Model Identification and Computer Algebra

Bollen, Kenneth A.; Bauldry, Shawn

doi:10.1177/0049124110366238

Cited by 26 publications

(22 citation statements)

References 21 publications

(47 reference statements)

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“…To address these needs, OpenMx offers (in part based on Bollen & Bauldry, 2010) and respectively. The algorithm repeatedly perturbs starting values and optimizes the model in an effort to find the best minimum.…”

Section: Likelihood-based Cismentioning

confidence: 99%

Likelihood-Based Confidence Intervals for a Parameter With an Upper or Lower Bound

Pritikin

Rappaport

Neale

2017

Structural Equation Modeling: A Multidisciplinary Journal

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The precision of estimates in many statistical models can be expressed by a confidence interval (CI). CIs based on standard errors (SE) are common in practice, but likelihood-based CIs are worth consideration. In comparison to SEs, likelihood-based CIs are typically more difficult to estimate, but are more robust to model (re)parameterization. In latent variable models, some parameters may take on values outside of their interpretable range. Therefore, it is desirable to place a bound to keep the parameter interpretable. For likelihood-based CI, a correction is needed when a parameter is bounded. The correction is known (Wu & Neale, 2012), but is difficult to implement in practice. A novel automatic implementation that is simple for an applied researcher to use is introduced. A simulation study demonstrates the accuracy of the correction using a latent growth curve model and the method is illustrated with a multilevel confirmatory factor analysis.

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Section: Likelihood-based Cismentioning

confidence: 99%

Likelihood-Based Confidence Intervals for a Parameter With an Upper or Lower Bound

Pritikin

Rappaport

Neale

2017

Structural Equation Modeling: A Multidisciplinary Journal

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“…For each condition and prior, replications were submitted in parallel in sets of 20. The method of identification used for ML (setting each factor mean and variance to 0 and 1, respectively), although only locally identifying the model (Bollen & Bauldry, 2010) lead to all solutions with a majority of positive factor loadings (i.e. sign indeterminacy was not an issue using ML estimation for this model and data in Mplus).…”

Section: Simulation Studymentioning

confidence: 99%

“… 9 This model specification is only locally identified (Bollen & Bauldry, 2010; Loken, 2005), as there is a sign indeterminacy for the factor loadings on one or both factors. For the estimation routines used in Mplus for these models and data, the sign indeterminacy is not an issue and leads to solutions with a majority of positive factor loadings.…”

mentioning

confidence: 99%

Bayesian Estimation for Item Factor Analysis Models with Sparse Categorical Indicators

Bainter

2017

Multivariate Behavioral Research

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Psychometric models for item level data are broadly useful in psychology. A recurring issue for estimating IFA models is low item endorsement (item sparseness), due to limited sample sizes or extreme items such as rare symptoms or behaviors. In this paper, I demonstrate that under conditions characterized by sparseness, currently available estimation methods, including maximum likelihood (ML), are likely to fail to converge or lead to extreme estimates and low empirical power. Bayesian estimation incorporating prior information is a promising alternative to maximum likelihood estimation for IFA models with item sparseness. In this article I use a simulation study to demonstrate that Bayesian estimation incorporating general prior information improves parameter estimate stability, overall variability in estimates, and power for IFA models with sparse, categorical indicators. Importantly, the priors proposed here can be generally applied to many research contexts in psychology, and they do not impact results compared to ML when indicators are not sparse. I then apply this method to examine the relationship between suicide ideation and insomnia in a sample of first year college students. This provides an important alternative for researchers who may need to model items with sparse endorsement.

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“…Empirical techniques for model identification are part of nearly all SEM software. The empirical procedures generally are accurate but not always, because they examine a more limited type of identification (17).…”

Section: What Are Sems?mentioning

confidence: 99%

Structural equation models and the quantification of behavior

Bollen

Noble

2011

Proc. Natl. Acad. Sci. U.S.A.

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188

119

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Quantifying behavior often involves using variables that contain measurement errors and formulating multiequations to capture the relationship among a set of variables. Structural equation models (SEMs) refer to modeling techniques popular in the social and behavioral sciences that are equipped to handle multiequation models, multiple measures of concepts, and measurement error. This work provides an overview of latent variable SEMs. We present the equations for SEMs and the steps in modeling, and we provide three illustrations of SEMs. We suggest that the general nature of the model is capable of handling a variety of problems in the quantification of behavior, where the researcher has sufficient knowledge to formulate hypotheses.error in variables | factor analysis | path analysis | LISREL | covariance structures A mong the many problems in quantifying behavior are the challenges presented by the multiple equations to study and the difficulty of accurately measuring key concepts. For instance, scientists might be interested in general arousal and how it relates to more specific forms of arousal, or researchers might want to analyze quality of sleep and it relationship to different forms and intensities of pain. Arousal, quality of sleep, pain intensity, and numerous other variables are difficult to measure without considerable measurement error. Additionally, studying how several or more of these difficult to measure latent variables relate to each other is an even more arduous task when the multiequation nature of the problem is included.Ignoring these issues leads to inaccuracy of findings. Ignoring the measurement error in arousal or pain data, for instance, leads to inaccurate assessments of effects. Therefore, our assessment of perception of pain on quality of sleep is unlikely to be correct if we do not take account of the measurement error. We might have several ways to measure the same latent arousal variable and not be sure how to incorporate these ways into the model. Also, if we ignore the indirect effects of one variable on another variable and concentrate only on the direct effect, we are more likely to be mistaken in our assessment of how one variable affects another variable.Structural equation models (SEMs) refer to modeling techniques popular in the social and behavioral sciences that are equipped to handle multiequation models, multiple measures of concepts, and measurement error. This general model incorporates more familiar models as special cases. For instance, multiple regression is a special form of SEM, where there is a single dependent variable and multiple covariates and the covariates are assumed to be measured without measurement error. ANOVA is a another specialization where the covariates are assumed to be dichotomous variables. Factor analysis is yet another special form of the latent variable SEM. Here, we assume that we have multiple indicators that measure one or more factors and that the factors are permitted to correlate or not correlate. Recursive models, nonrecursive model...

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Model Identification and Computer Algebra

Cited by 26 publications

References 21 publications

Likelihood-Based Confidence Intervals for a Parameter With an Upper or Lower Bound

Likelihood-Based Confidence Intervals for a Parameter With an Upper or Lower Bound

Bayesian Estimation for Item Factor Analysis Models with Sparse Categorical Indicators

Structural equation models and the quantification of behavior

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