scholarly journals Normal Theory Two-Stage ML Estimator When Data Are Missing at the Item Level

2017 ◽  
Vol 42 (4) ◽  
pp. 405-431 ◽  
Author(s):  
Victoria Savalei ◽  
Mijke Rhemtulla
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Estimation Method ◽  
Analytic Approach ◽  
Parameter Estimates ◽  
Two Stage ◽  
Data Set ◽  
Item Level

In many modeling contexts, the variables in the model are linear composites of the raw items measured for each participant; for instance, regression and path analysis models rely on scale scores, and structural equation models often use parcels as indicators of latent constructs. Currently, no analytic estimation method exists to appropriately handle missing data at the item level. Item-level multiple imputation (MI), however, can handle such missing data straightforwardly. In this article, we develop an analytic approach for dealing with item-level missing data—that is, one that obtains a unique set of parameter estimates directly from the incomplete data set and does not require imputations. The proposed approach is a variant of the two-stage maximum likelihood (TSML) methodology, and it is the analytic equivalent of item-level MI. We compare the new TSML approach to three existing alternatives for handling item-level missing data: scale-level full information maximum likelihood, available-case maximum likelihood, and item-level MI. We find that the TSML approach is the best analytic approach, and its performance is similar to item-level MI. We recommend its implementation in popular software and its further study.

scholarly journals Two-stage maximum likelihood approach for item-level missing data in regression

2020 ◽  
Vol 52 (6) ◽  
pp. 2306-2323 ◽  
Author(s):  
Lihan Chen ◽  
Victoria Savalei ◽  
Mijke Rhemtulla
Keyword(s):  
Missing Data ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
High Efficiency ◽  
Structural Equation Models ◽  
Small Sample ◽  
Parameter Estimates ◽  
Two Stage ◽  
Item Level ◽  
Scale Scores

AbstractPsychologists use scales comprised of multiple items to measure underlying constructs. Missing data on such scales often occur at the item level, whereas the model of interest to the researcher is at the composite (scale score) level. Existing analytic approaches cannot easily accommodate item-level missing data when models involve composites. A very common practice in psychology is to average all available items to produce scale scores. This approach, referred to as available-case maximum likelihood (ACML), may produce biased parameter estimates. Another approach researchers use to deal with item-level missing data is scale-level full information maximum likelihood (SL-FIML), which treats the whole scale as missing if any item is missing. SL-FIML is inefficient and it may also exhibit bias. Multiple imputation (MI) produces the correct results using a simulation-based approach. We study a new analytic alternative for item-level missingness, called two-stage maximum likelihood (TSML; Savalei & Rhemtulla, Journal of Educational and Behavioral Statistics, 42(4), 405–431. 2017). The original work showed the method outperforming ACML and SL-FIML in structural equation models with parcels. The current simulation study examined the performance of ACML, SL-FIML, MI, and TSML in the context of univariate regression. We demonstrated performance issues encountered by ACML and SL-FIML when estimating regression coefficients, under both MCAR and MAR conditions. Aside from convergence issues with small sample sizes and high missingness, TSML performed similarly to MI in all conditions, showing negligible bias, high efficiency, and good coverage. This fast analytic approach is therefore recommended whenever it achieves convergence. R code and a Shiny app to perform TSML are provided.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

scholarly journals Croon’s Bias-Corrected Factor Score Path Analysis for Small- to Moderate-Sample Multilevel Structural Equation Models

2019 ◽  
Vol 24 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Benjamin Kelcey ◽  
Kyle Cox ◽  
Nianbo Dong
Keyword(s):  
Maximum Likelihood ◽  
Path Analysis ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Factor Score ◽  
Likelihood Estimation ◽  
Bias Error ◽  
Parameter Estimates ◽  
Multilevel Structural Equation

Maximum likelihood estimation of multilevel structural equation model (MLSEM) parameters is a preferred approach to probe theories involving latent variables in multilevel settings. Although maximum likelihood has many desirable properties, a major limitation is that it often fails to converge and can incur significant bias when implemented in studies with a small to moderate multilevel sample (e.g., fewer than 100 organizations with 10 or less individuals/organization). To address similar limitations in single-level SEM, literature has developed Croon’s bias-corrected factor score path analysis estimator that converges more regularly than maximum likelihood and delivers less biased parameter estimates with small to moderate sample sizes. We derive extensions to this framework for MLSEMs and probe the degree to which the estimator retains these advantages with small to moderate multilevel samples. The estimator emerges as a useful alternative or complement to maximum likelihood because it often outperforms maximum likelihood in small to moderate multilevel samples in terms of convergence, bias, error variance, and power. The proposed estimator is implemented as a function in R using lavaan and is illustrated using a multilevel mediation example.

Sign in / Sign up

Export Citation Format

Share Document