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However, at baseline, high CRS were associated with high adiposity in each sex group. This cross-sectional association is insufficient to establish a long-term causal link between restrained eating and adiposity.

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The most likely explanation is that this association is confounded by some subjects' propensity to easily gain weight and their efforts to counterbalance this tendency through restrained eating. Accordingly, the longitudinal part of the model showed that, adjusting for baseline CRS, subjects with a high initial adiposity had a larger CRS increase during the 2-year follow-up than the others. The direct effect of baseline CRS on adiposity change was not significant for either sex, and of opposing signs for males and females.

The indirect effect through baseline adiposity is difficult to interpret because it relies on the strongly confounded cross-sectional association.

Latent Variable Models An Introduction to Factor, Path, and Structural Equation Analysis Latent Vari

In any case, its estimates were negative for females Finally, the longitudinal effect of baseline CRS, free of the cross-sectional confounding factors, is the sum of the direct effect and of the indirect effect through CRS change. The effect observed for males was found significantly positive, however we considered that the direct effect of CRS on adiposity change adjusted for CRS change provide the best measurement of the effect of CRS on adiposity change. The indirect effect through CRS change is at least partly due to the regression to the mean the expected negative relationships between baseline CRS and CRS change and to the physiologic effect of CRS change on adiposity change.

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The relationships observed between each baseline value and its change were negative, as expected, although only three of them were significant, probably because of limited statistical power. Cross-sectional studies have shown that restrained eating is frequent in those with high adiposity [ 18 — 20 ]. The results of prospective studies are more controversial. Higher restraint scores were associated with better weight maintenance after weight loss [ 21 ] or weight gain [ 22 ] prevention intervention. In the general population, Drapeau et al [ 23 ] found that initial restrained eating was related to subsequent weight gain positively in women but negatively in men, which is the opposite of our results.

Hays et al [ 24 ] found that restraint was protective against weight gain only in women with high levels of disinhibition. That latter study was retrospective and self-reporting of past body weight may have biased past relationships. In adults with a familial history of obesity, non-obese women with the highest CRS were those who had been obese in childhood or adolescence, suggesting a beneficial effect of cognitive restriction for weight control in these women [ 25 ].

This latent variable and structural equation model enabled us to present synthetic results rather than four separate analyses for each sex group and to perform a detailed analysis of the causal mechanisms involved.

It confirmed our previous observations; in the general population, restrained eating appears to be more of an adaptive response of subjects prone to gaining weight than a risk factor for increased fat mass. Each arrow in the diagramed model Figure 1 has an equation counterpart. The measurement model specifies the relationships between the two latent variables and their four indicators, displayed on the lower part of the diagram; it is expressed with the following equations:.

Note that, in agreement with the assumptions used in our analysis, the same four loadings are used for both latent variables.

[PDF Download] Latent Variable Models: An Introduction to Factor Path and Structural Analysis

A consequence of this constraint is that the model can be reparameterized as. This is the model and the parameterization used in the article. As a result, latent adiposity is arbitrarily expressed on the same measurement scale as percent body fat. Because the latent variable indicators are measured on various scales, it is useful to consider standardized estimates rather than raw loadings, using the observed standard deviations as measurement units for latent and manifest variables, namely. The structural model specifies all the relationships between the explanatory variables and the outcomes of interest, displayed on the upper part of the diagram; it is expressed with.

To simplify the equations, we centered all observed variables, so that intercepts no longer appear. Bollen KA: Structural equations with latent variables. Kaplan D: Structural equation modeling. Am J Epidemiol. Ann Epidemiol. Int J Epidemiol. Kaaks R, Ferrari P: Dietary intake assessments in epidemiology: can we know what we are measuring?. Singh-Manoux A, Clarke P, Marmot M: Multiple measures of socio-economic position and psychosocial health: proximal and distal measures.

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Am J Clin Nutr. J Pers. J Nutr. Bentler P, Bonett D: Significance tests and goodness of fit in the analysis of covariance structures. Psychological Bulletin. Cribbie RA, Jamieson J: Structural equation models and the regression bias for measuring correlates of change.

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Educ and Psychol Measurement. Meth Psychol Res Online. Shunk JA, Birch LL: Girls at risk for overweight at age 5 are at risk for dietary restraint, disinhibited overeating, weight concerns, and greater weight gain from 5 to 9 years. J Am Diet Assoc. Obes Res.

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Obesity Silver Spring. Results from the Quebec Family Study. Download references. All these funding sources were devoted to data collection, and did not interfere with analysis and interpretation of data, the writing of the manuscript or the decision to submit the manuscript for publication.

Correspondence to Michel Chavance. SE and MC developed the model, performed all statistical analyses and participated to article writing. All authors approved the final manuscript. This article is published under license to BioMed Central Ltd. Reprints and Permissions. Search all BMC articles Search. Abstract Background The use of structural equation modeling and latent variables remains uncommon in epidemiology despite its potential usefulness. Methods Using data from a longitudinal community-based study, we fitted structural equation models including two latent variables respectively baseline adiposity and adiposity change after 2 years of follow-up , each being defined, by the four following anthropometric measurement respectively by their changes : body mass index, waist circumference, skinfold thickness and percent body fat.

Results We found that high baseline adiposity was associated with a 2-year increase of the cognitive restraint score and no convincing relationship between baseline cognitive restraint and 2-year adiposity change could be established. Conclusions The latent variable modeling approach enabled presentation of synthetic results rather than separate regression models and detailed analysis of the causal effects of interest.

Open Peer Review reports. Background Structural equation and latent variable models [ 1 , 2 ] have previously been used in several fields of epidemiology. Latent variables and structural equation modeling We briefly recall here the principle of this approach. Fitted model To validate the use of a latent variable approach, we fitted preliminary latent variable models to the four baseline anthropometric measurements BMI, waist circumference, sum of skinfolds, percent body fat to create a measurement model, as only one latent variable and its four manifest variables assessments are considered.

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Figure 1. Full size image.

Results General characteristics of the dataset Characteristics of the sample are shown in Table 1. Table 1 Characteristic of the Studied Population Full size table. Various GoodnessofFit Indices. Phantom Variables. Data Matrix for Thurstones Box Problem. Table of Chi Square. Noncentral Chi Square for Estimating Power. Power of a test of poor fit and sample sizes needed for powers of 80 and Answers to Exercises.

Additional Product Features Dewey Edition. Contents: Preface. Fitting Path Models. Exploratory Factor Analysis--Basics. Exploratory Factor Analysis--Elaborations. Issues in the Application of Latent Variable Analysis. Show More Show Less. Any Condition Any Condition. Compare similar products. You Are Viewing. Trending Price New. People who bought this also bought.