Evaluation of the Bayesian and Maximum Likelihood Approaches in Analyzing Structural Equation Models with Small Sample Sizes

2004 ◽  
Vol 39 (4) ◽  
pp. 653-686 ◽  
Author(s):  
Sik-Yum Lee ◽  
Xin-Yuan Song
Keyword(s):  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Small Sample ◽  
Sample Sizes ◽  
Small Sample Sizes

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.

Consistency and Efficiency of Ordinary Least Squares, Maximum Likelihood, and Three Type II Linear Regression Models

Methodology ◽  
2007 ◽  
Vol 3 (2) ◽  
pp. 81-88 ◽  
Author(s):  
João Maroco
Keyword(s):  
Maximum Likelihood ◽  
Measurement Errors ◽  
Major Axis ◽  
Ordinary Least Squares ◽  
Small Sample ◽  
Type Ii ◽  
Linear Regression Models ◽  
Sample Sizes ◽  
Reduced Major Axis ◽  
Small Sample Sizes

Abstract. Type I linear regression models, which allow for measurement errors only in the criterion variable, are frequently used in modeling research in psychology and the social sciences. Although there are frequently measurement errors and large natural variation both in the criterion and predictor variables, type II regression methods that account for these errors are seldom used in these fields of study. The consistency and efficiency of three type II regression methods (reduced major axis, Kendall's robust line-fit and Bartlett's three-group) were evaluated in comparison to ordinary least squares (OLS) and the maximum likelihood with known variance ratio used frequently in biometrics and econometrics. When predictors are measured with error, OLS slope estimates are biased toward zero, and the same bias was observed with both Kendall's and Bartlett's methods. Reduced major axis produced consistent estimates even for small sample sizes, whenever the measurement errors in X are similar in magnitude to measurement errors in Y, but there was a consistent bias when the measurement error in X was smaller/greater than in Y. Maximum likelihood estimates behaved erroneously for small sample sizes, but for larger sample sizes they converged to the expected values.

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.

No Evidence that Experiencing Physical Warmth Promotes Interpersonal Warmth: Two Failures to Replicate Williams and Bargh (2008)

2018 ◽  
Author(s):  
Christopher Chabris ◽  
Patrick Ryan Heck ◽  
Jaclyn Mandart ◽  
Daniel Jacob Benjamin ◽  
Daniel J. Simons
Keyword(s):  
Null Hypothesis ◽  
Small Sample ◽  
Sample Sizes ◽  
Double Blind ◽  
Bayesian Analyses ◽  
Physical Warmth ◽  
Small Sample Sizes ◽  
Interpersonal Warmth

Williams and Bargh (2008) reported that holding a hot cup of coffee caused participants to judge a person’s personality as warmer, and that holding a therapeutic heat pad caused participants to choose rewards for other people rather than for themselves. These experiments featured large effects (r = .28 and .31), small sample sizes (41 and 53 participants), and barely statistically significant results. We attempted to replicate both experiments in field settings with more than triple the sample sizes (128 and 177) and double-blind procedures, but found near-zero effects (r = –.03 and .02). In both cases, Bayesian analyses suggest there is substantially more evidence for the null hypothesis of no effect than for the original physical warmth priming hypothesis.

scholarly journals G-computation and machine learning for estimating the causal effects of binary exposure statuses on binary outcomes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Florent Le Borgne ◽  
Arthur Chatton ◽  
Maxime Léger ◽  
Rémi Lenain ◽  
Yohann Foucher
Keyword(s):  
Machine Learning ◽  
Support Vector Machine ◽  
Statistical Power ◽  
Small Sample ◽  
Causal Effects ◽  
Small Samples ◽  
Support Vector ◽  
Sample Sizes ◽  
Super Learner ◽  
Small Sample Sizes

AbstractIn clinical research, there is a growing interest in the use of propensity score-based methods to estimate causal effects. G-computation is an alternative because of its high statistical power. Machine learning is also increasingly used because of its possible robustness to model misspecification. In this paper, we aimed to propose an approach that combines machine learning and G-computation when both the outcome and the exposure status are binary and is able to deal with small samples. We evaluated the performances of several methods, including penalized logistic regressions, a neural network, a support vector machine, boosted classification and regression trees, and a super learner through simulations. We proposed six different scenarios characterised by various sample sizes, numbers of covariates and relationships between covariates, exposure statuses, and outcomes. We have also illustrated the application of these methods, in which they were used to estimate the efficacy of barbiturates prescribed during the first 24 h of an episode of intracranial hypertension. In the context of GC, for estimating the individual outcome probabilities in two counterfactual worlds, we reported that the super learner tended to outperform the other approaches in terms of both bias and variance, especially for small sample sizes. The support vector machine performed well, but its mean bias was slightly higher than that of the super learner. In the investigated scenarios, G-computation associated with the super learner was a performant method for drawing causal inferences, even from small sample sizes.

Sign in / Sign up

Export Citation Format

Share Document