Semi-Nonparametric Methods for Detecting Latent Non-normality: A Fusion of Latent Trait and Ordered Latent Class Modeling

@article{Schmitt2006SemiNonparametricMF,
  title={Semi-Nonparametric Methods for Detecting Latent Non-normality: A Fusion of Latent Trait and Ordered Latent Class Modeling},
  author={J. Eric Schmitt and Paras D Mehta and Steven H. Aggen and Thomas S. Kubarych and Michael C. Neale},
  journal={Multivariate Behavioral Research},
  year={2006},
  volume={41},
  pages={427 - 443}
}
Ordered latent class analysis (OLCA) can be used to approximate unidimensional latent distributions. The main objective of this study is to evaluate the method of OLCA in detecting non-normality of an unobserved continuous variable (i.e., a common factor) used to explain the covariation between dichotomous item-level responses. Using simulation, we compared a model in which probabilities of class membership were estimated to a restricted submodel in which class memberships were fixed to normal… 
Computational methods for Bayesian semiparametric Item Response Theory models
TLDR
An in-depth study of Markov chain Monte Carlo posterior sampling efficiency for several sampling strategies and study how different sets of constraints can lead to model identifiability and give guidance on eliciting prior distributions.
The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions
TLDR
This paper presents the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastics error variances and a skew-normal latent trait and investigates the viability of the model and the specificity of the effects.
The effect of latent and error non-normality on corrections to the test statistic in structural equation modeling
TLDR
A Monte Carlo simulation to analyze the effect of non-normality in factors and errors on six different test statistics based on maximum likelihood estimation indicates that the values of the uncorrected test statistic are associated with a severely inflated type I error rate when latent variables are non-normal, but virtually no differences occur when errors arenon-normal.
Testing and modelling non-normality within the one-factor model.
TLDR
A model is presented based on marginal maximum likelihood to enable explicit tests of multivariate normality assumptions and is applied to IQ data to demonstrate its practical utility as a means to investigate ability differentiation.
DIF Testing With an Empirical-Histogram Approximation of the Latent Density for Each Group
This research introduces, illustrates, and tests a variation of IRT-LR-DIF, called EH-DIF-2, in which the latent density for each group is estimated simultaneously with the item parameters as an
Nonnormality in Latent Trait Modelling
This chapter presents tools to facilitate specific tests on three sources of nonnormality in subtest scores or latent response variates: nonnormality of the latent trait, heteroscedasticity of the
Bayesian item response model: a generalized approach for the abilities' distribution using mixtures
TLDR
A generalized approach for the distribution of the abilities in dichotomous 3-parameter Item Response models with a mixture of normal distributions is considered, allowing for features like skewness, multimodality and heavy tails.
Problems with using sum scores for estimating variance components: contamination and measurement noninvariance.
TLDR
It is shown that absence of measurement invariance across zygosity can bias estimates of genetic and environmental components of variance, and that the analysis of sum scores typically biases both MZ and DZ correlations compared to the true latent trait correlation.
Bayesian Item Response model: a generalised approach for the abilities' distribution using mixtures
TLDR
A generalised approach for the distribution of the abilities in dichotomous 3-parameter Item Response models is presented, with a mixture of normal distributions considered, allowing for features like skewness, multimodality and heavy tails.
A Comparison of Factor Score Estimation Methods in the Presence of Missing Data: Reliability and an Application to Nicotine Dependence
TLDR
A simulation study compares the reliability of sum scores, regression-based and expected posterior methods for factor score estimation for confirmatory factor models in the presence of missing data and shows that the full maximum likelihood method best preserves the relationship between nicotine dependence and a genetic predictor under missing data.
...
1
2
3
...

References

SHOWING 1-10 OF 45 REFERENCES
Estimating Johnson Curve Population Distributions in MULTILOG
The shape of the latent trait distribution can be of considerable theoretical and methodological importance. A simulation study was performed to examine the distribution of the likelihood ratio
The Use of Restricted Latent Class Models for Defining and Testing Nonparametric and Parametric Item Response Theory Models
A general class of ordinal logit models is presented that specifies equality and inequality constraints on sums of conditional response probabilities. Using these constraints in latent class
Consistent estimation in the rasch model based on nonparametric margins
Consider the class of two parameter marginal logistic (Rasch) models, for a test ofm True-False items, where the latent ability is assumed to be bounded. Using results of Karlin and Studen, we show
New Developments in Latent Class Theory
A feature common to most models considered in the first part of this book may be easily depicted by Figure 1. In latent trait models, the point of departure is a set of manifest categorical variables
Latent Class Models for Measuring
TLDR
Extensions and modifications of latent class models reported below are intended to remove a deficiency in latent class analysis that deals in a direct way with measurement.
Variance Decomposition Using an IRT Measurement Model
TLDR
It is argued that an IRT approach in combination with Markov chain Monte Carlo estimation provides a flexible and efficient framework for modelling behavioural phenotypes and it is shown that the framework of Item Response Theory (IRT) offers a solution to most of these problems.
Generalized multilevel structural equation modeling
TLDR
Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.
An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models
It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward
On the relationship between item response theory and factor analysis of discretized variables
Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory (IRT) and factor analysis of dichotomized variables (FA) was formally proved. The basic result on
Sequential item response models with an ordered response
  • G. Tutz
  • Computer Science, Mathematics
  • 1990
TLDR
A stepwise approach to the construction of latent trait models is outlined and an alternative estimation procedure which allows for ‘parameter separability’ is considered and its applicability is shown.
...
1
2
3
4
5
...