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Multiple Imputation to Estimate Hierarchical Models from Data Missing at Random: Latent Covariates, Random Coefficients, and Statistical Interactions
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Yongyun Shin; Stephen W. Raudenbush – Grantee Submission, 2025
Consider the conventional multilevel model Y=C[gamma]+Zu+e where [gamma] represents fixed effects and (u,e) are multivariate normal random effects. The continuous outcomes Y and covariates C are fully observed with a subset Z of C. The parameters are [theta]=([gamma],var(u),var(e)). Dempster, Rubin and Tsutakawa (1981) framed the estimation as a…
Descriptors: Hierarchical Linear Modeling, Maximum Likelihood Statistics, Sampling, Error of Measurement
Correcting Model Fit Criteria for Small Sample Latent Growth Models with Incomplete Data
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McNeish, Daniel; Harring, Jeffrey R. – Educational and Psychological Measurement, 2017
To date, small sample problems with latent growth models (LGMs) have not received the amount of attention in the literature as related mixed-effect models (MEMs). Although many models can be interchangeably framed as a LGM or a MEM, LGMs uniquely provide criteria to assess global data-model fit. However, previous studies have demonstrated poor…
Descriptors: Growth Models, Goodness of Fit, Error Correction, Sampling
Bootstrap Standard Errors for Maximum Likelihood Ability Estimates When Item Parameters Are Unknown
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Patton, Jeffrey M.; Cheng, Ying; Yuan, Ke-Hai; Diao, Qi – Educational and Psychological Measurement, 2014
When item parameter estimates are used to estimate the ability parameter in item response models, the standard error (SE) of the ability estimate must be corrected to reflect the error carried over from item calibration. For maximum likelihood (ML) ability estimates, a corrected asymptotic SE is available, but it requires a long test and the…
Descriptors: Sampling, Statistical Inference, Maximum Likelihood Statistics, Computation
Estimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm
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Yang, Ji Seung; Cai, Li – Journal of Educational and Behavioral Statistics, 2014
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…
Descriptors: Computation, Hierarchical Linear Modeling, Mathematics, Context Effect
Estimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm
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Yang, Ji Seung; Cai, Li – Grantee Submission, 2014
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can…
Descriptors: Computation, Hierarchical Linear Modeling, Mathematics, Context Effect
Ranked Set Sampling and Its Applications in Educational Statistics
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Stovall, Holly – ProQuest LLC, 2012
Over the past decade educational research has been stimulated by new legislation such as the No Child Left Behind Act. Increasing emphasis is being placed on accurately quantifying the success of treatment programs through student achievement scores, so precise estimation is vital for establishing the efficacy of new methodology. Ranked set…
Descriptors: Sampling, Educational Research, Hierarchical Linear Modeling, Nonparametric Statistics