Evaluation of Second- and Third-Level Variance Proportions in Multilevel Designs With Completely Observed Populations: A Note on a Latent Variable Modeling Procedure

Two- and three-level designs in educational and psychological research can involve entire populations of Level-3 and possibly Level-2 units, such as schools and educational districts nested within a given state, or neighborhoods and counties in a state. Such a design is of increasing relevance in empirical research owing to the growing popularity of large-scale studies in these and cognate disciplines. The present note discusses a readily applicable procedure for point-and-interval estimation of the proportions of second- and third-level variances in such multilevel settings, which may also be employed in model choice considerations regarding ensuing analyses for response variables of interest. The method is developed within the framework of the latent variable modeling methodology, is readily utilized with widely used software, and is illustrated with an example.

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Design Effect in Multilevel Settings: A Commentary on a Latent Variable Modeling Procedure for Its Evaluation

Educational and Psychological Measurement ◽

10.1177/00131644211019447 ◽

2021 ◽

pp. 001316442110194

Author(s):

Tenko Raykov ◽

Christine DiStefano

Keyword(s):

Latent Variable ◽

Intraclass Correlation ◽

Interval Estimation ◽

Standard Errors ◽

Latent Variable Modeling ◽

Interval Estimate ◽

Design Effect ◽

Modeling Methodology ◽

Relationship Of ◽

The Relationship

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to conducting single-level analyses. The approach can also be employed as an addendum to point and interval estimation of the intraclass correlation coefficient in empirical research. The discussed procedure makes it easily possible to evaluate the design effect in two-level studies by utilizing the popular latent variable modeling methodology and is illustrated with an example.

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Reliability of Scales With Second-Order Structure: Evaluation of Coefficient Alpha’s Population Slippage Using Latent Variable Modeling

Educational and Psychological Measurement ◽

10.1177/0013164417719948 ◽

2017 ◽

Vol 78 (6) ◽

pp. 1123-1135

Author(s):

Tenko Raykov ◽

Philippe Goldammer ◽

George A. Marcoulides ◽

Tatyana Li ◽

Natalja Menold

Keyword(s):

Latent Variable ◽

Complex Structure ◽

Interval Estimation ◽

Psychological Research ◽

Second Order ◽

Coefficient Alpha ◽

Latent Variable Modeling ◽

Order Structure ◽

Measuring Instruments ◽

Structure Evaluation

A readily applicable procedure is discussed that allows evaluation of the discrepancy between the popular coefficient alpha and the reliability coefficient of a scale with second-order factorial structure that is frequently of relevance in empirical educational and psychological research. The approach is developed within the framework of the widely used latent variable modeling methodology and permits point and interval estimation of the slippage of alpha from scale reliability in a population under investigation. The method is useful when examining the consistency of complex structure measuring instruments assessing higher order latent constructs and, under its assumptions, represents a generally recommendable alternative to coefficient alpha. The outlined procedure is illustrated using data from an authoritarianism study.

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Examining Population Differences in Within-Person Variability in Longitudinal Designs Using Latent Variable Modeling: An Application to the Study of Cognitive Functioning of Older Adults

Educational and Psychological Measurement ◽

10.1177/0013164418758834 ◽

2018 ◽

Vol 79 (3) ◽

pp. 598-609 ◽

Cited By ~ 1

Author(s):

N. Maritza Dowling ◽

Tenko Raykov ◽

George A. Marcoulides

Keyword(s):

Repeated Measures ◽

Latent Variable ◽

Cognitive Test ◽

Latent Variable Modeling ◽

Population Differences ◽

Modeling Framework ◽

Interval Estimates ◽

Modeling Methodology ◽

Multiple Dimensions ◽

Verbal Episodic Memory

Longitudinal studies have steadily grown in popularity across the educational and behavioral sciences, particularly with the increased availability of technological devices that allow the easy collection of repeated measures on multiple dimensions of substantive relevance. This article discusses a procedure that can be used to evaluate population differences in within-person (intraindividual) variability in such longitudinal investigations. The method is based on an application of the latent variable modeling methodology within a two-level modeling framework. The approach is used to obtain point and interval estimates of the differences in within-person variance and in the strength of correlative effects of repeated measures between normal and very mildly demented persons in a longitudinal study of a diagnostic cognitive test assessing verbal episodic memory.

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Examining Validity-Related Correlations and Their Differences Under Assumption Violations

Educational and Psychological Measurement ◽

10.1177/0013164418822703 ◽

2019 ◽

Vol 80 (2) ◽

pp. 389-398

Author(s):

Tenko Raykov ◽

Abdullah A. Al-Qataee ◽

Dimiter M. Dimitrov

Keyword(s):

Latent Variable ◽

Social Research ◽

Tertiary Education ◽

Model Fitting ◽

Interval Estimation ◽

Missing At Random ◽

Entrance Examination ◽

Data Sets ◽

Modeling Methodology ◽

Not Missing At Random

A procedure for evaluation of validity related coefficients and their differences is discussed, which is applicable when one or more frequently used assumptions in empirical educational, behavioral and social research are violated. The method is developed within the framework of the latent variable modeling methodology and accomplishes point and interval estimation of convergent and discriminant correlations as well as differences between them in cases of incomplete data sets with data not missing at random, nonnormality, and clustering effects. The procedure uses the full information maximum likelihood approach to model fitting and parameter estimation, does not assume availability of multiple indicators for underlying latent constructs, includes auxiliary variables, and accounts for within-group correlations on main response variables resulting from nesting effects involving studied respondents. The outlined procedure is illustrated on empirical data from a study using tertiary education entrance examination measures.

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Relationship between seaweeds consumption and hyperuricaemia in general adults: a Population-based study from the Tianjin Chronic Low-grade Systemic Inflammation and Health (TCLSIH) cohort study

British Journal Of Nutrition ◽

10.1017/s0007114521000891 ◽

2021 ◽

pp. 1-8

Author(s):

Tingjing Zhang ◽

Yawen Wang ◽

Yeqing Gu ◽

Ge Meng ◽

Qing Zhang ◽

...

Keyword(s):

Uric Acid ◽

Large Scale ◽

Adult Population ◽

Multiple Logistic Regression Analysis ◽

Population Based ◽

Biologically Active ◽

Low Grade ◽

Cross Sectional ◽

Level 3 ◽

Level 2

Abstract Seaweeds have numerous biologically active ingredients, such as polysaccharides, polyphenols and carotenoids, that are beneficial to human health. Although these benefits might be related to the synthesis, secretion or reabsorption of uric acid, no studies have explored the relationship between seaweeds consumption and hyperuricaemia (HUA) in the general population. The aim of this study was to investigate whether seaweeds consumption is related to HUA in a large-scale adult population. A cross-sectional study was conducted with 32 365 adults (17 328 men and 15 037 women) in Tianjin, People’s Republic of China. Frequency of seaweeds consumption was assessed by a validated self-administered FFQ. HUA was defined as serum uric acid levels >420 μmol/L in men and >350 μmol/L in women. The association between seaweeds consumption and HUA was assessed by multiple logistic regression analysis. Restricted cubic spline functions were used for non-linearity tests. The prevalence of HUA in men and women was 21·17 % and 5·93 %, respectively. After adjustments for potential confounding factors, the OR (95 % CI) for HUA across seaweed consumption (g/1000 kcal per d) were 1·00 (reference) for level 1, 0·91 (95 % CI 0·81, 1·02) for level 2; 0·90 (95 % CI 0·81, 1·01) for level 3; 0·86 (95 % CI 0·78, 0·97) for level 4 in men and 0·90 (95 % CI 0·73, 1·10) for level 2; 0·82 (95 % CI 0·67, 1·00) for level 3; 0·84 (95 % CI 0·68, 1·03) for level 4 in women, respectively. A negative correlation between seaweeds consumption and HUA in males but not in females was observed. Further studies are needed to explore the causal relationship.

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Evaluation of Variance Inflation Factors in Regression Models Using Latent Variable Modeling Methods

Educational and Psychological Measurement ◽

10.1177/0013164418817803 ◽

2018 ◽

Vol 79 (5) ◽

pp. 874-882 ◽

Cited By ~ 7

Author(s):

Katerina M. Marcoulides ◽

Tenko Raykov

Keyword(s):

Latent Variable ◽

Regression Models ◽

Interval Estimation ◽

Latent Variable Modeling ◽

Linear Regression Models ◽

Interval Estimates ◽

Explanatory Variables ◽

Modeling Methods ◽

Modeling Software ◽

Tolerance Indices

A procedure that can be used to evaluate the variance inflation factors and tolerance indices in linear regression models is discussed. The method permits both point and interval estimation of these factors and indices associated with explanatory variables considered for inclusion in a regression model. The approach makes use of popular latent variable modeling software to obtain these point and interval estimates. The procedure allows more informed evaluation of these quantities when addressing multicollinearity-related issues in empirical research using regression models. The method is illustrated on an empirical example using the popular software M plus. Results of a simulation study investigating the capabilities of the procedure are also presented.

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