Longitudinal Quantile Regression Research Articles

A prospective study of sedentary behavior and changes in the body mass index distribution.

We aimed to determine whether baseline sedentary behavior was associated with changes in body mass index (BMI) over 9 yr. Participants were enrolled into the National Institutes of Health American Association of Retired Persons (NIH-AARP) Diet and Health study in 1995-1996 (median age, 63 yr), and BMI was reported at baseline and 9 yr later (n = 158,436). Sitting time (<3 (referent), 3-4, 5-6, 7-8, or ≥9 h·d), television viewing (none, <1, 1-2, 3-4, 5-6, 7-8, or ≥9 h·d), and the covariates (age, sex, race, education, smoking, moderate-to-vigorous physical activity, caloric intake, and sleep duration) were reported at baseline. We used longitudinal quantile regression to model changes at the 10th, 25th, 50th, 75th, and 90th BMI percentiles. More sitting at baseline was associated with additional increases in BMI over time, and the association was stronger at the upper BMI percentiles (e.g., <3 (referent) vs 5-6 h·d of sitting additional increases: 50th percentile = 0.41 kg·m and 95% confidence interval (CI) = 0.34-0.48; 90th percentile = 0.85 kg·m and 95% CI = 0.72-0.98). Similar associations were observed between more television viewing at baseline and additional increases in BMI over time (e.g., no television (referent) vs 3-4 h·d of television: 50th percentile = 1.96 kg·m and 95% CI = 1.77-2.15; 90th percentile = 2.11 kg·m and 95% CI = 1.49-2.73). Reducing sedentary behavior could help prevent an increase in BMI in adulthood especially at the upper percentiles of the BMI distribution and thereby reduce the prevalence of obesity.

Italian Manufacturing and Service Firms Labor Productivity: a Longitudinal Quantile Regression Analysis

Labor productivity is very complex to analyze across time, sectors and countries. In particular, in Italy, labor productivity has shown a prolonged slowdown but sector analyses highlight the presence of specific niches that have good levels of productivity and performance. This paper investigates how firms' characteristics might have affected the dynamics of the Italian service and manufacturing firms labor productivity in recent years (1998-2007), comparing them and focusing on some relevant sectors. We use a micro level original panel from the Italian National Institute of Statistics (ISTAT) and a longitudinal quantile regression approach that allow us to show that labor productivity is highly heterogeneous across sectors and that the links between labor productivity and firms' characteristics are not constant across quantiles. We show that average estimates obtained via GLS do not capture the complex dynamics and heterogeneity of the service and manufacturing firms' labor productivity. Using this approach, we show that innovativeness and human capital, in particular, have a very strong impact on fostering labor productivity of lower productive firms. From the sector analysis on four service' sectors (restaurants & hotels, trade distributors, trade shops and legal & accountants) we show that heterogeneity is more intense at a sector level and we derive some common features that may be useful in terms of policy implications.

Differences in BMI z -Scores between Offspring of Smoking and Nonsmoking Mothers: A Longitudinal Study of German Children from Birth through 14 Years of Age

Background: Children of mothers who smoked during pregnancy have a lower birth weight but have a higher chance to become overweight during childhood.Objectives: We followed children longitudinally to assess the age when higher body mass index (BMI) z-scores became evident in the children of mothers who smoked during pregnancy, and to evaluate the trajectory of changes until adolescence.Methods: We pooled data from two German cohort studies that included repeated anthropometric measurements until 14 years of age and information on smoking during pregnancy and other risk factors for overweight. We used longitudinal quantile regression to estimate age- and sex-specific associations between maternal smoking and the 10th, 25th, 50th, 75th, and 90th quantiles of the BMI z-score distribution in study participants from birth through 14 years of age, adjusted for potential confounders. We used additive mixed models to estimate associations with mean BMI z-scores.Results: Mean and median (50th quantile) BMI z-scores at birth were smaller in the children of mothers who smoked during pregnancy compared with children of nonsmoking mothers, but BMI z-scores were significantly associated with maternal smoking beginning at the age of 4–5 years, and differences increased over time. For example, the difference in the median BMI z-score between the daughters of smokers versus nonsmokers was 0.12 (95% CI: 0.01, 0.21) at 5 years, and 0.30 (95% CI: 0.08, 0.39) at 14 years of age. For lower BMI z-score quantiles, the association with smoking was more pronounced in girls, whereas in boys the association was more pronounced for higher BMI z-score quantiles.Conclusions: A clear difference in BMI z-score (mean and median) between children of smoking and nonsmoking mothers emerged at 4–5 years of age. The shape and size of age-specific effect estimates for maternal smoking during pregnancy varied by age and sex across the BMI z-score distribution.Citation: Riedel C, Fenske N, Müller MJ, Plachta-Danielzik S, Keil T, Grabenhenrich L, von Kries R. 2014. Differences in BMI z-scores between offspring of smoking and nonsmoking mothers: a longitudinal study of German children from birth through 14 years of age. Environ Health Perspect 122:761–767; http://dx.doi.org/10.1289/ehp.1307139

Trends of body mass index among children and adolescents in China, 1997‐2011 (621.3)

This study is to analyze the association between energy intake and physical activity and changes in body mass index (BMI) among Chinese children and adolescents. We used a subsample of 2,814 participants aged 2‐18 years old from the China Health and Nutrition Survey (CHNS) who had anthropometric data and physical activity data measured at least twice in 1997 – 2011. We used longitudinal quantile regression to investigate changes in BMI over time and IOTF references to define overweight and obesity. The prevalence of overweight and obesity increased by 9.8% among boys and 5.8% among girls during this study period. BMI increased more in higher percentiles than in lower percentiles. An addition of 100 kilocalories per day would increase BMI by 0.02 kg/m2 among boys and 0.03 kg/m2 BMI among girls. An addition of 1 metabolic equivalent task (MET) per hour would decrease BMI by 0.12 kg/m2 (95% CI: 0.006 – 0.24) among girls but no effects among boys. This study may shed insights into preventing and controlling overweight and obesity among children and adolescents.This study was supported by NIH (R01‐HD30880) and Fogarty International Center, NIH (5D43TW007709).Grant Funding Source: NIH

Greater screen time is associated with adolescent obesity: A longitudinal study of the BMI distribution from Ages 14 to 18

Previous research has examined the association between screen time and average changes in adolescent body mass index (BMI). Until now, no study has evaluated the longitudinal relationship between screen time and changes in the BMI distribution across mid to late adolescence. Participants (n=1,336) were adolescents who were followed from age 14 to age 18 and surveyed every six months. Time spent watching television/videos and playing video games was self-reported (<1hr/d, 1hr/d, 2hrs/d, 3hrs/d, 4hrs/d, or 5+hrs/d). BMI (kg/m2) was calculated from self-reported height and weight. Longitudinal quantile regression was used to model the 10th, 25th, 50th, 75th and 90th BMI percentiles as dependent variables. Study wave and screen time were the main predictors, and adjustment was made for gender, race, maternal education, hours of sleep and physical activity. We observed increases at all the BMI percentiles over time, with the greatest increase at the 90th BMI percentile. Screen time was positively associated with changes in BMI at the 50th (0.17, 95% CI: 0.06, 0.27), 75th (0.31, 95% CI: 0.10, 0.52) and 90th BMI percentiles (0.56, 95% CI: 0.27, 0.82). No associations were observed between screen time and changes at the 10th and 25th BMI percentiles. We observed positive associations between screen time and changes in the BMI at the upper tail of the BMI distribution. Therefore lowering screen time, especially among overweight and obese adolescents, could contribute to reducing the prevalence of adolescent obesity.

Moderate‐To‐vigorous physical activity is associated with decreases in body mass index from ages 9 to 15 years

The purpose of this study is to determine whether time spent in objectively measured physical activity is associated with change in body mass index (BMI) from ages 9 to 15. The participants were enrolled in the National Institute of Child Health and Human Development Study of Early Child Care and Youth Development (n = 938). At ages 9, 11, 12, and 15 the time spent in moderate-to-vigorous physical activity (MVPA) was objectively measured, and BMI was calculated (kg/m(2) ). Longitudinal quantile regression was used to analyze the data. The 10th, 25th, 50th, 75th, and 90th BMI percentiles were modeled as the dependent variables with age and MVPA (h/day) modeled as predictors. Adjustment was also made for gender, race, sleep, healthy eating score, maternal education, and sedentary behavior. A negative association between MVPA and change in BMI was observed at the 90th BMI percentile (-3.57, 95% CI -5.15 to -1.99 kg/m(2) per hour of MVPA). The negative association between time spent in MVPA and change in BMI was progressively weaker toward the 10th BMI percentile (-0.27, 95% CI -0.62 to 0.07 kg/m(2) per hour of MVPA). The associations remained similar after adjusting for the covariates, and when the analyses were stratified by gender. Time spent in MVPA was negatively associated with change in BMI from age 9 to 15. The association was strongest at the upper tail of the BMI distribution, and increasing time spent in MVPA could help reduce the prevalence of childhood obesity.

Changes in cardiovascular disease risk factors from age 9 to 19 and the influence of television viewing

The purpose of this study was to determine if time spent watching television is associated with changes in cardiovascular disease (CVD) risk factors from age 9 to 19. Participants were girls enrolled in the NHLBI Growth and Health Study (n = 1,702), and CVD risk factors were measured at ages 10, 12, 14, 16, and 19. Longitudinal quantile regression was used to determine if television viewing was associated with changes in CVD risk factors over time at the 10th, 25th, 50th, 75th, and 90th percentiles of the CVD risk factors. In black girls, television viewing (h/wk) was positively associated with sum of skinfolds (mm) at the 75th (0.22, 99% CI, 0.06-0.38) and 90th percentiles (0.21, 99% CI, 0.05-0.36), but not at the 10th, 25th, or 50th percentiles. In white girls, television viewing (h/wk) was positively associated with sum of skinfolds (mm) with the strength of the associations progressively stronger toward the upper tail of the skinfold distribution, adjusting for physical activity and other covariates (10th percentile: 0.08, 99% CI, 0.03-0.13; 90th percentile: 0.42, 99% CI, 0.24-0.59). All associations were adjusted for physical activity, dietary factors, sleep, and maturation. No associations were observed between television viewing and changes in systolic blood pressure, triglycerides, or cholesterol levels in black or white girls. Girls who spent more time watching television had greater increases in sum of skinfolds from age 9 to 19, independent of physical activity levels and other covariates. The associations observed were stronger at the upper tail of the skinfold distribution.

Boosting Structured Additive Quantile Regression for Longitudinal Childhood Obesity Data

Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

Screen-based sedentary behavior and cardiorespiratory fitness from age 11 to 13.

The study's purpose was to determine whether time spent in screen-based sedentary behavior is associated with change in cardiorespiratory fitness (CRF) levels in children from age 11 to 13, adjusting for vigorous physical activity (VPA). Participants were children (n = 2097) enrolled in the control arm of the HEALTHY Study, who performed 20-m shuttle run tests at ages 11 and 13. Self-reported screen time was used as a measure of sedentary behavior. Longitudinal quantile regression was used to model the influence of predictors on changes at the 10th, 25th, 50th, 75th, and 90th shuttle run lap percentiles. Screen time (h·d(-1)) was the main predictor, and adjustment was also made for VPA, body mass index, and household education. In boys, more screen time was associated with fewer shuttle run laps completed from age 11 to 13 at the 25th, 50th, and 75th shuttle run lap percentiles; the strongest association was at the 75th shuttle run percentile (-0.57, 95% confidence interval = -0.93 to -0.21). In girls, more screen time was associated with fewer shuttle run laps completed from age 11 to 13 at the 50th, 75th, and 90th shuttle run lap percentiles; the strongest association was at the 90th shuttle run percentile (-0.65, -1.01 to -0.30). Borderline negative associations were found between screen time and shuttle run laps at the 10th shuttle run percentile in boys and girls (-0.28, -0.57 to 0.01, and -0.17, -0.41 to 0.06, respectively). More screen time was associated with lower CRF from age 11 to 13, independent of VPA. However, the association was weakest at the lower tail of the CRF distribution.

FAST FOOD PRICES AND ADULT BODY WEIGHT OUTCOMES: EVIDENCE BASED ON LONGITUDINAL QUANTILE REGRESSION MODELS

With a parallel increase in the consumption of food away from home, particularly fast food, and the obesity prevalence in the United States, evidence on the potential effectiveness of fiscal pricing policies to curb obesity is needed. We estimate changes in the dispersion of the entire conditional distribution of body mass index (BMI) associated with changes in fast food prices for adults using the National Longitudinal Survey of Youth 1979 in cross‐sectional and longitudinal quantile regression models. We find that the ordinary least squares estimate for men underestimates the negative relationship of fast food prices with BMI at the 50th and upper quantiles in cross‐sectional models although the statistical significance disappears in the longitudinal individual fixed effects quantile regression. Among subpopulations, we find that a 10% increase in the price of fast food is associated with 0.9% and 0.7% lower BMI for low‐income women and women with any children, respectively, at the 90th quantile in a longitudinal individual fixed effects model. Our results imply that fiscal pricing policies such as fast food taxes might have a greater impact on the weight outcomes of low‐income women or women with children in the upper tail of the conditional BMI distribution (JEL I00, I19).

Time spent in sedentary behavior and changes in childhood BMI: a longitudinal study from ages 9 to 15 years

To determine if time spent in objectively measured sedentary behavior is associated with a change in body mass index (BMI) between ages 9 and 15 years, adjusting for moderate-to-vigorous physical activity (MVPA). Prospective observational study of children at ages 9 (2000), 11 (2002), 12 (2003) and 15 years (2006). Longitudinal quantile regression was used to model the influence of predictors on changes at the 10th, 25th, 50th, 75th and 90th BMI percentiles over time. Participants were enrolled in the National Institute of Child Health and Human Development (NICHD) Study of Early Child Care and Youth Development and include both boys and girls (n=789). Objectively measured BMI (kg m(-2)) was the outcome variable and objectively measured sedentary behavior was the main predictor. Adjustment was also made for MVPA, gender, race, maternal education, hours of sleep and healthy eating index. Increases in BMI were observed at all percentiles, with the greatest increase observed at the 90th BMI percentile. Spending more time in sedentary behavior (h per day) was associated with additional increases in BMI at the 90th, 75th and 50th BMI percentiles, independent of MVPA and the other covariates (90th percentile=0.59, 95% confidence interval (95% CI): 0.19-0.98 kg m(-2); 75th percentile=0.48, 95% CI: 0.25-0.72 kg m(-2); and 50th percentile=0.19, 95% CI: 0.05-0.33 kg m(-2)). No associations were observed between sedentary behavior and changes at the 25th and 10th BMI percentiles. Sedentary behavior was associated with greater increases in BMI at the 90th, 75th and 50th BMI percentiles between ages 9 and 15 years, independent of MVPA. Preventing an increase in sedentary behavior from childhood to adolescence may contribute to reducing the number of children classified as obese.

Long-tail longitudinal modeling of insurance company expenses

The insurance industry is known to have high operating expenses in the financial services sector. Insurers, investors and regulators are interested in models to understand the behavior of expenses. However, the current practice ignores skewness, occasional negative values as well as their temporal dependence. Addressing these three features, this paper develops a longitudinal model of insurance company expenses that can be used for prediction, to identify unusual behavior, and to measure firm efficiency. Specifically, we use a three-parameter asymmetric Laplace density for the marginal distribution of insurers’ expenses in each year. Copula functions are employed to accommodate their temporal dependence. As a function of explanatory variables, the location parameter allows us to analyze an insurer’s expenses in light of the firm’s characteristics. Our model can be interpreted as a longitudinal quantile regression. The analysis is performed using property–casualty insurance company data from the National Association of Insurance Commissioners of years 2001–2006. Due to the long-tailed nature of insurers’ expenses, two alternative approaches are proposed to improve the performance of the longitudinal quantile regression model: rescaling and transformation. Predictive densities are derived that allow one to compare the predictions for individual insurers in a hold-out-sample. Both predictive models are shown to be reasonable with the rescaling method outperforming the transformation method. Compared with standard longitudinal models, our model is shown to be superior in identifying insurers’ unusual behavior.