LMS Regression Research Articles

Long Jump, Vertical Jump, and Vertical Jump Power Reference Curves for 10-18 Year Olds

ABSTRACT We developed age- and sex-specific smoothed percentiles for vertical and long jump, as well as vertical jump power, in healthy 10–18 year olds (n = 529, 47.1% female). Jump height and distance were measured and vertical jump power was assessed via mechanography. LMS regression was used to create smoothed age-specific reference curves, separated by sex. Pearson correlations between the jumps ranged from r = 0.22 to 0.64, varying by age and sex. Comparing medians, younger males had slightly higher values for vertical and long jump compared to females. Vertical jump power was more comparable between the sexes. For all measures, differences between the sexes become more pronounced at ages associated with the transition into adolescence. Growth model coefficients are reported for calculation of Z-scores. The growth curves can be used to compare samples, track lower body power, and link tests of fitness to athletic performance or health-related outcomes.

Comparing Spirometric Reference Values From Childhood to Old Age Estimated by LMS and Linear Regression Models

BackgroundProper reference values for lung function testing are essential for achieving adequate interpretations. The LMS procedure (lambda, mu, sigma) permits continuous analyses of entire populations avoiding gaps in the transition between childhood and adulthood. It also allows more precise calculations of average values, dispersion, and 5th percentiles, which are usually considered the lower limit of normality. The objective of this study was to compare our results fitted with the LMS method with standard multiple linear regression, and with those from international Global Lung Function Initiative (GLI) equations. MethodsData from 9835 healthy residents of the metropolitan area of Mexico City aged 8–80 years were compiled from several studies: EMPECE, PLATINO, adult Mexican workers and two unpublished studies. The LMS procedure and multiple linear regression models were fit to obtain reference equations using R software. ResultsResiduals from the LMS models had a median closer to zero, and smaller dispersion than those from the linear model, but differences although statistically significant were very small and of questionable practical relevance. For example, for females and ln(FEV1), median residual was −0.001 with p25 of −0.08 and p75 of 0.08 for LMS, compared with 0.004 (−0.08, 0.09) [p<0.05] for the linear model. Average spirometric values for a given height for our population, were higher than those predicted by the GLI study. ConclusionContinuous reference equations for the Mexican population calculated using the LMS technique showed slightly better fit than linear regression models.

Comparing Spirometric Reference Values From Childhood to Old Age Estimated by LMS and Linear Regression Models

BackgroundProper reference values for lung function testing are essential for achieving adequate interpretations. The LMS procedure (lambda, mu, sigma) permits continuous analyses of entire populations avoiding gaps in the transition between childhood and adulthood. It also allows more precise calculations of average values, dispersion, and 5th percentiles, which are usually considered the lower limit of normality. The objective of this study was to compare our results fitted with the LMS method with standard multiple linear regression, and with those from international Global Lung Function Initiative (GLI) equations. MethodsData from 9835 healthy residents of the metropolitan area of Mexico City aged 8–80 years were compiled from several studies: EMPECE, PLATINO, adult Mexican workers and two unpublished studies. The LMS procedure and multiple linear regression models were fit to obtain reference equations using R software. ResultsResiduals from the LMS models had a median closer to zero, and smaller dispersion than those from the linear model, but differences although statistically significant were very small and of questionable practical relevance. For example, for females and ln(FEV1), median residual was −0.001 with p25 of −0.08 and p75 of 0.08 for LMS, compared with 0.004 (−0.08, 0.09) [p<0.05] for the linear model. Average spirometric values for a given height for our population, were higher than those predicted by the GLI study. ConclusionContinuous reference equations for the Mexican population calculated using the LMS technique showed slightly better fit than linear regression models.

Statistical methodology for constructing gestational age-related charts using cross-sectional and longitudinal data: The INTERGROWTH-21st project as a case study.

Most studies aiming to construct reference or standard charts use a cross‐sectional design, collecting one measurement per participant. Reference or standard charts can also be constructed using a longitudinal design, collecting multiple measurements per participant. The choice of appropriate statistical methodology is important as inaccurate centiles resulting from inferior methods can lead to incorrect judgements about fetal or newborn size, resulting in suboptimal clinical care.Reference or standard centiles should ideally provide the best fit to the data, change smoothly with age (eg, gestational age), use as simple a statistical model as possible without compromising model fit, and allow the computation of Z‐scores from centiles to simplify assessment of individuals and enable comparison with different populations. Significance testing and goodness‐of‐fit statistics are usually used to discriminate between models. However, these methods tend not to be useful when examining large data sets as very small differences are statistically significant even if the models are indistinguishable on actual centile plots. Choosing the best model from amongst many is therefore not trivial. Model choice should not be based on statistical considerations (or tests) alone as sometimes the best model may not necessarily offer the best fit to the raw data across gestational age. In this paper, we describe the most commonly applied methodologies available for the construction of age‐specific reference or standard centiles for cross‐sectional and longitudinal data: Fractional polynomial regression, LMS, LMST, LMSP, and multilevel regression methods. For illustration, we used data from the INTERGROWTH‐21st Project, ie, newborn weight (cross‐sectional) and fetal head circumference (longitudinal) data as examples.

Reference Curves for Field Tests of Musculoskeletal Fitness in U.S. Children and Adolescents: The 2012 NHANES National Youth Fitness Survey.

Laurson, KR, Saint-Maurice, PF, Welk, GJ, and Eisenmann, JC. Reference curves for field tests of musculoskeletal fitness in U.S. children and adolescents: The 2012 NHANES National Youth Fitness Survey. J Strength Cond Res 31(8): 2075-2082, 2017-The purpose of the study was to describe current levels of musculoskeletal fitness (MSF) in U.S. youth by creating nationally representative age-specific and sex-specific growth curves for handgrip strength (including relative and allometrically scaled handgrip), modified pull-ups, and the plank test. Participants in the National Youth Fitness Survey (n = 1,453) were tested on MSF, aerobic capacity (via submaximal treadmill test), and body composition (body mass index [BMI], waist circumference, and skinfolds). Using LMS regression, age-specific and sex-specific smoothed percentile curves of MSF were created and existing percentiles were used to assign age-specific and sex-specific z-scores for aerobic capacity and body composition. Correlation matrices were created to assess the relationships between z-scores on MSF, aerobic capacity, and body composition. At younger ages (3-10 years), boys scored higher than girls for handgrip strength and modified pull-ups, but not for the plank. By ages 13-15, differences between the boys and girls curves were more pronounced, with boys scoring higher on all tests. Correlations between tests of MSF and aerobic capacity were positive and low-to-moderate in strength. Correlations between tests of MSF and body composition were negative, excluding absolute handgrip strength, which was inversely related to other MSF tests and aerobic capacity but positively associated with body composition. The growth curves herein can be used as normative reference values or a starting point for creating health-related criterion reference standards for these tests. Comparisons with prior national surveys of physical fitness indicate that some components of MSF have likely decreased in the United States over time.

Centile values for serum lipids in Colombian adolescents

ObjectiveTo assess age- and sex-specific percentile baseline data for total cholesterol (TC), triglycerides (TG), and high-density lipoprotein cholesterol (HDL-C) in Colombian children and adolescents aged 10–17 years. Patients and methodsA cross-sectional, descriptive study was conducted on 1773 children and adolescents. Each participant underwent a fasting measurement to quantify TC, HDL-C, and TG levels using enzymatic–colorimetric methods. Smoothed age- and sex-specific 5th, 25th, 50th, 75th, 90th and 95th percentile values were derived using LMS regression (Least Mean Square) using the statistical package Growth Analyzer. ResultsOverall, males had lower serum TC and TG levels as compared to females. P95 of TG and TC was higher in males aged 10–14 years as compared to females, while HDL-C levels were similar in both sexes. ConclusionsPercentile values will help classify children and adolescents as compared to other populations based on this health indicator.

Body Fat Percentile Curves for U.S. Children and Adolescents

To date, several studies have been published outlining reference percentiles for BMI in children and adolescents. In contrast, there are limited reference data on percent body fat (%BF) in U.S. youth. The purpose of this study was to derive smoothed percentile curves for %BF in a nationally representative sample of U.S. children and adolescents. Percent fat was derived from the skinfold thicknesses of those aged 5-18 years from three cross-sectional waves of the National Health and Nutrition Examination Survey (NHANES) IV (1999-2000, 2001-2002, and 2003-2004; N=8269). The LMS (L=skewness, M=median, and S=coefficient of variation) regression method was used to create age- and gender-specific smoothed percentile curves of %BF. Growth curves are similar between boys and girls until age 9 years. However, whereas %BF peaks for boys at about age 11 years, it continues to increase for girls throughout adolescence. Median %BF at age 18 years is 17.0% and 27.8% for boys and girls, respectively. Growth charts and LMS values based on a nationally representative sample of U.S. children and adolescents are provided so that future research can identify appropriate cut-off values based on health-related outcomes. These percentiles are based on skinfolds, which are widely available and commonly used. Using %BF instead of BMI may offer additional information in epidemiologic research, fitness assessment, and clinical settings.

Centiles de lípidos séricos en adolescentes de Colombia

To assess age- and sex-specific percentile baseline data for total cholesterol (TC), triglycerides (TG), and high-density lipoprotein cholesterol (HDL-C) in Colombian children and adolescents aged 10 to 17 years.A cross-sectional, descriptive study was conducted on 1,773 children and adolescents. Each participant underwent a fasting measurement to quantify TC, HDL-C, and TG levels using enzymatic-colorimetric methods. Smoothed age- and sex-specific 5(th), 25(th), 50(th), 75(th), 90(th) and 95(th) percentile values where derived using LMS regression (Least Mean Square) using the statistical package Growth Analyzer.Overall, males had lower serum TC and TG levels as compared to females. P95 of TG and TC was higher in males aged 10 to 14 years as compared to females, while HDL-C levels were similar in both sexes.Percentile values will help classify children and adolescents as compared to other populations based on this health indicator.

Age- and Gender-Specific Smoothed Waist Circumference Percentiles for Kuwaiti Adolescents

Objective: To ascertain abdominal obesity prevalence (waist circumference, WC) in adolescents and to develop smoothed WC percentile charts for Kuwaiti adolescents for public health use. Subjects and Methods: A cross-sectional study of 4,219 healthy Kuwaiti male and female secondary school students between the ages of 11–19 years was examined. Adolescents were drawn from all geographical regions of the country, as part of the Kuwait Nutrition Surveillance Program (KNSP). The KNSP consists of yearly data collections of variables, including weights, heights, and WCs and several sociodemographic variables. LMS regression was used to develop smoothed WC percentile curves. The final percentile curves presented are the result of smoothing three age-specific curves, termed lambda (L), mu (M), and sigma (S) for each gender. Results: Between 5.9 and 12.8% of females and 8.0–30.3% males had WC values ≧90th percentile. Moreover, the mean WC of males was consistently higher than those of females at each age and the percent of adolescents who exceed the 90th percentile increased with age in males, but not in females. Conclusion: Mean WC was higher in males than in females at every age. In most cases, two to three times greater percentages of males, compared to females, equaled or exceeded the 90th percentile, a value frequently associated with higher cardiovascular risk. These results indicate the urgent need to reduce abdominal obesity, an important indicator of the metabolic syndrome, in Kuwaiti adolescents.

Waist circumference percentiles for Canadian youth 11-18y of age.

To develop age- and sex-specific waist circumference reference data for Canadian youth. Cross-sectional population survey. 1981 Canada Fitness Survey. Nationally representative sample of 3064 youth (1540 boys and 1524 girls) 11-18 y of age. Waist circumference was measured with a flexible anthropometric tape. Smoothed and weighted 5th, 10th, 25th, 50th, 75th, 90th, and 95th waist circumference percentiles derived from LMS regression. Waist circumference increases with age in both boys and girls, and boys have higher values of waist circumference than girls at every age and percentile level. These reference data can be used to identify youth with an elevated risk of developing obesity-related disorders and can serve as a baseline for future studies of temporal trends in waist circumference. This research was funded by the Heart and Stroke Foundation of Ontario (Grant #T4946).

Least trimmed squares regression, least median squares regression, and mathematical programming

In this paper, we study LTS and LMS regression, two high breakdown regression estimators, from an optimization point of view. We show that LTS regression is a nonlinear optimization problem that can be treated as a concave minimization problem over a polytope. We derive several important properties of the corresponding objective function that can be used to obtain algorithms for the exact solution of LTS regression problems, i.e., to find a global optimum to the problem. Because of today's limited problem-solving capabilities in exact concave minimization, we give an easy-to-implement pivoting algorithm to determine regression parameters corresponding to local optima of the LTS regression problem. For the LMS regression problem, we briefly survey the existing solution methods which are all based on enumeration. We formulate the LMS regression problem as a mixed zero-one linear programming problem which we analyze in depth to obtain theoretical insights required for future algorithmic and computational work.

Regression by least median squares, a methodological contribution to titration analysis

Robust regression by least median squares, LMS, which is able to determine linear tendency provided that at least 50% of the experimental points comply with this tendency, has been applied to data from various titrations. The procedure based on the LMS regression provides an objective criterion for the determination of the end point; it can be reproduced and automated completely, thus contributing to a more versatile titration analysis. Under normal working conditions, concentrations with variation coefficients between 2% and 4% have been determined in amperometric titrations, between 0.5% and 5% in conductometric titrations of strong/weak acid and its mixtures, and around 1.5% in spectrophotometric and potentiometric titrations.

Regression by least median squares, a methodological contribution to titration analysis

Robust regression by least median squares, LMS, which is able to determine linear tendency provided that at least 50% of the experimental points comply with this tendency, has been applied to data from various titrations. The procedure based on the LMS regression provides an objective criterion for the determination of the end point; it can be reproduced and automated completely, thus contributing to a more versatile titration analysis. Under normal working conditions, concentrations with variation coefficients between 2% and 4% have been determined in amperometric titrations, between 0.5% and 5% in conductometric titrations of strong/weak acid and its mixtures, and around 1.5% in spectrophotometric and potentiometric titrations.

Time- and Space-Efficient Algorithms for Least Median of Squares Regression

Abstract The least median of squared residuals regression line (or LMS line) is that line y = ax + b for which the median of the residuals |yi - axi - b |2 is minimized over all choices of a and b. If we rephrase the traditional ordinary least squares (OLS) problem as finding the a and b that minimize the mean of | yi - axi - b |2, one can see that in a formal sense LMS just replaces a “mean” by a “median.” This way of describing LMS regression does not do justice to the remarkable properties of LMS. In fact, LMS regression behaves in ways that distinguish it greatly from OLS as well as from many other methods for robustifying OLS (see, e.g., Rousseeuw 1984). As illustrations given here show, the LMS regression line should provide a valuable tool for studying those data sets in which the usual linear model assumptions are violated by the presence of some (not too small) groups of data values that behave distinctly from the bulk of the data. This feature of LMS regression is illustrated by the fit given in...