Location-scale Model Research Articles

Model construction and sample size planning for mixed-effects location-scale models

Model construction and sample size planning for mixed-effects location-scale models

Inferring Cognitive Abilities from Response Times to Web-Administered Survey Items in a Population-Representative Sample.

Monitoring of cognitive abilities in large-scale survey research is receiving increasing attention. Conventional cognitive testing, however, is often impractical on a population level highlighting the need for alternative means of cognitive assessment. We evaluated whether response times (RTs) to online survey items could be useful to infer cognitive abilities. We analyzed >5 million survey item RTs from >6000 individuals administered over 6.5 years in an internet panel together with cognitive tests (numerical reasoning, verbal reasoning, task switching/inhibitory control). We derived measures of mean RT and intraindividual RT variability from a multilevel location-scale model as well as an expanded version that separated intraindividual RT variability into systematic RT adjustments (variation of RTs with item time intensities) and residual intraindividual RT variability (residual error in RTs). RT measures from the location-scale model showed weak associations with cognitive test scores. However, RT measures from the expanded model explained 22−26% of the variance in cognitive scores and had prospective associations with cognitive assessments over lag-periods of at least 6.5 years (mean RTs), 4.5 years (systematic RT adjustments) and 1 year (residual RT variability). Our findings suggest that RTs in online surveys may be useful for gaining information about cognitive abilities in large-scale survey research.

Construction of a new complete growth reference for urban Chinese children

BackgroundGrowth chart is a valuable clinical tool to monitor the growth and nutritional status of children. A growth chart widely used in China is based on the merged data sets of national surveys in 2005. We aimed to establish an up-to-date, complete growth curve for urban Chinese children and adolescents with a full range of ages.MethodsUsing data collected in a large-scale, cross-sectional study (Prevalence and Risk factors for Obesity and Diabetes in Youth (PRODY), 2017–2019), we analyzed 201,098 urban children aged 3 to 18 years from 11 provinces, autonomous regions, and municipalities that are geographically representative of China. All participants underwent physical examinations. Sex-specific percentiles of height-for-age and weight-for-age were constructed by Generalized Additive Models for Location Scale and Shape (GAMLSS) model. We also compared the median values of height-for-age or weight-for-age between our growth chart and the established growth reference using Welch-Satterthwaite T-Test.ResultsConsistent with the established growth reference, we observed that the P50 percentile of height-for-age reached plateaus at the age of 15 years (172 cm) and 14 years (160 cm) for boys and girls, respectively. In addition, boys aged 10 ~ 14 years and girls aged 10 ~ 12 years exhibited the most dramatic weight difference compared to those of other age groups (19.5 kg and 10.3 kg, respectively). However, our growth chart had higher median values of weight-for-age and height-for-age than the established growth reference with mean increases in weight-for-age of 1.36 kg and 1.17 kg for boys and girls, respectively, and in height-for-age of 2.9 cm and 2.6 cm for boys and girls, respectively.ConclusionsOur updated growth chart can serve as a reliable reference to assess the growth and nutritional status in urban Chinese children throughout the entire childhood.

Expression of type 1 cannabinoid receptor gene in bipolar disorder

BackgroundThe Endocannabinoid System (ECBs) may have a crucial role in bipolar disorder (BD). Previous reports have not detected abnormalities in the expression of the cannabinoid receptor gene CNR1, encoding for CB1. However, we hypothesized that differentiating between mania and depression may uncover differences in CNR1 expression levels. MethodsWe recruited 44 subjects with BD type I (BD-I), in mania (n = 22) and depression (n = 22) and 25 Healthy Controls (HC). CNR1 gene expression was analyzed using a quantitative real-time polymerase chain reaction from peripheral blood mononuclear cells. Data were analyzed using frequentist non-parametric and Bayesian approaches (generalized location-scale model based on lognormal and gamma distributions). ResultsUsing the frequentist non-parametric approach, the depression group had lower CNR1 expression compared to the mania group (p = 0.004). In addition, there was a negative correlation between CNR1 expression and Hamilton Depression Scale score (rho = −0.37; p = 0.007). Bayesian analyses further revealed that CNR1 expression in the mania group was higher and less variable than among HC (>95% probability), while CNR1 expression in the depression group was lower and more variable than among HC (100% probability). LimitationsLack of participants with bipolar disorder in the euthymic phase, lack of toxicology screening and evaluation of CNR1 variants. ConclusionCNR1 expression is higher and less variable in mania than in depression. It is highly probable that these differences also distinguish individuals in different illness phases from healthy controls. Future studies are needed to clarify the role of the endocannabinoid system in bipolar disorder.

Stochastic comparison of the second-order statistics arising from exponentiated location-scale model

In this article, we consider stochastic comparisons between second-order statistics arising from general exponentiated location-scale models. When the random variables are independent, we establish usual stochastic and hazard rate orders between second-order statistics. Further, similar ordering results are obtained when the random observations are dependent. Some applications of the established results are presented.

Extremal Dependence-Based Specification Testing of Time Series

We propose a specification test for conditional location–scale models based on extremal dependence properties of the standardized residuals. We do so comparing the left-over serial extremal dependence—as measured by the pre-asymptotic tail copula—with that arising under serial independence at different lags. Our main theoretical results show that the proposed Portmanteau-type test statistics have nuisance parameter-free asymptotic limits. The test statistics are easy to compute, as they only depend on the standardized residuals, and critical values are likewise easily obtained from the limiting distributions. This contrasts with some extant tests (based, e.g., on autocorrelations of squared residuals), where test statistics depend on the parameter estimator of the model and critical values may need to be bootstrapped. We show that our tests perform well in simulations. An empirical application to S&P 500 constituents illustrates that our tests can uncover violations of residual serial independence that are not picked up by standard autocorrelation-based specification tests, yet are relevant when the model is used for, for example, risk forecasting.

SIMULTANEOUS CONFIDENCE BANDS FOR CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL

Conditional value-at-risk (CVaR) and conditional expected shortfall (CES) are widely adopted risk measures which help monitor potential tail risk while adapting to evolving market information. In this paper, we propose an approach to constructing simultaneous confidence bands (SCBs) for tail risk as measured by CVaR and CES, with the confidence bands uniformly valid for a set of tail levels. We consider one-sided tail risk (downside or upside tail risk) as well as relative tail risk (the ratio of upside to downside tail risk). A general class of location-scale models with heavy-tailed innovations is employed to filter out the return dynamics. Then, CVaR and CES are estimated with the aid of extreme value theory. In the asymptotic theory, we consider two scenarios: (i) the extreme scenario that allows for extrapolation beyond the range of the available data and (ii) the intermediate scenario that works exclusively in the case where the available data are adequate relative to the tail level. For finite-sample implementation, we propose a novel bootstrap procedure to circumvent the slow convergence rates of the SCBs as well as infeasibility of approximating the limiting distributions. A series of Monte Carlo simulations confirm that our approach works well in finite samples.

Food insecurity, hunger, stress, and homelessness among young adults.

Compared to the effects of stress on hunger, the temporal effect of hunger on stress levels is less understood, especially in the context of everyday lives of vulnerable populations with unstable access to food. Our objective was to examine the effects of food insecurity and momentary hunger on momentary stress and stress variability in a sample of currently and formerly homeless young adults. We used a 7-day ecological momentary assessment study querying affect, hunger, and risky behaviors. A mixed-effects location scale model was used to examine the effects of hunger on mean levels and within- and between-subjects variability of stress with 100 currently homeless and 69 formerly homeless young adults ages 18-29 in Los Angeles County, California. When individuals experienced greater-than-average hunger, they then experienced greater stress variability at the next prompt, showing the impact of hunger on stress at the momentary level. Those with higher average levels of stress, regardless of hunger, became substantially more stressed when becoming hungry compared to their generally less stressed counterparts. The study shows the extent to which food insecurity results in erratic stress among vulnerable populations and how high levels of hunger may lead to a more inconsistent stress response. Findings reinforce the need for more mental health services and food programs for young adults who have experienced homelessness. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Defining R-squared measures for mixed-effects location scale models.

Ecological momentary assessment and other modern data collection technologies facilitate research on both within‐subject and between‐subject variability of health outcomes and behaviors. For such intensively measured longitudinal data, Hedeker et al extended the usual two‐level mixed‐effects model to a two‐level mixed‐effects location scale (MELS) model to accommodate covariates' influence as well as random subject effects on both mean (location) and variability (scale) of the outcome. However, there is a lack of existing standardized effect size measures for the MELS model. To fill this gap, our study extends Rights and Sterba's framework of R2 measures for multilevel models, which is based on model‐implied variances, to MELS models. Our proposed framework applies to two different specifications of the random location effects, namely, through covariate‐influenced random intercepts and through random intercepts combined with random slopes of observation‐level covariates. We also provide an R function, R2MELS, that outputs summary tables and visualization for values of our R2 measures. This framework is validated through a simulation study, and data from a health behaviors study and a depression study are used as examples to demonstrate this framework. These R2 measures can help researchers provide greater interpretation of their findings using MELS models.

Testing stochastic dominance with many conditioning variables

We propose tests of the conditional first- and second-order stochastic dominance in the presence of growing numbers of covariates. Our approach builds on a semiparametric location-scale model, where the conditional distribution of the outcome given the covariates is characterized by nonparametric mean and skedastic functions with independent innovations from an unknown distribution. The nonparametric regression functions are estimated by utilizing the ℓ1-penalized nonparametric series estimation with thresholding. Deviation bounds for the regression functions and series coefficients estimates are obtained allowing for the time series dependence. We propose test statistics, which are the maximum (integrated) deviation of a composite of the estimated regression functions and the residual empirical distribution, and introduce a smooth stationary bootstrap to compute p-values. We investigate the finite sample performance of the bootstrap critical values by a set of Monte Carlo simulations. Finally, our method is illustrated by an application to stochastic dominance among portfolio returns given all the past information.

A New Optimization Scheme for Robust Design Modeling with Unbalanced

The Lin and Tu (LT) optimization scheme which is based on mean squared error (MSE) objective function is the commonly used optimization scheme for estimating the optimal mean response in robust dual response surface optimization. The ordinary least squares (OLS) method is often used to estimate the parameters of the process location and process scale models of the responses. However, the OLS is not efficient for the unbalanced design data since this kind of data make the errors of a model become heteroscedastic, which produces large standard errors of the estimates. To remedy this problem, a weighted least squares (WLS) method is put forward. Since the LT optimization scheme produces a large difference between the estimates of the mean response and the experimenter actual target value, we propose a new optimization scheme. The OLS and the WLS are integrated in the proposed scheme to determine the optimal solution of the estimated responses. The results of the simulation study and real example indicate that the WLS is superior when compared with the OLS method irrespective of the optimization scheme used. However, the combination of WLS and the proposed optimization scheme (PFO) signify more efficient results when compared to the WLS combined with the LT optimization scheme.

0188 Associations between Preschoolers’ Behavioral Difficulties and Variability in Sleep Duration and Bedtime

Abstract Introduction Variability in children’s sleep patterns has been linked with health outcomes including obesity, poor mood, and behavioral difficulties. However, much of this evidence stems from parent-reported measures of sleep. Understanding these associations in preschool-age children using device-based measures is important as sleep habits tend to develop and stabilize during this time. The purpose of this study was to examine associations between parent-reported behavioral difficulties and device-measured sleep among preschoolers. Methods Ninety-five preschool-aged children (3-5 years, 51% female, 30% Black) with at least two valid nights of sleep were in included in this analysis. Children were asked to wear an Axivity AX3 accelerometer on their non-dominant wrist for 30 days. Parents completed the Strengths and Difficulties Questionnaire which assessed child behaviors over the past 6 months. Raw accelerometry data were processed with GGIR (v2.3). We used MixWild to conduct mixed effects location scale models with a random intercept and scale predicting nocturnal duration variability and bedtime variability. Time invariant behavior subscales (conduct problems, hyperactivity/inattention, peer relationship problems, emotional symptoms, prosocial behavior, and total difficulties) were included as predictors of child sleep duration and bedtime variability. Results Children had an average of 13.4 ± 7.4 (range 2-29) nights of valid data. Average nocturnal sleep duration was 9.7 ± 1.4 hours and average bedtime was 9:48 PM. There were no statistically significant associations between any SDQ subscales and variability in children’s sleep duration and bedtime. There was an association between random location and scale such that participants with later average bedtimes also had more variability in their bedtime (p < 0.001). Conclusion Variability in nocturnal sleep was not associated with parent reported behavioral difficulties, which is contrary to recent findings. It is unclear if sleep duration and bedtime variability are associated with day-level changes in children’s behavior. Additional work that emphasizes aspects of sleep beyond sleep duration is needed to advance our understanding of preschool-age children’s sleep. Support (If Any) This was supported by the National Institute of General Medical Sciences of the NIH for the UofSC Research Center for Child Well-Being (P20GM130420) and by the National Heart, Lung, and Blood Institute (F32HL154530).

A Latent Variable Mixed-Effects Location Scale Model with an Application to Daily Diary Data

A mixed-effects location scale model allows researchers to study within- and between-person variation in repeated measures. Key components of the model include separate variance models to study predictors of the within-person variance, as well as predictors of the between-person variance of a random effect, such as a random intercept. In this paper, a latent variable mixed-effects location scale model is developed that combines a longitudinal common factor model and a mixed-effects location scale model to characterize within- and between-person variation in a common factor. The model is illustrated using daily reports of positive affect and daily stressors for a large sample of adult women.

Location-scale models for meta-analysis.

Heterogeneity is commonplace in meta-analysis. When heterogeneity is found, researchers often aim to identify predictors that account for at least part of such heterogeneity by using mixed-effects meta-regression models. Another potentially relevant goal is to focus on the amount of heterogeneity as a function of one or more predictors, but this cannot be examined with standard random- and mixed-effects models, which assume a constant (i.e., homoscedastic) value for the heterogeneity variance component across studies. In this paper, we describe a location-scale model for meta-analysis as an extension of the standard random- and mixed-effects models that not only allows an examination of whether predictors are related to the size of the outcomes (i.e., their location), but also the amount of heterogeneity (i.e., their scale). We present estimation methods for such a location-scale model through maximum and restricted maximum likelihood approaches, as well as methods for inference and suggestions for visualization. We also provide an implementation via the metafor package for R that makes this model readily available to researchers. Location-scale models can provide a useful tool to researchers interested in heterogeneity in meta-analysis, with the potential to enhance the scope of research questions in the field of evidence synthesis.

Ordering fail-safe systems having dependent components with Archimedean copula and exponentiated location-scale distributions

In this paper, we study stochastic comparisons of two fail-safe systems with dependent components having an Archimedean copula for the joint survival function and general exponentiated location-scale lifetime distributions. We first present sufficient conditions for the usual stochastic order between fail-safe systems when the components have different exponentiated location-scale distributions but with the same Archimedean copula. Next, the hazard rate ordering of fail-safe systems is discussed when the components in the two systems are independent and follow multiple-outlier exponentiated location-scale models. Several examples are then presented to illustrate the theoretical results established here.

How acute affect dynamics impact longitudinal changes in physical activity among children.

Research examined how acute affect dynamics, including stability and context-dependency, contribute to changes in children's physical activity levels as they transition from late-childhood to early-adolescence. Children (N = 151) (ages 8-12years at baseline) participated in an ecological momentary assessment and accelerometry study with six semi-annual bursts (7days each) across three years. A two-stage mixed-effects multiple location-scale model tested random intercept, variance, and slope estimatesfor positive affect as predictors of moderate-to-vigorous physical activity (MVPA). Multi-year declines in MVPA were greater for children who had greater subject-level variance in positive affect. Children who experienced more positive affect when alone did not experience steeper declines in physical activity. Interventions aiming for long-term modifications in children's physical activity may focus on buffering the effects of within-day fluctuations in affect or tailoring programs to fit the needs of "acute dynamic process phenotypes."

Improving mental, physical, and social functioning through participation in a 3-week cognitive processing therapy-based intensive PTSD treatment

Research has supported the utility of brief intensive treatment programs (ITPs) which utilize interventions, such as Cognitive Processing Therapy (CPT), for reducing severity of symptoms among veterans with posttraumatic stress disorder (PTSD). These treatments have produced large overall reductions in PTSD severity and demonstrated the persistence of these gains following treatment. However, the potential effects of ITPs on mental, physical, and social functioning following treatment completion has been largely unexplored. We utilized data from 204 veterans and 5 service members who completed a 3-week CPT-based ITP and 3-month follow-up assessments. We used a two-stage mixed effects location-scale model approach to initially model each participant’s amount of PTSD change over time and used these estimates to predict mental, physical, and social functioning three months following treatment. Veterans reported moderate improvements in mental, physical, and social functioning from pre-treatment to 3-month follow-up (ds = 0.52,.42,.55, and.47, respectively). Results indicated that reductions in PTSD severity during treatment, rather than fluctuation in symptom reporting from one assessment to the next, significantly predicted improved mental, physical, and social functioning at follow-up. This study supports the ability of ITPs to enact meaningful improvement in functioning among veterans with PTSD in a short timeframe.

The reliability of adult self-reported height: The role of interviewers

Surveys serve as an important source of information on key anthropometric characteristics such as body height or weight in the population. Such data are often obtained by directly asking respondents to report those values. Numerous studies have examined measurement errors in this context by comparing reported to measured values. However, little is known on the role of interviewers on the prevalence of irregularities in anthropometric survey data. In this study, we explore such interviewer effects in two ways. First, we use data from the US National Health and Nutrition Examination Survey and the UK Household Longitudinal Study to evaluate whether differences between reported and measured values are clustered within interviewers. Second, we investigate changes in adult self-reported height over survey waves in two German large-scale panel surveys. Here, we exploit that height should be constant over time for the majority of adult age groups. In both analyses, we use multilevel location-scale models to identify interviewers who enhance reporting errors and interviewers for whom unlikely height changes over waves occur frequently. Our results reveal that interviewers can play a prominent role in differences between reported and measured height values and changes in reported height over survey waves. We further provide an analysis of the consequences of height misreporting on substantive regression coefficients where we especially focus on the role of interviewers who reinforce reporting errors and unlikely height changes.

A shared-parameter location-scale mixed model to link the responsivity in self-initiated event reports and the event-contingent Ecological Momentary Assessments.

We address the issue of (non-) responsivity of self-initiated assessments in Ecological Momentary Assessment (EMA) or other mobile health (mHealth) studies, where subjects are instructed to self-initiate reports when experiencing defined events, for example, smoking. Since such reports are self-initiated, the frequency and determinants of nonresponse to these event reports is usually unknown, however it may be suspected that nonresponse of such self-initiated reports is not random. In this case, existing methods for missing data may be insufficient in the modeling of these observed self-initiated reports. In certain EMA studies, random prompts, distinct from the self-initiated reports, may be converted to event reports. For example, such a conversion can occur if during a random prompt a subject is assessed about the event (eg, smoking) and it is determined that the subject is engaging in the event at the time of the prompt. Such converted prompts can provide some information about the subject's non-responsivity of event reporting. Furthermore, such non-responsivity can be associated with the primary longitudinal EMA outcome (eg, mood) in which case a joint modeling of the non-responsivity and the mood outcome is possible. Here, we propose a shared-parameter location-scale model to link the primary outcome model for mood and a model for subjects' non-responsivity by shared random effects which characterize a subject's mood level, mood change pattern, and mood variability. Via simulations and real data analysis, our proposed model is shown to be more informative, have better coverage of parameters, and provide better fit to the data than more conventional models.

Adaptiveness of the empirical distribution of residuals in semi-parametric conditional location scale models

This paper addresses the problem of deriving the asymptotic distribution of the empirical distribution function Fˆn of the residuals in a general class of time series models, including conditional mean and conditional heteroscedaticity, whose independent and identically distributed errors have unknown distribution F. We show that, for a large class of time series models (including the standard ARMA-GARCH with symmetric innovations), the asymptotic distribution of n{Fˆ n(·)−F(·)} is impacted by the estimation but does not depend on the model parameters. It is thus neither asymptotically estimation free, as is the case for purely linear models, nor asymptotically model dependent, as is the case for some nonlinear models. The asymptotic stochastic equicontinuity is also established. We consider an application to the estimation of the conditional Value-at-Risk.