antitypes with sufficient accuracy. For one of the data generation models investigated, implicitly underlying knowledge space theory, it was shown that zero‐order CFA can be used to reconstruct the predefined types (which can be interpreted in this context as knowledge states) with sufficient accuracy. Theoretical considerations show that first‐order CFA cannot be used for this data generation model. Thus, it is wrong to consider first‐order CFA, as is done in many publications, as the standard or even only method of CFA.     

Conditions for the acceptance of deontic conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed.     

A neural network approach to movement pattern analysis

Movements are time-dependent processes and so can be modelled by time-series of coordinates: E.g., each articulation has geometric coordinates; the set of the coordinates of the relevant articulations build a high-dimensional configuration. These configurations--or "patterns"--give reason for analysing movements by means of neural networks: The Kohonen Feature Map (KFM) is a special type of neural network, which (after having been coined by training with appropriate pattern samples) is able to recognize single patterns as members of pattern clusters. This way, for example, the particular configurations of a given movement can be identified as belonging to respective configuration clusters, where the sequence of clusters to which the time-depending configurations belong, characterizes the process as a 2-dimensional trajectory. The advantages of this method are that: the high dimensionality of the original processes is reduced to two dimensional trajectories, the clusters are automatically determined by the network, and all data for further analyses can automatically be transferred into a data base. Thus, the processes can either be visualized and analysed by an expert or again processed by further automatic analysing tools, as has been done with similarity matrices. The disadvantage is that a KFM-training needs a huge amount of information, which normally is not available from experiments. However, the Dynamically Controlled Network DyCoN (a special type of KFM) makes it possible to reduce the amount of original training data substantially--e.g., by adding stochastically generated ones. Currently, DyCoN is used in several projects in order to generally support analyses of processes in sport. It should be emphasized that the presented approach is not meant to improve the understanding or to develop models of human movement but to give a survey of the advantages and methodological aspects of net-based movement analysis.     

Conditionals As Representative Inferences

According to Adams (Inquiry 8:166–197, 1965), the acceptability of an indicative conditional goes with the conditional probability of the consequent given the antecedent. However, some conditionals seem to be inappropriate, although their corresponding conditional probability is high. These are cases with a missing link between antecedent and consequent. Other conditionals are appropriate even though the conditional probability is low. Finally, we have the so-called biscuit conditionals. In this paper we will generalize analyses of Douven (Synthese 164:19–44, 2008) and others to account for the appropriateness of conditionals in terms of evidential support. Our generalization involves making use of Value, or intensity. We will show how this generalization helps to account for biscuit conditionals and conditional threats and promises. Finally, a link is established between this analysis of conditionals and an analysis of generic sentences.

     

Kaufmann on the Probabilities of Conditionals

Kaufmann has recently argued that the thesis according to which the probability of an indicative conditional equals the conditional probability of the consequent given the antecedent under certain specifiable circumstances deviates from intuition. He presents a method for calculating the probability of a conditional that does seem to give the intuitively correct result under those circumstances. However, the present paper shows that Kaufmann’s method is inconsistent in that it may lead one to assign different probabilities to a single conditional at the same time.     

Temporal patterns of variable relationships in person-oriented research: longitudinal models of configural frequency analysis

This article reviews the premises of configural frequency analysis (CFA), including methods of choosing significance tests and base models, as well as protecting alpha, and discusses why CFA is a useful approach when conducting longitudinal person-oriented research. CFA operates at the manifest variable level. Longitudinal CFA seeks to identify those temporal patterns that stand out as more frequent (CFA types) or less frequent (CFA antitypes) than expected with reference to a base model. A base model that has been used frequently in CFA applications, prediction CFA, and a new base model, auto-association CFA, are discussed for analysis of cross-classifications of longitudinal data. The former base model takes the associations among predictors and among criteria into account. The latter takes the auto-associations among repeatedly observed variables into account. Application examples of each are given using data from a longitudinal study of domestic violence. It is demonstrated that CFA results are not redundant with results from log-linear modeling or multinomial regression and that, of these approaches, CFA shows particular utility when conducting person-oriented research.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

The analysis of multitrait-multimethod matrices via constrained components analysis

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.     

Confirmatory factor analysis using Microsoft Excel

This article presents a method for using Microsoft (MS) Excel for confirmatory factor analysis (CFA). CFA is often seen as an impenetrable technique, and thus, when it is taught, there is frequently little explanation of the mechanisms or underlying calculations. The aim of this article is to demonstrate that this is not the case; it is relatively straightforward to produce a spreadsheet in MS Excel that can carry out simple CFA. It is possible, with few or no programming skills, to effectively program a CFA analysis and, thus, to gain insight into the workings of the procedure.     

Identity configurations: a new perspective on identity formation in contemporary society

This paper deals with the theoretical construct of "identity configuration." It portrays the different possible ways in which individuals configure the relationship among potentially conflicting identifications in the process of identity formation. In order to explicate these configurations, I analyzed narratives of identity development retold by individuals describing personal identity conflicts that arise within a larger context of sociocultural conflict. Thirty Jewish modern orthodox young adults were interviewed regarding a potentially conflictual identity issue (i.e. their religious and sexual development). Their deliberations, as described in the interviews, were examined, and four different configurations were identified: a configuration based on choice and suppression; an assimilative and synthesizing configuration; a confederacy of identifications; and a configuration based on the thrill of dissonance. The different configurations are illustrated through exemplars, and the possible implications of the concept of "configuration" for identity theory are discussed.     

Recovering Substantive Factor Loadings in the Presence of Acquiescence Bias: A Comparison of Three Approaches

Researchers are often advised to write balanced scales (containing an equal number of positively and negatively worded items) when measuring psychological attributes. This practice is recommended to control for acquiescence bias (ACQ). However, little advice has been given on what to do with such data if the researcher subsequently wants to evaluate a 1-factor model for the scale. This article compares 3 approaches for dealing with the presence of ACQ bias, which make different assumptions: an ipsatization approach based on the work of Chan and Bentler (CB; 1993), a confirmatory factor analysis (CFA) approach that includes an ACQ factor with equal loadings (Billiet & McClendon, 2000; Mirowsky & Ross, 1991), and an exploratory factor analysis (EFA) approach with a target rotation (Ferrando, Lorenzo-Seva, & Chico, 2003). We also examine the “do nothing” approach which fits the 1-factor model to the data ignoring the presence of ACQ bias. Our main findings are that the CFA method performs best overall and that it is robust to the violation of its assumptions, the EFA and the CB approaches work well when their assumptions are strictly met, and the “do nothing” approach can be surprisingly robust when the ACQ factor is not very strong.     

The degree of epistemic justification and the conjunction fallacy

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy.     

Testing Event-Based Forms of Causality

Three fundamental types of causal relations are those of necessity, sufficiency, and necessity and sufficiency. These types are defined in contexts of categorical variables or events. Using statement calculus or Boolean algebra, one can determine which patterns of events are in support of a particular form of causal relation. In this article, we approach the analysis of these forms of causality taking the perspective of the analyst of empirical data. It is proposed using Configural Frequency Analysis (CFA) to test hypotheses about type of causal relation. Models are proposed for two-variable and multi-variable cases. Two CFA approaches are proposed. In the first, individual patterns (configurations) are examined under the question whether they are in support of a particular type of causal relation. In the second, patterns that are in support are compared with corresponding patterns that are not in support. In an empirical example, hypotheses are tested on the prediction of sustainability of change in dietary fat intake habits.     

Conditional probability and components of rt in the variable foreperiod experiment

If the passage of time during the foreperiod in a variable foreperiod experiment is marked by a series of tones, RT decreases with the conditional probability of stimulus occurrence. RTs at short foreperiods, however, are rather slower than would be expected on the basis of a simple conditional probability effect. It is suggested that this is attributable to an independent “initial slow reaction” effect, and it is shown that the degree of this effect is influenced by the duration of the prior foreperiod. The results are related to those of variable foreperiod a-reactions in which no conditional probability effect has been found, and it is argued that in a marked reaction of the kind described above, the initial slow reaction effect behaves like an a-reaction component of RT. It is suggested that the absence of a conditional probability effect in the a-reaction and its presence in the marked reaction are related to the fact that a different type of sensory process is used to identify the signal in each case.     

Normative versus ipsative configural frequency analysis in personality research—their use discussed in a reanalysis of data on situation-bound anxiety

Configural frequency analysis (CFA) tests whether certain individual patterns in different variables are observed more frequently in a sample than expected by chance. In normative CFA, these patterns are derived from the subject's specific position in relation to sample characteristics such as the median or the mean. In ipsative CFA, patterns are defined within an individual reference system, e.g. relative to the subject's median of different variable scores. Normative CFA examines dimensionality of scales and is comparable to factor analysis in this respect. Ipsative CFA rather yields information about location of scores in different variables, in a similar way to ANOVA or Friedman testing. However, both normative and ipsative CFA may supply information not obtainable by means of the aforementioned methods. This is illustrated in a reanalysis of data in four scales of an anxiety inventory. © 1997 John Wiley & Sons, Ltd.     

Category-based and attribute-based reactions to others: Some informational conditions of stereotyping and individuating processes

This paper suggests that people can form impressions in a variety of ways that range from primarily category-based processes to primarily attribute-based processes, and that the process partially depends on the configuration of available information. Easily categorized configurations are hypothesized to elicit relatively category-based processes, while not easily categorized configurations are hypothesized to elicit relatively attribute-based processes. In Experiment 1, subjects first rated the likability of job-category labels and relevant trait attributes, in isolation from each other. At a later session, stimulus people were depicted by category labels (occupations) and relevant attributes (traits) in varying combinations. Typicality ratings confirmed the manipulated ease of categorizing the various information combinations. Correlations between subjects' evaluations of each stimulus person and their independent prior ratings of the components supported the idea of a continuum anchored respectively by relatively category-based and by relatively attribute-based impression formation processes. In the second study, think-aloud data further supported the current hypotheses: subjects spontaneously examined the fit between category and attributes, and they used the attributes more in the attribute-based conditions than in the category-based conditions. The protocol data also reveal some processes intermediate on the continuum between primarily category-based and primarily attribute-based processes; these include subcategorizing, generating new categories, and self-reference. Social perceivers apparently use flexible impression formation processes, depending on the configuration of available information.     

The First-Order Theories of Dedekind Algebras

A Dedekind Algebra is an ordered pair (B,h) where B is a non-empty set and h is an injective unary function on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called configurations of the Dedekind algebra. There are N₀ isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on omega called its configuration signature. The configuration signature of a Dedekind algebra counts the number of configurations in the decomposition of the algebra in each isomorphism type.The configuration signature of a Dedekind algebra encodes the structure of that algebra in the sense that two Dedekind algebras are isomorphic iff their configuration signatures are identical. Configuration signatures are used to establish various results in the first-order model theory of Dedekind algebras. These include categoricity results for the first-order theories of Dedekind algebras and existence and uniqueness results for homogeneous, universal and saturated Dedekind algebras. Fundamental to these results is a condition on configuration signatures that is necessary and sufficient for elementary equivalence.