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Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, M plus , is also featured and provides researchers with a flexible tool to analyze their data with an easy-to-use interface and graphical displays of data and analysis results.

By following the examples provided in this book, readers will be able to build their own SEM models using M plus.

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Teachers, graduate students, and researchers in social sciences and health studies will also benefit from this book. Jichuan Wang , Xiaoqian Wang. Key features: Presents a useful reference guide for applications of SEM whilst systematically demonstrating various advanced SEM models, such as multi-group and mixture models using M plus. Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes.

Provides step-by-step instructions of model specification and estimation, as well as detail interpretation of M plus results. We conducted a cross-sectional study with 5, mothers and their newborns using a Brazilian birth cohort study. In the proposed model, estimated by structural equation modeling, we tested socioeconomic status, age, marital status, pre-pregnancy body mass index, smoking habit and alcohol consumption during pregnancy, hypertension and gestational diabetes, gestational weight gain, and type of delivery as determinants of the baby's birth weight.

A 6 kg increase 1 SD in gestational weight gain represented a 0. The effect of gestational weight gain on the increase in birth weight was greater than that of pre-pregnancy body mass index. Birth weight is an indicator of perinatal risk and has been used in epidemiological studies as a representation of fetal nutritional exposure.

Structural equation modeling with Mplus : applications using Mplus

A secular trend toward increased birth weight related to greater maternal weight has been observed in developed countries 18 Scientific Advisory Committee on Nutrition. The influence of maternal, fetal and child nutrition on the development of chronic disease in later life. London: The Stationery Office; Birth weight reflects the conditions of pregnancy and influences the quality of life, the growth, and the development of the child, as well as childhood morbidity and mortality 22 Stang J, Huffman LG. Position of the Academy of Nutrition and Dietetics: obesity, reproduction, and pregnancy outcomes.

J Acad Nutr Diet. Particularly important among the factors that influence birth weight are the pre-pregnancy and gestational inadequacies of the maternal nutritional status 20 A systematic review of outcomes of maternal weight gain according to the Institute of Medicine recommendations: birthweight, fetal growth, and postpartum weight retention. Am J Obstet Gynecol. Plos One.

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Pre-pregnancy overweight and obesity have been associated with gestational hypertension and diabetes, preterm birth, cesarean delivery, and low or high birth weight 22 In turn, a low pre-pregnancy body mass index BMI has been associated with low birth weight and preterm birth 22 A systematic meta-analysis of 45 studies has revealed that low pre-pregnancy BMI increases the risk of infants born small for gestational age with low birth weight, while high pre-pregnancy BMI increases the risk of infants born large for gestational age with high birth weight, macrosomia, and future overweight or obesity 27 A systematic review of 35 studies has detected strong evidence that excessive gestational weight gain is associated with increased newborn weight large for gestational age and that inadequate gestational weight gain is a risk factor for a lower birth weight and for small for gestational age infants 20 An Argentinian study with 9, neonates using multiple forward stepwise linear regression models has shown that lower pre-pregnancy BMI was associated with lower birth weight, with no influence of gestational weight gain on birth weight outcome 9 9.

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Structural Equation Modeling: what is it and what can we use it for? (part 1 of 6)

Arch Latinoam Nutr. Despite the results showing association of pre-pregnancy BMI and weight gain during pregnancy with birth weight, these studies have not investigated whether weight gain during pregnancy is a mediator of the association between pre-pregnancy BMI and birth weight 20 Furthermore, most of these studies have used logistic regression analysis with simultaneous adjustment of multiple confounders 9 9. This type of statistical analysis has been criticized in the literature since it only allows the investigation of associations between the explanatory variables and the outcome, without the possibility of assessing the direct and indirect effects and identifying mediating variables 12 Kline RB.

Principles and practice of structural equation modeling. New York: Guilford Press; Methodology in the Social Sciences. Wang J, Wang X. Structural equation modeling: applications using Mplus. Noida: Thomson Digital; Wiley Series in Probability and Statistics. From this perspective, the objective of this study was to respond to the following questions: Is there an association of pre-pregnancy maternal BMI and gestational weight gain with birth weight? Which of the two associations is of greater magnitude? Are these effects direct or do they occur by means of mediators?

Is gestational weight gain a mediator of the association between maternal pre-pregnancy BMI and birth weight?


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The method has been detailed elsewhere 21 Cad SaudePublica. The sample was stratified according to maternity hospital with division proportional to the number of deliveries and was systematic at each maternity. A total of 21, births occurred at the maternity hospitals investigated, one third of which were systematically selected from an ordered list of births by hour of occurrence, corresponding to 7, births.

Of these, 5, involved families residing in the municipality for the last three months and therefore eligible for the study. We chose to remove puerperae who showed three standard deviations SD of total weight gain above or below the mean Thus, the final study sample consisted of 5, births. The puerperae were preferentially interviewed during the first 24 hours after delivery. The interviewers used a standardized questionnaire and, after obtaining written informed consent, read the questions to the puerperae in order to ensure uniform questions.

Information about the newborns was then obtained from the mothers and from the medical records. The infants were weighed on digital baby scales with 5 g graduations. The infants were weighed wearing no clothing and, if they were crying, their weight was obtained during a deep inspiration. The mothers self-reported their pre-pregnancy weight, weight at the end of pregnancy, and height. All instruments were calibrated regularly using standard measurements. Premature babies or babies in poor condition at birth, who could not be weighed and measured soon after birth, were reevaluated as soon as their clinical condition allowed.

In the theoretical model proposed, socioeconomic status SES was a latent variable that occupied the distal-most position and determined the demographic and nutritional characteristics of the pregnant women, as well as their morbidities, life habits, and type of delivery, which led to the birth weight of their newborns Figure. The instrument used to measure economic class was the Brazilian Criteria of Economic Classification created by the Brazilian Association of Research Enterprises ABEP , which considers the ownership of goods and the schooling of the family head 2 2.

The economic classes A-B are the more affluent and the D-E classes are the less privileged. The explanatory variables were pre-pregnancy BMI and gestational weight gain. Pre-pregnancy BMI was determined by dividing the pre-pregnancy weight kg by height squared m , treated in a continuous manner in the model. Gestational weight gain was calculated as the difference between weight at the end of pregnancy and weight before pregnancy. This variable was used in a continuous manner in the model. The remaining maternal variables analyzed were maternal age treated as a continuous numerical variable , marital situation without a partner, consensual union, or married , smoking during pregnancy yes or no , alcohol intake during pregnancy yes or no , type of delivery vaginal or cesarean , arterial hypertension during pregnancy yes or no , and gestational diabetes yes or no , with the last two being self-reported based on the information provided by a physician during prenatal care.

The dependent variable was newborn weight, treated as a continuous numerical variable. Structural equation modeling was used to investigate the association of pre-pregnancy BMI and gestational weight gain with the covariables and their effects on birth weight. This modeling has the advantage of simultaneously handling multiple dependence relationships and it can represent concepts that are not observed latent variables in these relationships, modeling the error of measurement in the estimate process 10 Porto Alegre: Bookman; According to the proposed theory, SES, marital situation mari , maternal age wage , pre-pregnancy BMI bmi , systemic arterial hypertension hypertg , gestational diabetes diabg , smoking smok , alcohol intake alc , total gestational weight gain wgain , and type of delivery delivery would have a direct effect on birth weight bweight.

In addition, the indirect pathways were proposed starting from SES, maternal age, pre-pregnancy BMI, systemic arterial hypertension, gestational diabetes, smoking, alcohol intake, and gestational weight gain via type of delivery in order to reach the outcome. We analyzed statistically the data using the Mplus software, version 7. We used the weighted least squares mean and variance adjusted WLSMV estimation for continuous and categorical variables. We also used the theta parametrization. Data regarding some variables were missing data considered to be ignored in the descriptive analysis , especially pre-pregnancy BMI.

However, the WLSMV method for estimation allowed us to the imput these data based on the variables that preceded them in the theoretical model, using frequency analysis and Bayesian analysis 14 Mplus: statistical analysis with latent variables: user's guide. Version 6. We considered the following adjustment indices to determine whether the model showed goof fit: a p-value p higher than 0. Wiley Series in Probability and Statistics , c values higher than 0. In the analyses of the standardized estimates for the construction of the latent variable, we considered a factor load of more than 0.

When the proposed modifications were considered to be plausible from a theoretical viewpoint, a new model was elaborated and analyzed if the value of the modification index was higher than 10 25 Total, direct, and indirect effects of the latent variable and of the observed variables were assessed in the final model. The mean and SD of the continuous variables were calculated to facilitate the interpretation of the results. The results of the descriptive analysis are presented in Table 1. It is important to note that mean pre-pregnancy BMI was The latent variable SES formed a good construct with all indicators having a load factor higher than 0.


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The standardized coefficients of the total and direct effect of indicator and latent variables on birth weight are listed in Table 3. The total direct and indirect effects of pre-pregnancy BMI and weight gain during pregnancy on birth weight can be seen in Table 4. Pre-pregnancy BMI had positive total and direct effects, revealing that there was an increase of 0. Pre-pregnancy BMI also had an indirect and negative effect on birth weight mainly from a gain in gestational weight and on arterial hypertension during pregnancy.

There was a negative association between pre-pregnancy BMI and total weight gain at the end of pregnancy and a positive association between pre-pregnancy BMI and hypertension during pregnancy Table 4. Weight gain at the end of pregnancy had a positive total effect and a positive direct effect.

For each increase of 1 SD in maternal weight gain during pregnancy 6 kg , there was a 0. Route of delivery also had a small positive indirect effect on weight gain Table 4. In this study, higher pre-pregnancy BMI values increase birth weight. The positive effect of weight gain during pregnancy was higher than that of pre-pregnancy BMI.