Sequential analysis of latent variables using mixed-effect latent variable models: Impact of non-informative and informative missing data

2007 ◽  
Vol 26 (27) ◽  
pp. 4889-4904 ◽  
Author(s):  
Véronique Sébille ◽  
Jean-Benoit Hardouin ◽  
Mounir Mesbah
Keyword(s):  
Missing Data ◽  
Latent Variables ◽  
Latent Variable ◽  
Sequential Analysis ◽  
Latent Variable Models ◽  
Mixed Effect ◽  
Informative Missing Data

Using and expanding hybrid latent variable models for modelling missing data and for discovering influential points

2014 ◽  
Author(s):  
Ευγενία Τσομπανάκη
Keyword(s):  
Missing Data ◽  
Latent Variable ◽  
Latent Variable Models ◽  
Limited Information ◽  
Local Independence ◽  
Influential Points ◽  
Response Propensity

Ο όρος Υβριδικός χρησιμοποιείται γενικά για να περιγράψει το μεικτό χαρακτήρα ενός αντικειμένου το οποίο αποτελείται από δύο στοιχεία. Τα Υβριδικά μοντέλα λανθανουσών μεταβλητών επιτρέπουν τον ορισμό δύο ή περισσοτέρων κλάσεων και δομές εντός των ομάδων οι οποίες καλύπτουν ένα μεγάλο εύρος από απλή ανεξαρτησία (local independence) έως σύνθετες σχέσεις μεταξύ των λανθανουσών μεταβλητών. Στο Κεφάλαιο 1 γίνεται αναφορά και σχολιασμός της βιβλιογραφίας στο πεδίο των Υβριδικών μοντέλων καθώς και λεπτομερής παρουσίαση της διαδικασίας εκτίμησης με χρήση του ΕΜ ενός Υβριδικού Hybrid 2LC/2PL-Hom μοντέλου. Ο συμβολισμός 2LC/2PL-Hom δηλώνει ένα μοντέλο για το οποίο οι απαντήσεις στα ερωτήματα προς απόκριση εξαρτώνται από μία διακριτή λανθάνουσα μεταβλητή η οποία διαιρεί τον πληθυσμό σε δύο ομάδες (2LC) και επιπλέον ότι οι απαντήσεις στα ερωτήματα σε μία από τις δύο αυτές ομάδες εξαρτώνται από μία συνεχή λανθάνουσα μεταβλητή. Η πιθανότητα απάντησης για αυτή την ομάδα δίνεται από το μοντέλο δύο παραμέτρων (2PL-IRT). Η άλλη ομάδα θεωρείται ομογενής (Homogeneous-Hom) χωρίς κάποια άλλη λανθάνουσα δομή. Η προσαρμογή του μοντέλου αποτελεί το αντικείμενο συζήτησης και έρευνας των επόμενων δύο κεφαλαίων. Τεστ τα οποία εμπεριέχουν όλη την πληροφορία (Overall tests) και μέρος της πληροφορίας (Limited-information tests) των δεδομένων παρουσιάζονται και διερευνάται η συμπεριφορά τους μέσω προσομοίωσης για το 2LC/2PL-Hom μοντέλο σε ότι αφορά την ισχύ και το σφάλμα Τύπου Ι. Έμφαση δίνεται στην περίπτωση των δεδομένων τα οποία είναι αραιά (sparse) και τα οποία συναντάμε συχνά στο πεδίο εφαρμογής των λανθανουσών μοντέλων. Ως μέτρο για το πόσο αραιά είναι τα δεδομένα χρησιμοποιείται το ποσοστό των αναμενόμενων συχνοτήτων οι οποίες είναι μικρότερες ή ίσες με 5. Στο Κεφάλαιο 4 προτείνεται η χρήση του Hybrid 2LC/2PL-2PL μοντέλου για δίτιμα δεδομένα με ελλιπείς παρατηρήσεις οι οποίες δεν έχουν προέλθει τυχαία (MNAR) κατά τη διαδικασία απόκρισης των υποκειμένων. Το μοντέλο αυτό θεωρεί ότι τα ελλιπή (μη παρατηρούμενα) δεδομένα εξαρτώνται από κάτι επιπλέον σε σχέση με τα παρατηρούμενα και κάτω από τις απαραίτητες υποθέσεις και περιορισμούς επιτρέπει τα ελλιπή δεδομένα να συμπεριληφθούν στην ανάλυση. Συγκεκριμένα σύμφωνα με το προτεινόμενο μοντέλο η τάση των ερωτώμενων να αποκριθούν (response propensity) σχετίζεται με τις συγκεκριμένες ομάδες στις οποίες διαιρείται ο πληθυσμός από τη διακριτή λανθάνουσα μεταβλητή, η οποία μετράται από ένα σύνολο δίτιμων ερωτήσεων οι οποίες υποβάλλονται στα υποκείμενα. Στο Κεφάλαιο 5 γίνεται ανίχνευση σημείων επιρροής για δίτιμα δεδομένα με ένα 2PL-IRT μοντέλο με κύριο στόχο τον εντοπισμό τυχόν περιπτώσεων όπου τα αποτελέσματα της προσαρμογής ενός τέτοιου μοντέλου είναι παραπλανητικά και το προσδιορισμό της πηγής αυτού του φαινομένου.

Latent variable models are network models

2010 ◽  
Vol 33 (2-3) ◽  
pp. 166-166 ◽  
Author(s):  
Peter C. M. Molenaar
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Network Models ◽  
Latent Variable Models ◽  
Variable Theory ◽  
The Relationship

AbstractCramer et al. present an original and interesting network perspective on comorbidity and contrast this perspective with a more traditional interpretation of comorbidity in terms of latent variable theory. My commentary focuses on the relationship between the two perspectives; that is, it aims to qualify the presumed contrast between interpretations in terms of networks and latent variables.

Comparison of partial least square algorithms in hierarchical latent variable model with missing data

SIMULATION ◽  
2020 ◽  
Vol 96 (10) ◽  
pp. 825-839
Author(s):  
Hao Cheng
Keyword(s):  
Missing Data ◽  
Quantile Regression ◽  
Latent Variables ◽  
Latent Variable ◽  
Partial Least Square ◽  
Least Square ◽  
Latent Variable Model ◽  
Data Handling ◽  
Variable Model ◽  
Handling Methods

Missing data is almost inevitable for various reasons in many applications. For hierarchical latent variable models, there usually exist two kinds of missing data problems. One is manifest variables with incomplete observations, the other is latent variables which cannot be observed directly. Missing data in manifest variables can be handled by different methods. For latent variables, there exist several kinds of partial least square (PLS) algorithms which have been widely used to estimate the value of latent variables. In this paper, we not only combine traditional linear regression type PLS algorithms with missing data handling methods, but also introduce quantile regression to improve the performances of PLS algorithms when the relationships among manifest and latent variables are not fixed according to the explored quantile of interest. Thus, we can get the overall view of variables’ relationships at different levels. The main challenges lie in how to introduce quantile regression in PLS algorithms correctly and how well the PLS algorithms perform when missing manifest variables occur. By simulation studies, we compare all the PLS algorithms with missing data handling methods in different settings, and finally build a business sophistication hierarchical latent variable model based on real data.

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.

Comorbidity: A network perspective

2010 ◽  
Vol 33 (2-3) ◽  
pp. 137-150 ◽  
Author(s):  
Angélique O. J. Cramer ◽  
Lourens J. Waldorp ◽  
Han L. J. van der Maas ◽  
Denny Borsboom
Keyword(s):  
Major Depression ◽  
Mental Disorder ◽  
Latent Variables ◽  
Latent Variable ◽  
Latent Variable Models ◽  
The Other ◽  
Generalized Anxiety ◽  
Network Approach ◽  
Variable Theory ◽  
Diagnostic Categories

AbstractThe pivotal problem of comorbidity research lies in the psychometric foundation it rests on, that is, latent variable theory, in which a mental disorder is viewed as a latent variable that causes a constellation of symptoms. From this perspective, comorbidity is a (bi)directional relationship between multiple latent variables. We argue that such a latent variable perspective encounters serious problems in the study of comorbidity, and offer a radically different conceptualization in terms of a network approach, where comorbidity is hypothesized to arise from direct relations between symptoms of multiple disorders. We propose a method to visualize comorbidity networks and, based on an empirical network for major depression and generalized anxiety, we argue that this approach generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models: Some pathways to comorbidity through the symptom space are more likely than others; those pathways generally have the same direction (i.e., from symptoms of one disorder to symptoms of the other); overlapping symptoms play an important role in comorbidity; and boundaries between diagnostic categories are necessarily fuzzy.

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 Characterizing the nonlinear structure of shared variability in cortical neuron populations using latent variable models

2018 ◽  
Author(s):  
Matthew R Whiteway ◽  
Karolina Socha ◽  
Vincent Bonin ◽  
Daniel A Butts
Keyword(s):  
Neural Activity ◽  
Latent Variables ◽  
Latent Variable ◽  
Large Scale ◽  
Latent Variable Models ◽  
Neural Population ◽  
Variable Model ◽  
Experimental Conditions ◽  
Affine Model ◽  
Nonlinear Latent Variable Models

AbstractSensory neurons often have variable responses to repeated presentations of the same stimulus, which can significantly degrade the information contained in those responses. Such variability is often shared across many neurons, which in principle can allow a decoder to mitigate the effects of such noise, depending on the structure of the shared variability and its relationship to sensory encoding at the population level. Latent variable models offer an approach for characterizing the structure of this shared variability in neural population recordings, although they have thus far typically been used under restrictive mathematical assumptions, such as assuming linear transformations between the latent variables and neural activity. Here we leverage recent advances in machine learning to introduce two nonlinear latent variable models for analyzing large-scale neural recordings. We first present a general nonlinear latent variable model that is agnostic to the stimulus tuning properties of the individual neurons, and is hence well suited for exploring neural populations whose tuning properties are not well characterized. This motivates a second class of model, the Generalized Affine Model, which simultaneously determines each neuron’s stimulus selectivity and a set of latent variables that modulate these stimulus responses both additively and multiplicatively. While these approaches can detect general nonlinear relationships in shared neural variability, we find that neural activity recorded in anesthetized primary visual cortex (V1) is best described by a single additive and single multiplicative latent variable, i.e., an “affine model”. In contrast, application of the same models to recordings in awake macaque prefrontal cortex discover more general nonlinearities to compactly describe the population response variability. These results thus demonstrate how nonlinear latent variable models can be used to describe population variability, and suggest that a range of methods is necessary to study different brain regions under different experimental conditions.

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