scholarly journals The Role of Conditional Likelihoods in Latent Variable Modeling

Psychometrika ◽  
2022 ◽  
Author(s):  
Anders Skrondal ◽  
Sophia Rabe-Hesketh
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Multilevel Models ◽  
Explanatory Variables ◽  
Measurement Models ◽  
Retrospective Sampling ◽  
The Rasch Model ◽  
Elementary Entity ◽  
Cluster Level

AbstractIn psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, “cluster” refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and “unit” refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

Bayesian Adaptive Lasso for Ordinal Regression With Latent Variables

2015 ◽  
Vol 46 (4) ◽  
pp. 926-953 ◽  
Author(s):  
Xiang-Nan Feng ◽  
Hao-Tian Wu ◽  
Xin-Yuan Song
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Social Research ◽  
Ordinal Regression ◽  
Adaptive Lasso ◽  
Simultaneous Estimation ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Explanatory Variables ◽  
Ordinal Regression Model

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct simultaneous estimation and variable selection. Nice features including empirical performance of the proposed methodology are demonstrated by simulation studies. The model is applied to a study on happiness and its potential determinants from the Inter-university Consortium for Political and Social Research.

scholarly journals Distilling vector space model scores for the assessment of constructed responses with bifactor Inbuilt Rubric method and latent variables

2022 ◽  
Author(s):  
José Ángel Martínez-Huertas ◽  
Ricardo Olmos ◽  
Guillermo Jorge-Botana ◽  
José A. León
Keyword(s):  
Vector Space ◽  
Undergraduate Students ◽  
Latent Variables ◽  
Measurement Errors ◽  
Latent Variable ◽  
Discriminant Validity ◽  
Semantic Analysis ◽  
Measurement Models ◽  
Accurate Performance ◽  
Constructed Responses

AbstractIn this paper, we highlight the importance of distilling the computational assessments of constructed responses to validate the indicators/proxies of constructs/trins using an empirical illustration in automated summary evaluation. We present the validation of the Inbuilt Rubric (IR) method that maps rubrics into vector spaces for concepts’ assessment. Specifically, we improved and validated its scores’ performance using latent variables, a common approach in psychometrics. We also validated a new hierarchical vector space, namely a bifactor IR. 205 Spanish undergraduate students produced 615 summaries of three different texts that were evaluated by human raters and different versions of the IR method using latent semantic analysis (LSA). The computational scores were validated using multiple linear regressions and different latent variable models like CFAs or SEMs. Convergent and discriminant validity was found for the IR scores using human rater scores as validity criteria. While this study was conducted in the Spanish language, the proposed scheme is language-independent and applicable to any language. We highlight four main conclusions: (1) Accurate performance can be observed in topic-detection tasks without hundreds/thousands of pre-scored samples required in supervised models. (2) Convergent/discriminant validity can be improved using measurement models for computational scores as they adjust for measurement errors. (3) Nouns embedded in fragments of instructional text can be an affordable alternative to use the IR method. (4) Hierarchical models, like the bifactor IR, can increase the validity of computational assessments evaluating general and specific knowledge in vector space models. R code is provided to apply the classic and bifactor IR method.

scholarly journals Causal Effects Based on Latent Variable Models

2019 ◽  
Author(s):  
Axel Mayer
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Stochastic Theory ◽  
Latent Variable Models ◽  
Causal Effects ◽  
Equation Modeling ◽  
Differential Effectiveness ◽  
Measurement Models ◽  
Effect Model

Building on the stochastic theory of causal effects and latent state-trait theory, this article shows how a comprehensive analysis of the effectiveness of interventions can be conducted based on latent variable models. The proposed approach offers new ways to evaluate the differential effectiveness of interventions for substantive researchers in experimental and observational studies while allowing for complex measurement models. The key definitions and assumptions of the stochastic theory of causal effects are first introduced and then four statistical models that can be used to estimate various types of causal effects with latent state-trait models are developed and illustrated: The multistate effect model with and without method factors, the true-change effect model, and the multitrait effect model. All effect models with latent variables are implemented based on multigroup structural equation modeling with the EffectLiteR approach. Particular emphasis is placed on the development of models with interactions that allow for interindividual differences in treatment effects based on latent variables. Open source software code is provided for all models.

scholarly journals Causal Effects Based on Latent Variable Models

Methodology ◽  
2019 ◽  
Vol 15 (Supplement 1) ◽  
pp. 15-28 ◽  
Author(s):  
Axel Mayer
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Structural Equation ◽  
Stochastic Theory ◽  
Latent Variable Models ◽  
Causal Effects ◽  
Equation Modeling ◽  
Measurement Models ◽  
Effect Model ◽  
Multigroup Structural Equation Modeling

Abstract. Building on the stochastic theory of causal effects and latent state-trait theory, this article shows how a comprehensive analysis of the effects of interventions can be conducted based on latent variable models. The proposed approach offers new ways to evaluate the differential effects of interventions for substantive researchers in experimental and observational studies while allowing for complex measurement models. The key definitions and assumptions of the stochastic theory of causal effects are first introduced and then four statistical models that can be used to estimate various types of causal effects with latent state-trait models are developed and illustrated: The multistate effect model with and without method factors, the true-change effect model, and the multitrait effect model. All effect models with latent variables are implemented based on multigroup structural equation modeling with the EffectLiteR approach. Particular emphasis is placed on the development of models with interactions that allow for interindividual differences in treatment effects based on latent variables. Open source software code is provided for all models.

scholarly journals Estimating Parameters of Dichotomous and Ordinal Item Response Models with Gllamm

2007 ◽  
Vol 7 (3) ◽  
pp. 313-333 ◽  
Author(s):  
Xiaohui Zheng ◽  
Sophia Rabe-Hesketh
Keyword(s):  
Item Response ◽  
Latent Variable ◽  
Rating Scale ◽  
Ordinal Scale ◽  
Response Models ◽  
Item Response Models ◽  
Explanatory Variables ◽  
Test Items ◽  
Measurement Models ◽  
Latent Traits

Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by using an ordinal scale (a grade from poor to excellent). Item response models also apply equally for measurement of other latent traits. Here we describe the one- and two-parameter logit models for dichotomous items, the partial-credit and rating scale models for ordinal items, and an extension of these models where the latent variable is regressed on explanatory variables. We show how these models can be expressed as generalized linear latent and mixed models and fitted by using the user-written command gllamm.

scholarly journals A Novel Multimodal Approach for Studying the Dynamics of Curiosity in Small Group Learning

2021 ◽  
Author(s):  
Tanmay Sinha ◽  
Zhen Bai ◽  
Justine Cassell
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Theoretical Framework ◽  
Social Contexts ◽  
Learning Technologies ◽  
Multimodal Learning ◽  
Love Of Learning ◽  
Multimodal Learning Analytics ◽  
Predictive Relationship

Curiosity is a vital metacognitive skill in educational contexts, leading to creativity, and a love of learning. And while many school systems increasingly undercut curiosity by teaching to the test, teachers are increasingly interested in how to evoke curiosity in their students to prepare them for a world in which lifelong learning and reskilling will be more and more important. One aspect of curiosity that has received little attention, however, is the role of peers in eliciting curiosity. We present what we believe to be the first theoretical framework that articulates an integrated socio-cognitive account of curiosity that ties observable behaviors in peers to underlying curiosity states. We make a bipartite distinction between individual and interpersonal functions that contribute to curiosity, and multimodal behaviors that fulfill these functions. We validate the proposed framework by leveraging a longitudinal latent variable modeling approach. Findings confirm a positive predictive relationship between the latent variables of individual and interpersonal functions and curiosity, with the interpersonal functions exercising a comparatively stronger influence. Prominent behavioral realizations of these functions are also discovered in a data-driven manner. We instantiate the proposed theoretical framework in a set of strategies and tactics that can be incorporated into learning technologies to indicate, evoke, and scaffold curiosity. This work is a step towards designing learning technologies that can recognize and evoke moment-by-moment curiosity during learning in social contexts and towards a more complete multimodal learning analytics. The underlying rationale is applicable more generally for developing computer support for other metacognitive and socio-emotional skills.

Measurement

2009 ◽  
Author(s):  
Simon Jackman
Keyword(s):  
Item Response ◽  
Latent Variables ◽  
Latent Variable ◽  
Convergent Validity ◽  
Measurement Model ◽  
Response Models ◽  
Item Response Models ◽  
Measurement Models ◽  
Dynamic Setting

This article shows that the words ‘behavioural’ and ‘behaviour’ turn out to be better measures as judged by tests of criterion and convergent validity. It specifically discusses measurement problems. Further, it pertains to statistical models that link latent variables and their observed indicators as measurement models. The success of measurement — the quality of the inferences provided by a measurement model — is usually assessed with reference to two key concepts: validity and reliability. The distinct uses of measures of latent variables are reported. The article then deals with the costs of ignoring measurement error. Additionally, a quick introduction to factor analysis, item-response models, and a very general class of latent variable models are briefly given. Moreover, it describes the inference for discrete latent variables and the measurement in a dynamic setting.

Symptom Presence and Symptom Severity as Unique Indicators of Psychopathology: An Application of Multidimensional Zero-Inflated and Hurdle Graded Response Models

2021 ◽  
pp. 001316442110618
Author(s):  
Brooke E. Magnus ◽  
Yang Liu
Keyword(s):  
Symptom Severity ◽  
Latent Variables ◽  
Latent Variable ◽  
Suicide Attempts ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Response Models ◽  
Explanatory Variables ◽  
Graded Response ◽  
Scale Scores

Questionnaires inquiring about psychopathology symptoms often produce data with excess zeros or the equivalent (e.g., none, never, and not at all). This type of zero inflation is especially common in nonclinical samples in which many people do not exhibit psychopathology, and if unaccounted for, can result in biased parameter estimates when fitting latent variable models. In the present research, we adopt a maximum likelihood approach in fitting multidimensional zero-inflated and hurdle graded response models to data from a psychological distress measure. These models include two latent variables: susceptibility, which relates to the probability of endorsing the symptom at all, and severity, which relates to the frequency of the symptom, given its presence. After estimating model parameters, we compute susceptibility and severity scale scores and include them as explanatory variables in modeling health-related criterion measures (e.g., suicide attempts, diagnosis of major depressive disorder). Results indicate that susceptibility and severity uniquely and differentially predict other health outcomes, which suggests that symptom presence and symptom severity are unique indicators of psychopathology and both may be clinically useful. Psychometric and clinical implications are discussed, including scale score reliability.

Probability-Based and Measurement-Related Hypotheses With Full Restriction for Investigations by Means of Confirmatory Factor Analysis

Methodology ◽  
2011 ◽  
Vol 7 (4) ◽  
pp. 157-164
Author(s):  
Karl Schweizer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Cognitive Processing ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Model Fit ◽  
Repeated Measures Data ◽  
Confirmatory Factor ◽  
And Performance

Probability-based and measurement-related hypotheses for confirmatory factor analysis of repeated-measures data are investigated. Such hypotheses comprise precise assumptions concerning the relationships among the true components associated with the levels of the design or the items of the measure. Measurement-related hypotheses concentrate on the assumed processes, as, for example, transformation and memory processes, and represent treatment-dependent differences in processing. In contrast, probability-based hypotheses provide the opportunity to consider probabilities as outcome predictions that summarize the effects of various influences. The prediction of performance guided by inexact cues serves as an example. In the empirical part of this paper probability-based and measurement-related hypotheses are applied to working-memory data. Latent variables according to both hypotheses contribute to a good model fit. The best model fit is achieved for the model including latent variables that represented serial cognitive processing and performance according to inexact cues in combination with a latent variable for subsidiary processes.

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