scholarly journals Choosing the number of factors in independent factor analysis model

2005 ◽  
Vol 2 (2) ◽  
Author(s):  
Cinzia Viroli
Keyword(s):  
Factor Analysis ◽  
Latent Variables ◽  
Latent Variable ◽  
Information Criteria ◽  
Ratio Test ◽  
Independent Factor ◽  
Analysis Model ◽  
Variable Model ◽  
Factor Analysis Model ◽  
Independent Factor Analysis

Independent Factor Analysis (IFA) has recently been proposed in the signal processing literature as a way to model a set of observed variables through linear combinations of hidden independent ones plus a noise term. Despite the peculiarity of its origin the method can be framed within the latent variable model domain and some parallels with the ordinary factor analysis can be drawn. If no prior information on the latent structure is available a relevant issue concerns the correct specification of the model. In this work some methods to detect the number of significant latent variables are investigated. Moreover, since the method defines a probability density function for the latent variables by mixtures of gaussians, the correct number of mixture components must also be determined. This issue will be treated according to two main approaches. The first one amounts to carry out a likelihood ratio test. The other one is based on a penalized form of the likelihood, that leads to the so called information criteria. Some simulations and empirical results on real data sets are finally presented.

scholarly journals Noisy independent factor analysis model for density estimation and classification

2010 ◽  
Vol 4 (0) ◽  
pp. 707-736 ◽  
Author(s):  
Umberto Amato ◽  
Anestis Antoniadis ◽  
Alexander Samarov ◽  
Alexandre B. Tsybakov
Keyword(s):  
Factor Analysis ◽  
Density Estimation ◽  
Independent Factor ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Independent Factor Analysis

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.

Bayesian analysis of two-part nonlinear latent variable model: Semiparametric method

2021 ◽  
pp. 1471082X2110592
Author(s):  
Jian-Wei Gou ◽  
Ye-Mao Xia ◽  
De-Peng Jiang
Keyword(s):  
Factor Analysis ◽  
Latent Variables ◽  
Latent Variable ◽  
Latent Variable Model ◽  
Continuous Data ◽  
Model Assessment ◽  
Continuous Variables ◽  
Continuous Part ◽  
Variable Model ◽  
Log Normal

Two-part model (TPM) is a widely appreciated statistical method for analyzing semi-continuous data. Semi-continuous data can be viewed as arising from two distinct stochastic processes: one governs the occurrence or binary part of data and the other determines the intensity or continuous part. In the regression setting with the semi-continuous outcome as functions of covariates, the binary part is commonly modelled via logistic regression and the continuous component via a log-normal model. The conventional TPM, still imposes assumptions such as log-normal distribution of the continuous part, with no unobserved heterogeneity among the response, and no collinearity among covariates, which are quite often unrealistic in practical applications. In this article, we develop a two-part nonlinear latent variable model (TPNLVM) with mixed multiple semi-continuous and continuous variables. The semi-continuous variables are treated as indicators of the latent factor analysis along with other manifest variables. This reduces the dimensionality of the regression model and alleviates the potential multicollinearity problems. Our TPNLVM can accommodate the nonlinear relationships among latent variables extracted from the factor analysis. To downweight the influence of distribution deviations and extreme observations, we develop a Bayesian semiparametric analysis procedure. The conventional parametric assumptions on the related distributions are relaxed and the Dirichlet process (DP) prior is used to improve model fitting. By taking advantage of the discreteness of DP, our method is effective in capturing the heterogeneity underlying population. Within the Bayesian paradigm, posterior inferences including parameters estimates and model assessment are carried out through Markov Chains Monte Carlo (MCMC) sampling method. To facilitate posterior sampling, we adapt the Polya-Gamma stochastic representation for the logistic model. Using simulation studies, we examine properties and merits of our proposed methods and illustrate our approach by evaluating the effect of treatment on cocaine use and examining whether the treatment effect is moderated by psychiatric problems.

Bayesian proportional hazards model with latent variables

2017 ◽  
Vol 28 (4) ◽  
pp. 986-1002 ◽  
Author(s):  
Deng Pan ◽  
Kai Kang ◽  
Chunjie Wang ◽  
Xinyuan Song
Keyword(s):  
Risk Factors ◽  
Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Latent Variables ◽  
Proportional Hazards ◽  
Proportional Hazards Model ◽  
Failure Time ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Hazards Model

We consider a joint modeling approach that incorporates latent variables into a proportional hazards model to examine the observed and latent risk factors of the failure time of interest. An exploratory factor analysis model is used to characterize the latent risk factors through multiple observed variables. In commonly used confirmatory factor analysis, the number of latent variables and their observed indicators are specified prior to analysis. By contrast, the exploratory factor analysis model allows such information to be fully determined by the data. A Bayesian approach coupled with efficient sampling methods is developed to conduct statistical inference, and the performance of the proposed methodology is confirmed through simulations. The model is applied to a study on the risk factors of chronic kidney disease for patients with type 2 diabetes.

scholarly journals Application of Confirmatory Factor Analysis for Correlate of Students Attitude, Self-Belief, Students Engagement in Mathematics Lessons and Mathematics Achievement

2018 ◽  
Vol 7 (2.29) ◽  
pp. 535 ◽  
Author(s):  
Desi Rahmatina
Keyword(s):  
Factor Analysis ◽  
Mathematics Achievement ◽  
Confirmatory Factor Analysis ◽  
Latent Variables ◽  
Negative Relationship ◽  
Mathematics Lesson ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Data Set ◽  
Confirmatory Factor

The study aimed to propose the Confirmatory Factor Analysis via four latent variables : 1) Students Attitude toward mathematics, 2) Self-belief in mathematics, 3) Students engagement in mathematics lessons and 4) Mathematics Achievement  and 19 observed variables and then we conduct to the correlations between latent variables and observed variables. The subjects were 5795 eight grades students from the result of the Trends in International Mathematics and Science Study (TIMSS) 2011 assessment conducted in Indonesia. Data Analysis were undertaken using the Lisrel software to examine the effect of students attitude toward mathematics, students self belief and students engagement in mathematics lesson for mathematics achievement. The proposed Confirmatory Factor Analysis model of the latent variables and observed variables fit well with the empirical data set (RMSEA = 0,071). The results of multivariate analyses has shown a strong negative relationship between student attitude toward mathematics, self-belief in mathematics and their mathematics achievement (t value = -6.32 and t = -6.10, respectively) and a strong positive relationship between students engagement in mathematics lesson with mathematics achievement (t value = 8,28).   

scholarly journals The Noetic Experience and Belief Scale: A validation and reliability study

F1000Research ◽  
2020 ◽  
Vol 8 ◽  
pp. 1741
Author(s):  
Helané Wahbeh ◽  
Garret Yount ◽  
Cassandra Vieten ◽  
Dean Radin ◽  
Arnaud Delorme
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Internal Consistency ◽  
Latent Variables ◽  
Convergent Validity ◽  
The United States ◽  
Divergent Validity ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Confirmatory Factor

Background: Belief in the paranormal is widespread worldwide. Recent surveys suggest that subjective experiences of the paranormal are common. A concise instrument that adequately evaluates beliefs as distinct from experiences does not currently exist. To address this gap, we created the Noetic Experiences and Beliefs Scale (NEBS) which evaluates belief and experience as separate constructs. Methods: The NEBS is a 20-item survey with 10 belief and 10 experience items rated on a visual analog scale from 0-100. In an observational study, the survey was administered to 361 general population adults in the United States and a subsample of 96 one month later. Validity, reliability and internal consistency were evaluated. A confirmatory factor analysis was conducted to confirm the latent variables of belief and experience. The survey was then administered to a sample of 646 IONS Discovery Lab participants to evaluate divergent validity and confirm belief and experience as latent variables of the model in a different population. Results: The NEBS demonstrated convergent validity, reliability and internal consistency (Cronbach’s alpha Belief 0.90; Experience 0.93) and test-retest reliability (Belief: r = 0.83; Experience: r = 0.77). A confirmatory factor analysis model with belief and experience as latent variables demonstrated a good fit. The factor model was confirmed as having a good fit and divergent validity was established in the sample of 646 IONS Discovery Lab participants. Conclusions: The NEBS is a short, valid, and reliable instrument for evaluating paranormal belief and experience.

scholarly journals Measuring extraordinary experiences and beliefs: A validation and reliability study

F1000Research ◽  
2020 ◽  
Vol 8 ◽  
pp. 1741
Author(s):  
Helané Wahbeh ◽  
Garret Yount ◽  
Cassandra Vieten ◽  
Dean Radin ◽  
Arnaud Delorme
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Internal Consistency ◽  
Latent Variables ◽  
Convergent Validity ◽  
The United States ◽  
Divergent Validity ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Confirmatory Factor

Background: Belief in the paranormal is widespread worldwide. Recent surveys suggest that subjective experiences of the paranormal are common. A concise instrument that adequately evaluates beliefs as distinct from experiences does not currently exist. To address this gap, we created the Noetic Experiences and Beliefs Scale (NEBS) which evaluates belief and experience as separate constructs. Methods: The NEBS is a 20-item survey with 10 belief and 10 experience items rated on a visual analog scale from 0-100. In an observational study, the survey was administered to 361 general population adults in the United States and a subsample of 96 one month later. Validity, reliability and internal consistency were evaluated. A confirmatory factor analysis was conducted to confirm the latent variables of belief and experience. The survey was then administered to a sample of 646 IONS Discovery Lab participants to evaluate divergent validity and confirm belief and experience as latent variables of the model in a different population. Results: The NEBS demonstrated convergent validity, reliability and internal consistency (Cronbach’s alpha Belief 0.90; Experience 0.93) and test-retest reliability (Belief: r = 0.83; Experience: r = 0.77). A confirmatory factor analysis model with belief and experience as latent variables demonstrated a good fit. The factor model was confirmed as having a good fit and divergent validity was established in the sample of 646 IONS Discovery Lab participants. Conclusions: The NEBS is a short, valid, and reliable instrument for evaluating paranormal belief and experience.

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