Multilevel and Latent Variable Modeling with Composite Links and Exploded Likelihoods

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation. We wish to thank The Research Council of Norway for a grant supporting our collaboration.     

Log-Multiplicative Association Models as Item Response Models

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson &; Vermunt, 2000; Anderson &; Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.     

Organization and predictive power of general and relationship-specific attachment models: one for all, and all for one?

Given recent evidence for multiple attachment models, we examined the organization and predictive power of general and relationship-specific attachment representations in two samples using two distinct measures of attachment models. With regard to associations among relationship-specific models, peer models (romantic partner and friend) and parental models (mother and father) were more similar to each other than to any other models, and anxiety/self-model representations were more consistent across relationships than avoidance/other-model representations. With regard to links between general and specific models, romantic and friend models made the strongest and independent contributions to general models, and romantic relationship involvement moderated the importance of romantic models to general models. With regard to differential predictive power of multiple models, general, romantic partner, and mother attachment made unique contributions to well-being indicators; relationship outcomes, however, were only predicted by individuals' corresponding relationship-specific models. Implications for the measurement and conceptualization of adult attachment are discussed.     

Assessing The Discriminant Validity Of Regression Models And Subjectively Weighted Models Of Judgments

When either regression models or subjectively weighted models are used as aids in making placement decisions, the discriminant validity of these models is of interest. When all predictor information is used in all decisions, models which assign equal weights cannot simultaneously show high levels of predictive accuracy and discriminant validity; in some settings, both regression models and subjectively weighted models may. The discriminant validity of regression models and of subjectively weighted models was investigated in two judgment experiments. Both types of models showed high levels of accuracy and cross-validity in both experiments. Regression models showed discriminant validity in both experiments, while subjectively weighted models failed to show discriminant validity in the second. The homogeneity of cue validities appeared to moderate both the level of discriminant validity and the relationship between similarity of subjective models, across tasks, and discriminant validity.     

Waif goodbye! Average-size female models promote positive body image and appeal to consumers

Despite consensus that exposure to media images of thin fashion models is associated with poor body image and disordered eating behaviours, few attempts have been made to enact change in the media. This study sought to investigate an effective alternative to current media imagery, by exploring the advertising effectiveness of average-size female fashion models, and their impact on the body image of both women and men. A sample of 171 women and 120 men were assigned to one of three advertisement conditions: no models, thin models and average-size models. Women and men rated average-size models as equally effective in advertisements as thin and no models. For women with average and high levels of internalisation of cultural beauty ideals, exposure to average-size female models was associated with a significantly more positive body image state in comparison to exposure to thin models and no models. For men reporting high levels of internalisation, exposure to average-size models was also associated with a more positive body image state in comparison to viewing thin models. These findings suggest that average-size female models can promote positive body image and appeal to consumers.     

Waif goodbye! Average-size female models promote positive body image and appeal to consumers

Despite consensus that exposure to media images of thin fashion models is associated with poor body image and disordered eating behaviours, few attempts have been made to enact change in the media. This study sought to investigate an effective alternative to current media imagery, by exploring the advertising effectiveness of average-size female fashion models, and their impact on the body image of both women and men. A sample of 171 women and 120 men were assigned to one of three advertisement conditions: no models, thin models and average-size models. Women and men rated average-size models as equally effective in advertisements as thin and no models. For women with average and high levels of internalisation of cultural beauty ideals, exposure to average-size female models was associated with a significantly more positive body image state in comparison to exposure to thin models and no models. For men reporting high levels of internalisation, exposure to average-size models was also associated with a more positive body image state in comparison to viewing thin models. These findings suggest that average-size female models can promote positive body image and appeal to consumers.     

Generalized bilinear models

Generalized bilinear models are presented for the statistical analysis of two-way arrays. These models combine bilinear models and generalized linear modeling, and yield a family of models that includes many existing models, as well as suggest other potentially useful ones. This approach both unifies and extends models for two-way arrays, including the ability to treat response and explanatory variables differently in the models, and the incorporation of external information about the variables directly into the analysis. A unifying framework for the generalized bilinear models is provided by considering four particular cases which have been proposed and used in the existing statistical literature. A three-step procedure is proposed to analyze data sets by generalized bilinear models. Two data sets of different nature are analyzed.     

情境模型研究中的分离与整合

情境模型概念出现后,有关情境模型研究重点解决以下两大问题：其一,情境模型不是课文基础表征;其二,情境模型具有多维结构。前者表现为情境模型与课文基础表征的分离研究,后者表现为情境模型从单维向多维的整合研究。在此基础上,研究者进一步统合情境模型研究,初步考察情境模型的实质问题。基于情境模型研究的分离与整合的趋势,情境模型的未来研究将进一步发展研究范式,深入探讨“情境模型是什么”与“情境模型的加工机制是怎么样”等问题。     

Equivalent Dynamic Models

Equivalences of two classes of dynamic models for weakly stationary multivariate time series are discussed: dynamic factor models and autoregressive models. It is shown that exploratory dynamic factor models can be rotated, yielding an infinite set of equivalent solutions for any observed series. It also is shown that dynamic factor models with lagged factor loadings are not equivalent to the currently popular state-space models, and that restriction of attention to the latter type of models may yield invalid results. The known equivalent vector autoregressive model types, standard and structural, are given a new interpretation in which they are conceived of as the extremes of an innovating type of hybrid vector autoregressive models. It is shown that consideration of hybrid models solves many problems, in particular with Granger causality testing.     

对以类别为基础的归纳推理的几种理论模型的评价

当前关于以类别为基础的归纳推理理论模型大致可以分为两种：强调相似性作用的归纳推理的理论模型和强调知识作用的归纳推理的理论模型。前者能较好的解释人们在知识贫乏领域的归纳推理现象,而后者则能够较好的解释人们在知识丰富领域的归纳推理现象。     

On measurement properties of continuation ratio models

Three classes of polytomous IRT models are distinguished. These classes are the adjacent category models, the cumulative probability models, and the continuation ratio models. So far, the latter class has received relatively little attention. The class of continuation ratio models includes logistic models, such as the sequential model (Tutz, 1990), and nonlogistic models, such as the acceleration model (Samejima, 1995) and the nonparametric sequential model (Hemker, 1996). Four measurement properties are discussed. These are monotone likelihood ratio of the total score, stochastic ordering of the latent trait by the total score, stochastic ordering of the total score by the latent trait, and invariant item ordering. These properties have been investigated previously for the adjacent category models and the cumulative probability models, and for the continuation ratio models this is done here. It is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models, while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models. Only the sequential rating scale model implies the property of invariant item ordering. Also, we present a Venn-diagram showing the relationships between all known polytomous IRT models from all three classes.     

Theoretical and empirical review of multinomial process tree modeling

We review a current and popular class of cognitive models calledmultinomial processing tree (MPT) models. MPT models are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. We formally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPT models to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPT models, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.     

GI Joe or Average Joe? The impact of average-size and muscular male fashion models on men's and women's body image and advertisement effectiveness

Increasing body size and shape diversity in media imagery may promote positive body image. While research has largely focused on female models and women's body image, men may also be affected by unrealistic images. We examined the impact of average-size and muscular male fashion models on men's and women's body image and perceived advertisement effectiveness. A sample of 330 men and 289 women viewed one of four advertisement conditions: no models, muscular, average-slim or average-large models. Men and women rated average-size models as equally effective in advertisements as muscular models. For men, exposure to average-size models was associated with more positive body image in comparison to viewing no models, but no difference was found in comparison to muscular models. Similar results were found for women. Internalisation of beauty ideals did not moderate these effects. These findings suggest that average-size male models can promote positive body image and appeal to consumers.     

Estimating Complex Measurement and Growth Models Using the R Package PLmixed

Measurement models, such as factor analysis and item response theory models, are commonly implemented within educational, psychological, and behavioral science research to mitigate the negative effects of measurement error. These models can be formulated as an extension of generalized linear mixed models within a unifying framework that encompasses various kinds of multilevel models and longitudinal models, such as partially nonlinear latent growth models. We introduce the R package PLmixed, which implements profile maximum likelihood estimation to estimate complex measurement and growth models that can be formulated within the general modeling framework using the existing R package lme4 and function optim. We demonstrate the use of PLmixed through two examples before concluding with a brief overview of other possible models.     

Separating trait effects from trait-specific method effects in multitrait-multimethod models: a multiple-indicator CT-C(M-1) model

An overview of several models of confirmatory factor analysis for analyzing multitrait-multimethod (MTMM) data and a discussion of their advantages and limitations are provided. A new class of multi-indicator MTMM models combines several strengths and avoids a number of serious shortcomings inherent in previously developed MTMM models. The new models enable researchers to specify and to test trait-specific-method effects. The trait and method concepts composing these models are explained in detail and are contrasted with those of previously developed MTMM models for multiple indicators. The definitions of the models are explained step by step, and a practical empirical application of the models to the measurement of 3 traits x 3 methods is used to demonstrate their advantages and limitations.     

A general framework for using latent class analysis to test hierarchical and nonhierarchical learning models

Several articles in the past fifteen years have suggested various models for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure. This paper shows that many models are special cases of latent class analysis. A currently available computer program for latent class analysis allows parameter estimates and goodness-of-fit tests not only for the models suggested by previous authors, but also for many models which they could not test with the more specialized computer programs they developed. Several examples are given of the variety of models which may be generated and tested. In addition, a general framework for conceptualizing all such models is given. This framework should be useful for generating models and for comparing various models.     

Scientific models and fictional objects

In this paper, I distinguish scientific models in three kinds on the basis of their ontological status—material models, mathematical models and fictional models, and develop and defend an account of fictional models as fictional objects—i.e. abstract objects that stand for possible concrete objects.     

Action Emulation between Canonical Models

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in van Eijck et al. (Synthese 185(1):131–151, 2012).     

Maps and mapmaking: Developing the systemic paradigm of family functioning

This paper presents the Systemic Paradigm of Family Functioning (SPFF) as an organizing framework for integrating models of family therapy. Therapists can use the SPFF to understand and integrate existing models of family therapy and to create their own personal models of family therapy. The SPFF framework highlights the interrelationships among the four generic models which dominate the field of family therapy. Personal models of family therapy are based on maps of family functioning derived from one of these more generic models.     

Nontransitive Decomposable Conjoint Measurement

Traditional models of conjoint measurement look for an additive representation of transitive preferences. They have been generalized in two directions. Nontransitive additive conjoint measurement models allow for nontransitive preferences while retaining the additivity feature of traditional models. Decomposable conjoint measurement models are transitive but replace additivity by a mere decomposability requirement. This paper presents generalizations of conjoint measurement models combining these two aspects. This allows us to propose a simple axiomatic treatment that shows the pure consequences of several cancellation conditions used in traditional models. These nontran- sitive decomposable conjoint measurement models encompass a large number of aggregation rules that have been introduced in the literature.