scholarly journals Testing Procedure for Item Response Probabilities of 2Class Latent Model

2020 ◽  
Vol 39 (3) ◽  
pp. 657-667
Author(s):  
Bushra Shamshad ◽  
Junaid Sagheer Siddiqui
Keyword(s):  
Item Response ◽  
Latent Variable ◽  
Goodness Of Fit ◽  
Latent Class ◽  
Latent Class Model ◽  
Likelihood Method ◽  
Model Parameters ◽  
Estimation Of Parameters ◽  
Goodness Of Fit Test ◽  
Significant Difference

This paper presents Hotelling T2 as a procedure for the testing of significance difference between the item response probabilities (ωij′s) of classes in a Latent Class Model (LCM). Parametric bootstrap technique is used in order to generate samples for ωij′s. These samples are based on the estimated parameters of 2-class latent model. The estimation of parameters in either situation is done using the Expectation Maximization (EM) algorithm through Maximum likelihood method. The hypothesis under consideration is whether the response probabilities (ωij′s) are equal against each item in both the classes. { H0 : ωi1 = ωi2. against H1 : =ωi1 ≠ ωi2}. If the test exhibits significant difference between response probabilities in both classes, it will be a clear indication of a presence of latent variable. We consider both training and testing data sets to develop the test. In order to apply Hotelling T2 test the basic assumptions of normality and homogeneity of variance are also checked. Chi-square goodness of fit test is used for assessing normal distribution to be good fitted on the hypothesized (bootstrap samples) based on 2-class latent model parameters for each data and Bartlett test to check heterogeneity of variances in ωij′s. Moreover, our procedure produces a minimum standard error of estimates as compared to those obtained through the package in R.Gui environment

Psychology of Computer Use: VIII. Utilizing a Nonparametric Item Response Model to Develop Unidimensional Scales: Mokscal

1989 ◽  
Vol 68 (3) ◽  
pp. 987-1000 ◽  
Author(s):  
Elisabeth Tenvergert ◽  
Johannes Kingma ◽  
Terry Taerum
Keyword(s):  
Item Response ◽  
Goodness Of Fit ◽  
Functional Form ◽  
Search Procedure ◽  
Response Model ◽  
Scale Analysis ◽  
Item Response Model ◽  
Goodness Of Fit Test ◽  
Item Coefficient ◽  
Nonparametric Item Response

MOKSCAL is a program for the Mokken (1971) scale analysis based on a nonparametric item response model that makes no assumptions about the functional form of the item trace lines. The only constraint the Mokken model puts on the trace lines is the assumption of double monotony; that is, the item trace lines must be nondecreasing and the lines are not allowed to cross. MOKSCAL provides three procedures of scaling: a search procedure, an evaluation of the whole set of items, and an extension of an existing scale. All procedures provide a coefficient of scalability for all items that meet the criteria of the Mokken model and an item coefficient of scalability of every item. A test of robustness of the found scale can be performed to analyze whether the scale is invariant across different subgroups or samples. This robustness test may serve as a goodness-of-fit test for the established scale. The program is written in FORTRAN 77 and is suitable for both mainframe and microcomputers.

Cluster Analysis with General Latent Class Model

2011 ◽  
pp. 225-230
Author(s):  
Dingxi Qiu ◽  
Edward C. Malthouse
Keyword(s):  
Cluster Analysis ◽  
Statistical Models ◽  
Latent Variable ◽  
Latent Class ◽  
Latent Class Model ◽  
Teaching Style ◽  
Teaching Styles ◽  
Binary Responses ◽  
Cluster Membership ◽  
Wide Range

Cluster analysis is a set of statistical models and algorithms that attempt to find “natural groupings” of sampling units (e.g., customers, survey respondents, plant or animal species) based on measurements. The observable measurements are sometimes called manifest variables and cluster membership is called a latent variable. It is assumed that each sampling unit comes from one of K clusters or classes, but the cluster identifier cannot be observed directly and can only be inferred from the manifest variables. See Bartholomew and Knott (1999) and Everitt, Landau and Leese (2001) for a broader survey of existing methods for cluster analysis. Many applications in science, engineering, social science, and industry require grouping observations into “types.” Identifying typologies is challenging, especially when the responses (manifest variables) are categorical. The classical approach to cluster analysis on those data is to apply the latent class analysis (LCA) methodology, where the manifest variables are assumed to be independent conditional on the cluster identity. For example, Aitkin, Anderson and Hinde (1981) classified 468 teachers into clusters according to their binary responses to 38 teaching style questions. This basic assumption in classical LCA is often violated and seems to have been made out of convenience rather than it being reasonable for a wide range of situations. For example, in the teaching styles study two questions are “Do you usually allow your pupils to move around the classroom?” and “Do you usually allow your pupils to talk to one another?” These questions are mostly likely correlated even within a class.

Bayesian nonparametric latent class model for longitudinal data

2020 ◽  
Vol 29 (11) ◽  
pp. 3381-3395
Author(s):  
Wonmo Koo ◽  
Heeyoung Kim
Keyword(s):  
Longitudinal Data ◽  
Latent Class ◽  
Latent Class Model ◽  
Latent Class Models ◽  
Model Parameters ◽  
Latent Classes ◽  
Bayesian Nonparametric ◽  
Class Model ◽  
Proposed Model ◽  
Class Models

Latent class models have been widely used in longitudinal studies to uncover unobserved heterogeneity in a population and find the characteristics of the latent classes simultaneously using the class allocation probabilities dependent on predictors. However, previous latent class models for longitudinal data suffer from uncertainty in the choice of the number of latent classes. In this study, we propose a Bayesian nonparametric latent class model for longitudinal data, which allows the number of latent classes to be inferred from the data. The proposed model is an infinite mixture model with predictor-dependent class allocation probabilities; an individual longitudinal trajectory is described by the class-specific linear mixed effects model. The model parameters are estimated using Markov chain Monte Carlo methods. The proposed model is validated using a simulated example and a real-data example for characterizing latent classes of estradiol trajectories over the menopausal transition using data from the Study of Women’s Health Across the Nation.

Predictive Performance and Variability of the Cardiac Anesthesia Risk Evaluation Score

2004 ◽  
Vol 100 (6) ◽  
pp. 1405-1410 ◽  
Author(s):  
Alexandre Ouattara ◽  
Michaëla Niculescu ◽  
Sarra Ghazouani ◽  
Ario Babolian ◽  
Marc Landi ◽  
...  
Keyword(s):  
Receiver Operating Characteristic ◽  
Risk Evaluation ◽  
Goodness Of Fit ◽  
Operating Characteristic ◽  
Characteristic Curve ◽  
Predictive Performance ◽  
Cardiac Anesthesia ◽  
Goodness Of Fit Test ◽  
Significant Difference ◽  
Receiver Operating

Background The Cardiac Anesthesia Risk Evaluation (CARE) score, a simple Canadian classification for predicting outcome after cardiac surgery, was evaluated in 556 consecutive patients in Paris, France. The authors compared its performance to those of two multifactorial risk indexes (European System for Cardiac Operative Risk Evaluation [EuroSCORE] and Tu score) and tested its variability between groups of physicians (anesthesiologists, surgeons, and cardiologists). Methods Each patient was simultaneously assessed using the three scores by an attending anesthesiologist in the immediate preoperative period. In a blinded study, the CARE score category was also determined by a cardiologist the day before surgery, by a surgeon in the operating room, and by a second anesthesiologist at arrival in intensive care unit. Calibration and discrimination for predicting outcomes were assessed by goodness-of-fit test and area under the receiver operating characteristic curve, respectively. The level of agreement of the CARE scoring between the three physicians was then assessed. Results The calibration analysis revealed no significant difference between expected and observed outcomes for the three classifications. The areas under the receiver operating characteristic curves for mortality were 0.77 with the CARE score, 0.78 with the EuroSCORE, and 0.73 with the Tu score (not significant). The agreement rate of the CARE scoring between two anesthesiologists, between anesthesiologists and surgeons, and between anesthesiologists and cardiologists were 90%, 83%, and 77%, respectively. Conclusions Despite its simplicity, the CARE score predicts mortality and major morbidity as well the EuroSCORE. In addition, it remains devoid of significant variability when used by groups of physicians of different specialties.

scholarly journals The Q-Matrix Anchored Mixture Rasch Model

2021 ◽  
Vol 12 ◽  
Author(s):  
Ming-Chi Tseng ◽  
Wen-Chung Wang
Keyword(s):  
Rasch Model ◽  
Latent Variable ◽  
Latent Class ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Latent Classes ◽  
Modeling Framework ◽  
Class Invariant ◽  
Common Scale ◽  
Q Matrix

Mixture item response theory (IRT) models include a mixture of latent subpopulations such that there are qualitative differences between subgroups but within each subpopulation the measure model based on a continuous latent variable holds. Under this modeling framework, students can be characterized by both their location on a continuous latent variable and by their latent class membership according to Students’ responses. It is important to identify anchor items for constructing a common scale between latent classes beforehand under the mixture IRT framework. Then, all model parameters across latent classes can be estimated on the common scale. In the study, we proposed Q-matrix anchored mixture Rasch model (QAMRM), including a Q-matrix and the traditional mixture Rasch model. The Q-matrix in QAMRM can use class invariant items to place all model parameter estimates from different latent classes on a common scale regardless of the ability distribution. A simulation study was conducted, and it was found that the estimated parameters of the QAMRM recovered fairly well. A real dataset from the Certificate of Proficiency in English was analyzed with the QAMRM, LCDM. It was found the QAMRM outperformed the LCDM in terms of model fit indices.

scholarly journals Flow With an Intelligent Tutor: A Latent Variable Modeling Approach to Tracking Flow During Artificial Tutoring

2021 ◽  
Author(s):  
Hyeon-Ah Kang ◽  
Adam Sales ◽  
Tiffany A. Whittaker
Keyword(s):  
Latent Variable ◽  
Latent Class ◽  
Intelligent Tutoring System ◽  
Latent Class Model ◽  
Model Fitting ◽  
Latent Variable Modeling ◽  
Flow State ◽  
Modeling Framework ◽  
Modeling Approach ◽  
Comprehensive Survey

Increasing use of intelligent tutoring system (ITS) in education calls for analytic methods that can unravel students' learning behaviors. In this study we suggest a latent variable modeling approach to tracking flow during artificial tutoring. Flow is a mental state a student achieves when immersed in deep learning. Modeling latent flow helps identify when and how students flow during tutoring. The result of the model can also inform the functioning of ITS and provide instrumental information for designing interventions. Three latent variable models are considered to draw discrete inference on the flow state: the (i) latent class model, (ii) latent transition model, and (iii) hidden Markov model. For each of the models, we suggest practical model-fitting strategies, addressing the assumptions and estimation constraints. Using example data from Cognitive Tutor Algebra I, we show that each model provides unique and meaningful information about student's learning process. Through comprehensive survey of the models, we evaluate merits and drawbacks of each modeling framework and illuminate areas that need future development.

Adjusting a subject-specific time of event in longitudinal studies

2019 ◽  
Vol 29 (7) ◽  
pp. 1787-1798
Author(s):  
Hyunkeun Ryan Cho ◽  
Seonjin Kim ◽  
Myung Hee Lee
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Model Parameters ◽  
Specific Time ◽  
Goodness Of Fit Test ◽  
Proposed Model ◽  
Subject Specific ◽  
The Subject ◽  
The Mean ◽  
Over Time

Biomedical studies often involve an event that occurs to individuals at different times and has a significant influence on individual trajectories of response variables over time. We propose a statistical model to capture the mean trajectory alteration caused by not only the occurrence of the event but also the subject-specific time of the event. The proposed model provides a post-event mean trajectory smoothly connected with the pre-event mean trajectory by allowing the model parameters associated with the post-event mean trajectory to vary over time of the event. A goodness-of-fit test is considered to investigate how well the proposed model is fit to the data. Hypothesis tests are also developed to assess the influence of the subject-specific time of event on the mean trajectory. Theoretical and simulation studies confirm that the proposed tests choose the correctly specified model consistently and examine the effect of the subject-specific time of event successfully. The proposed model and tests are also illustrated by the analysis of two real-life data from a biomarker study for HIV patients along with their own time of treatment initiation and a body fatness study in girls with different age of menarche.

Fitting The Best–Fit Distribution For The Hourly Rainfall Amount In The Wilayah Persekutuan

2012 ◽  
Author(s):  
Fadhilah Y. ◽  
Zalina Md. ◽  
Nguyen V–T–V. ◽  
Suhaila S. ◽  
Zulkifli Y.
Keyword(s):  
Maximum Likelihood ◽  
Goodness Of Fit ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Exceedance Probability ◽  
Parameter Estimates ◽  
Goodness Of Fit Test ◽  
Hourly Rainfall ◽  
Best Fit ◽  
Mixed Exponential Distribution

Dalam mengenal pasti model yang terbaik untuk mewakili taburan jumlah hujan bagi data selang masa satu jam di 12 stesen di Wilayah Persekutuan empat taburan digunakan iaitu Taburan Eksponen, Gamma, Weibull dan Gabungan Eksponen. Parameter–parameter dianggar menggunakan kaedah kebolehjadian maksimum. Model yang terbaik dipilih berdasarkan nilai minimum yang diperolehi daripada ujian–ujian kebagusan penyuaian yang digunakan dalam kajian ini. Ujian ini dipertahankan lagi dengan plot kebarangkalian dilampaui. Taburan Gabungan Eksponen di dapati paling baik untuk mewakili taburan jumlah hujan dalam selang masa satu jam. Daripada anggaran parameter bagi taburan Gabungan Eksponen ini, boleh diterjemah bahawa jumlah hujan tertinggi yang direkodkan diperolehi daripada hujan yang dikategorikan sebagai hujan lebat, walaupun hujan renyai–renyai berlaku lebih kerap. Kata kunci: Jumlah hujan dalam selang masa sejam, ujian kebagusan penyuaian, kebolehjadian maksimum In determining the best–fit model for the hourly rainfall amounts for the twelve stations in the Wilayah Persekutuan, four distributions namely, the Exponential, Gamma, Weibull and Mixed–Exponential were used. Parameters for each distribution were estimated using the maximum likelihood method. The best–fit model was chosen based upon the minimum error produced by the goodness–offit tests used in this study. The tests were justified further by the exceedance probability plot. The Mixed–Exponential was found to be the most appropriate distribution in describing the hourly rainfall amounts. From the parameter estimates for the Mixed–Exponential distribution, it could be implied that most of the hourly rainfall amount recorded were received from the heavy rainfall even though there was a high occurrences of light rainfall. Key words: Hourly rainfall amount, goodness-of-fit test, exceedance probability, maximum likelihood

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