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This article studies how sampling ratio variation affects the measurement of Level 2 (L2) latent constructs, using doubly latent MSEM with a two-step Monte Carlo simulation and an applied survey-data example, concluding with design implications for educational research.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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does the sampling ratio mean in multilevel structural equation modeling (MSEM)?","Question",{"text":63,"@type":64},"The sampling ratio is the proportion of Level 1 (L1) cases sampled out of the total available L1 cases within each Level 2 (L2) group.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How did the study evaluate the impact of different sampling ratios?",{"text":68,"@type":64},"It used a two-step Monte Carlo simulation study to examine how sampling ratio variation affects bias and variability in aggregated L2 latent construct measurement and estimation, followed by an applied example using empirical survey data.",{"name":70,"@type":61,"acceptedAnswer":71},"What were the main findings about lower sampling ratios?",{"text":72,"@type":64},"Lower sampling ratios were associated with increased bias, standard errors, and root mean square error, but the overall magnitude of these errors was negligible, making the doubly latent model an appealing 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Kush 1, Timothy R. Konold 1 and Catherine P. Bradshaw 1  \nEducational and Psychological Measurement  \n2022, Vol. 82(3) 409–443  \n􀀂 The Author(s) 2021 Article reuse guidelines:  \n[sagepub.com/journals-permissions](sagepub.com/journals-permissions)[ ](sagepub.com/journals-permissions)[DOI: 10.1177/00131644211020112](DOI: 10.1177/00131644211020112)[ ](DOI: 10.1177/00131644211020112)[journals.sagepub.com/home/epm](journals.sagepub.com/home/epm)  \nAbstract  \nMultilevel structural equation modeling (MSEM) allows researchers to model latent factor structures at multiple levels simultaneously by decomposing within- and between-group variation. Yet the extent to which the sampling ratio (i.e., proportion of cases sampled from each group) influences the results of MSEM models remains unknown. This article explores how variation in the sampling ratio in MSEM affects the measurement of Level 2 (L2) latent constructs. Specifically, we investigated whether the sampling ratio is related to bias and variability in aggregated L2 construct measurement and estimation in the context of doubly latent MSEM models utilizing a two-step Monte Carlo simulation study. Findings suggest that while lower sampling ratios were related to increased bias, standard errors, and root mean square error, the overall size of these errors was negligible, making the doubly latent model an appealing choice for researchers. An applied example using empirical survey data is further provided to illustrate the application and interpretation of the model. We conclude by considering the implications of various sampling ratios on the design of MSEM studies, with a particular focus on educational research.  \nKeywords  \nmultilevel, structural equation model, sampling ratio, doubly latent, sampling and measurement error, interchangeability and exchangeability  \n1 University of Virginia, Charlottesville, VA, USA  \nCorresponding Author:  \nJoseph M. Kush, Research, Statistics, & Evaluation, University of Virginia, School of Education and Human Development, 207 Ruffner Hall, Charlottesville, VA 22904, USA.  \nEmail: [jmk7cj@virginia.edu](jmk7cj@virginia.edu)  \nClustered data structures can present challenges for general linear models that assume independence of observations (Bentler & Chou, 1987; Raudenbush & Bryk, 2002) . Yet clustered data structures can provide an opportunity for understanding how variables are related at more than one level. Multilevel modeling (MLM) adjusts for the violation of the homoskedasticity (or exogeneity) assumption of single-level linear regression, in which residual variance are no longer independent (Bentler & Chou, 1987; Rabe-Hesketh & Skrondal, 2008; Raudenbush & Bryk, 2002) . MLM is frequently used to account for clustered data, where data are often clustered within higher level units, and thus continues to grow in popularity among applied researchers in the social and behavioral sciences (Raudenbush & Bryk, 2002; Snijders & Bosker, 1999) . For instance, students may be clustered within schools, teachers maybe clustered within districts, and individuals may be clustered within neighborhoods. By partitioning variation at different levels, multilevel modeling allows researchers to explore relationships among variables at two or more levels, and at the same time control for violations of independence that can have an adverse impact on the standard errors of model parameter estimates.  \nWhile observed variable multilevel analysis has a long-standing history in the social sciences, multilevel structural equation modeling (MSEM) continues to make substantial progress both in theory and application (see Hox & Maas, 2001; Jia & Konold, 2019; Muth´en & Asparouhov, 2011; Preacher et al., 2010) . MSEM is useful in accounting for measurement and/or sampling error, where Level 1 (L1) and Level 2 (L2) substantive latent constructs are estimated from ","cbCaipx1B8tnpIKp","https://ap.wps.com/l/cbCaipx1B8tnpIKp","pdf",679487,35,"English","# Abstract\n# Keywords\n# Multilevel Modeling Background\n# Multilevel Structural Equation Modeling (MSEM)\n# Sampling Ratio in MSEM\n# Prior Research on Sampling Ratio\n# L2 Construct Measurement and Contextual Effects","[{\"question\":\"What does the sampling ratio mean in multilevel structural equation modeling (MSEM)?\",\"answer\":\"The sampling ratio is the proportion of Level 1 (L1) cases sampled out of the total available L1 cases within each Level 2 (L2) group.\"},{\"question\":\"How did the study evaluate the impact of different sampling ratios?\",\"answer\":\"It used a two-step Monte Carlo simulation study to examine how sampling ratio variation affects bias and variability in aggregated L2 latent construct measurement and estimation, followed by an applied example using empirical survey data.\"},{\"question\":\"What were the main findings about lower sampling ratios?\",\"answer\":\"Lower sampling ratios were associated with increased bias, standard errors, and root mean square error, but the overall magnitude of these errors was negligible, making the doubly latent model an appealing choice.\"}]","The Sampling Ratio in Multilevel Structural Equation Models - Considerations to Inform Study Design | PDF",1792093961,88]