Exploratory Measurement Modeling with Lasso: �The Role of Measurement Quality
Youngwon Kim, Ph.D., & Elizabeth A. Sanders Ph.D., University of Washington
IMPS 2023 Annual Conference, University of Maryland, College Park
METHODS
BACKGROUND
Sample Size
(100, 150, 1000)
Variable per Factors (VPF)
(3, 4, 5, 10)
Factor-Factor Correlation �(0, .2, .5)
Measurement Quality �(Low: .4-.6, High: .7-.9)
All Conditions (72 = 3x4x3x2)
Algorithmic-based exploratory approaches for measurement modeling may be useful with large-scale survey and assessment data for which researchers have little theory to guide model selection. For example, the least absolute shrinkage and selection operator (Lasso), adaptive Lasso (aLasso), and minimax concave penalty (MCP) algorithms have been successfully applied within the IRT framework as well as within the SEM framework.
Using Monte Carlo simulation, we evaluated the performance (bias and variable factor matching) of different regularization methods (Lasso, aLasso, and MCP) in estimating factor loadings.
RESULTS
Average Factor Loading Estimation Bias
Variable-Factor Matching Accuracy (%)
Zero-Valued Loading Estimates for Factors
> Although the mean and variability of the estimates varied slightly between the methods. the estimates for all methods were centered around zero.
Non-Zero-Valued Target Loading Estimates
> As the VPF increased, the mean loading biases decreased. The loadings with low measurement quality were less biased.
> The Lasso and aLasso methods generally tended to yield more biases than other methods across all conditions.
> Except for the case (Factor Cor 0), MCP had more bias than ESEM and less bias than Lasso and aLasso.
Zero-Valued Cross-Loading Estimates
> As the VPF and measurement quality increased, all methods exhibited higher levels of bias in the loading estimates.
> Lasso and aLasso showed relatively better performance in estimating cross-loadings with less bias, followed by MCP.
> ESEM had the highest bias among the methods.
Variable-Factor Matching Accuracy
> All methods performed well in accurately matching variables to factors, especially non-zero variables, compared to the other methods.� �> (Non-zero-valued) As the VPF increased, the matching accuracy increased. The loadings with low measurement quality relatively had lower accuracy.
> (Zero-cross- loadings) As the VPF increased, the matching accuracy decreased.
> Within regularization methods for non-zero-valued loadings, MCP performed better than Lasso and aLasso. ��> ESEM was particularly effective in detecting non-zero relationships, while the other methods were more proficient in identifying and excluding cross-loadings.
LIMITATIONS & FUTURE WORK
> The findings are limited to the conditions used: Needs to include more conditions.
> Small number of replications per conditions: In the future more replications per condition would yield more reliable results.
> Only three regularization terms: Future work needs to investigate other additional terms (e.g., SCAD) more fully.
> Default the epsilon value of Geomin rotation: Needs to use a different epsilon value (e.g., 0.50)
> Only regsem package : Needs to use different packages (e.g., lslx, penfa, and lessSEM)
PRACTICAL RECOMMENDATIONS
What is the most important part of the measurement model for your research?
ESEM
Detect Unrelated Items
Less Bias (Accuracy and Precision)
RSEM
Penalize Cross-Loadings
MCP
Accuracy
Lasso/aLasso
Precision
Removing Item(s)
Manual
Automatic
QUESTIONS?
Thank you!
Questions? Please contact:
youngwonkim.ywk@gmail.com
When choosing an appropriate method for exploratory measurement modeling, it is important to consider the impact of measurement quality, correlations between factors, sample size, and the variable-to-factor ratio.