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We propose a multivariate GARCH model for non-stationary health time series by modifying the observation-level variance of the standard state space model. The proposed model provides an intuitive and novel way of dealing with heteroskedastic data using the conditional nature of state-space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. We use the forward filtering backward sampling algorithm to efficiently obtain samples from the posterior distribution of the latent state. The proposed model also handles missing data in a fully Bayesian fashion. We validate our model on synthetic data and analyze a data set obtained from an intensive care unit in a Montreal hospital and the MIMIC dataset. We further show that our proposed models offer better performance, in terms of WAIC than standard state space models. The proposed model provides a new way to model multivariate heteroskedastic non-stationary time series data. Model comparison can then be easily performed using the WAIC.

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Seasonality and volatility of vegetation in the ecosystem are associated with climatic sensitivity, which can have severe consequences for the environment as well as on the social and economic well-being of the nation. Monitoring and forecasting vegetation growth patterns in ecosystems significantly rely on remotely sensed vegetation indices, such as Normalized Difference Vegetation Index (NDVI). A novel integration of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and the Holt-Winters (H-W) models was used to simulate the seasonality and volatility of the three different agro-climatic zones in Jharkhand, India: the central north-eastern, eastern, and south-eastern agro-climatic zones. MODIS Terra Vegetation Indices NDVI data MOD13Q1, from 2001 to 2021, was used to create NDVI time series volatility and seasonality modeled by the GARCH and the H-W models, respectively. GARCH-based Exponential GARCH (EGARCH) [1,1] and Standard GARCH (SGARCH) [1,1] models were used to check the volatility of vegetation growth in three different agro-climatic zones of Jharkhand. The SGARCH [1,1] and EGARCH [1,1] models for the western agro-climatic zone experienced the best indicator as it has maximum likelihood and minimal Schwarz-Bayesian criterion and Akaike information criterion. The seasonality results showed that the additive H-W model showed better results in the eastern agro-climatic zone with the optimized values of MAE (16.49), MAPE (0.49), NSE (0.86), RMSE (0.49), and R2 (0.82) followed by the south-eastern and central north-eastern agro-climatic zones. By utilizing the H-W and GARCH models, the finding demonstrates that vegetation orientation and monitoring seasonality can be predicted using NDVI.

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Previous observations on a group of exceptionally healthy "Super-Seniors" showed a lower variance of multiple physiological measures relevant for health than did a less healthy group of the same age. The finding was interpreted as the healthier individuals having physiological measurement values closer to an optimal level, or "sweet spot." Here, we tested the generalizability of the sweet-spot hypothesis in a larger community sample, comparing differences in the variance between healthier and less healthy groups. We apply this method to the Canadian Longitudinal Study on Aging (CLSA) comprehensive cohort of 30,097 participants aged 45 to 85 years with deep phenotype data. Data from both sexes and four age ranges were analyzed. Five instruments were used to represent different aspects of health, physical, and cognitive functioning. We tested 231 phenotypic measures for lower variance in the most healthy vs. least healthy quartile of each sex and age group, as classified by the five instruments. Segmented regression was used to determine sex-specific optimal values. One hundred forty-two physiological measures (61%) showed lower variance in the healthiest than in the least healthy group, in at least one sex and age group. The difference in variance was most significant for hemoglobin A1c and was also significant for many body composition measurements, but not for bone mineral density. Ninety-four phenotypes showed a nonmonotonic relationship with health, consistent with the idea of a sweet spot; for these, we determined optimal values and 95% confidence intervals that were generally narrower than the ranges of current clinical reference intervals. These findings for sweet spot discovery validate the proposed approach for identifying traits important for healthy aging.

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BACKGROUND: The non-inferiority test is a reasonable approach to assessing a new treatment in a three-arm trial. The three-arm trial consists of a placebo, reference, and an experimental treatment. The non-inferiority is often measured by the mean differences between the experimental and the placebo groups relative to the mean differences between the reference and the placebo groups. METHODS: To cope with possible estimation distortion due to the allowance of heteroskedasticity, we adjust the measurement of non-inferiority by the incorporation of coefficient of variation (CV) of the experimental, the reference and the placebo groups. In this research, we propose a generalized [Formula: see text]-value based method (GPV-based method) to facilitate non-inferiority tests for the means with unknown coefficient of variation in a three-arm trial. RESULTS: The simulation results show that the GPV-based method can not only adequately control type I error rate at nominal level better but also provide power higher than those from Delta method and the empirical bootstrap method, which verifies the feasibility of our adjustment. CONCLUSIONS: We revise the measurement of non-inferiority by deducting the CV of each kind of treatment from the average effect of trials. CVs are included in the non-inferiority explicitly to help prevent possible estimating distortion if heteroskedasticity is allowed. Through the simulation study, the performance of GPV-based method for facilitating non-inferiority tests for the means with unknown CV in a three-arm trial is better than those from empirical bootstrap method and Delta method for small, medium and large sample sizes. Hence, the GPV-based method is recommended to be used to conduct the non-inferiority test for the means with unknown CV in a three-arm trial. The GPV-based method still performs well in non-normality cases.

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Multivariate heterogeneous responses and heteroskedasticity have attracted increasing attention in recent years. In genome-wide association studies, effective simultaneous modeling of multiple phenotypes would improve statistical power and interpretability. However, a flexible common modeling system for heterogeneous data types can pose computational difficulties. Here we build upon a previous method for multivariate probit estimation using a two-stage composite likelihood that exhibits favorable computational time while retaining attractive parameter estimation properties. We extend this approach to incorporate multivariate responses of heterogeneous data types (binary and continuous), and possible heteroskedasticity. Although the approach has wide applications, it would be particularly useful for genomics, precision medicine, or individual biomedical prediction. Using a genomics example, we explore statistical power and confirm that the approach performs well for hypothesis testing and coverage percentages under a wide variety of settings. The approach has the potential to better leverage genomics data and provide interpretable inference for pleiotropy, in which a locus is associated with multiple traits.

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Test equating is a statistical procedure to make scores from different test forms comparable and interchangeable. Focusing on an IRT approach, this paper proposes a novel method that simultaneously links the item parameter estimates of a large number of test forms. Our proposal differentiates itself from the current state of the art by using likelihood-based methods and by taking into account the heteroskedasticity and the correlation of the item parameter estimates of each form. Simulation studies show that our proposal yields equating coefficient estimates which are more efficient than what is currently available in the literature.

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The multivariate delta method was used by Yuan and Chan to estimate standard errors and confidence intervals for standardized regression coefficients. Jones and Waller extended the earlier work to situations where data are nonnormal by utilizing Browne's asymptotic distribution-free (ADF) theory. Furthermore, Dudgeon developed standard errors and confidence intervals, employing heteroskedasticity-consistent (HC) estimators, that are robust to nonnormality with better performance in smaller sample sizes compared to Jones and Waller's ADF technique. Despite these advancements, empirical research has been slow to adopt these methodologies. This can be a result of the dearth of user-friendly software programs to put these techniques to use. We present the betaDelta and the betaSandwich packages in the R statistical software environment in this manuscript. Both the normal-theory approach and the ADF approach put forth by Yuan and Chan and Jones and Waller are implemented by the betaDelta package. The HC approach proposed by Dudgeon is implemented by the betaSandwich package. The use of the packages is demonstrated with an empirical example. We think the packages will enable applied researchers to accurately assess the sampling variability of standardized regression coefficients.

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BACKGROUND: Preference heterogeneity in health valuation has become a topic of greater discussion among health technology assessment agencies. To better understand heterogeneity within a national population, valuation studies may identify latent groups that place different absolute and relative importance (i.e., scale and taste parameters) on the attributes of health profiles. OBJECTIVE: Using discrete choice responses from a Peruvian valuation study, we estimated EQ-5D-5L values on a quality-adjusted life-year (QALY) scale accounting for latent heterogeneity in scale and taste, as well as controlling heteroskedasticity at task level variation. METHOD: We conducted a series of latent class analyses, each including the 20 main effects of the EQ-5D-5L and a power function that relaxes the constant proportionality assumption (i.e., discounting) between value and lifespan. Taste class membership was conditional on respondent-specific characteristics and their experience with the composite time trade-off (cTTO) tasks. Scale class membership was conditional on behavioral characteristics such as survey duration and self-stated difficulty level in understanding tasks. Each analysis allowed the scale factor to vary by task type and completion time (i.e., heteroskedasticity). RESULTS: The results indicated three taste classes: a quality-of-life oriented class (33.35%) that placed the highest value on levels of severity, a length-of-life oriented class (26.72%) that placed the highest value on lifespan, and a middle class (39.71%) with health attribute effects lower than the quality class and lifespan effect lower than the length-of-life oriented class. The EQ-5D-5L values ranged from - 2.11 to 0.86 (quality-of-life oriented class), from - 0.38 to 1.02 (middle class), and from 0.36 to 1.01 (length-of-life oriented class). The likelihood of being a member of the quality-of-life class was highly dependent on whether the respondent completed the cTTO tasks (p-value < 0.001), which indicated that the cTTO tasks might cause the Peru respondents to inflate the burden of health problems on a QALY scale compared to those who did not complete the cTTO tasks. The results also showed two scale classes as well as heteroskedasticity within each scale class. CONCLUSION: Accounting for taste and scale classes simultaneously improveds understanding of preference heterogeneity in health valuation. Future studies may confirm the differences in taste between classes in terms of the effect of quality of life and lifespan attributes. Furthermore, confirmatory evidence is needed on how behavioral variables captured within a study protocol may enhance analyses of preference heterogeneity.

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Homogeneity of variance (HOV) is a well-known but often untested assumption in the context of multilevel models (MLMs). However, depending on how large the violation is, how different group sizes are, and the variance pairing, standard errors can be over or underestimated even when using MLMs, resulting in questionable inferential tests. We evaluate several tests (e.g., the H statistic, Breusch Pagan, Levene's test) that can be used with MLMs to assess violations of HOV. Although the traditional robust standard errors used with MLMs require at least 50 clusters to be effective, we assess a robust standard error adjustment (i.e., the CR2 estimator) that can be used even with a few clusters. Findings are assessed using a Monte Carlo simulation and are further illustrated using an applied example. We show that explicitly modeling the heterogenous variance structures or using the CR2 estimator are both effective at ameliorating the issues associated with the fixed effects of the regression model related to violations of HOV resulting from between-group differences.

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The DerSimonian-Laird (DL) weighted average method for aggregated data meta-analysis has been widely used for the estimation of overall effect sizes. It is criticized for its underestimation of the standard error of the overall effect size in the presence of heterogeneous effect sizes. Due to this negative property, many alternative estimation approaches have been proposed in the literature. One of the earliest alternative approaches was developed by Hardy and Thompson (HT), who implemented a profile likelihood instead of the moment-based approach of DL. Others have further extended this likelihood approach and proposed higher-order likelihood inferences (e.g., Bartlett-type corrections). In addition, corrections factors for the estimated DL standard error, like the Hartung-Knapp-Sidik-Jonkman (HKSJ) adjustment, and the restricted maximum likelihood (REML) estimation have been suggested too. Although these improvements address the uncertainty in estimating the between-study variance better than the DL method, they all assume that the true within-study standard errors are known and equal to the observed standard errors of the effect sizes. Here, we will treat the observed standard errors as estimators for the within-study variability and we propose a bivariate likelihood approach that jointly estimates the overall effect size, the between-study variance, and the potentially heteroskedastic within-study variances. We study the performance of the proposed method by means of simulation, and compare it to DL (with and without HKSJ), HT, their higher-order likelihood methods, and REML. Our proposed approach seems to have better or similar coverages compared to the other approaches and it appears to be less biased in the case of heteroskedastic within-study variances when this heteroskedasticty is correlated with the effect size.

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BACKGROUND: Respondents in a health valuation study may have different sources of error (i.e., heteroskedasticity), tastes (differences in the relative effects of each attribute level), and scales (differences in the absolute effects of all attributes). Although prior studies have compared values by preference-elicitation tasks (e.g., paired comparison [PC] and best-worst scaling case 2 [BWS]), no study has yet controlled for heteroskedasticity and heterogeneity (taste and scale) simultaneously in health valuation. METHODS: Preferences on EQ-5D-5L profiles were elicited from a random sample of 380 adults from the general population of the Netherlands, using 24 PC and 25 BWS case 2 tasks. To control for heteroskedasticity and heterogeneity (taste and scale) simultaneously, we estimated Dutch EQ-5D-5L values using conditional, heteroskedastic, and scale-adjusted latent class (SALC) logit models by maximum likelihood. RESULTS: After controlling for heteroskedasticity, the PC and BWS values were highly correlated (Pearson's correlation: 0.9167, CI: 0.9109-0.9222) and largely agreed (Lin's concordance: 0.7658, CI: 0.7542-0.7769) on a pits scale. In terms of preference heterogeneity, some respondents (mostly young men) failed to account for any of the EQ-5D-5L attributes (i.e., garbage class), and others had a lower scale (59%; p-value: 0.123). Overall, the SALC model produced a consistent Dutch EQ-5D-5L value set on a pits scale, like the original study (Pearson's correlation:0.7295; Lin's concordance: 0.6904). CONCLUSIONS: This paper shows the merits of simultaneously controlling for heteroskedasticity and heterogeneity in health valuation. In this case, the SALC model dispensed with a garbage class automatically and adjusted the scale for those who failed the PC dominant task. Future analysis may include more behavioral variables to better control heteroskedasticity and heterogeneity in health valuation. HIGHLIGHTS: The Dutch EQ-5D-5L values based on paired comparison [PC] and best-worst scaling [BWS] responses were highly correlated and largely agreed after controlling for heteroskedasticity. Controlling for taste and scale heterogeneity simultaneously enhanced the Dutch EQ-5D-5Lvalues by automatically dispensing with a garbage class and adjusting the scale for those who failed the dominant task. After controlling for heteroskedasticity and heterogeneity, this study produced Dutch EQ-5D-5L values on a pits scale moderately concordant with the original values.

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In psychometrics, the canonical use of conditional likelihoods is for the Rasch model in measurement. Whilst not disputing the utility of conditional likelihoods in measurement, we examine a broader class of problems in psychometrics that can be addressed via conditional likelihoods. Specifically, we consider cluster-level endogeneity where the standard assumption that observed explanatory variables are independent from latent variables is violated. Here, "cluster" refers to the entity characterized by latent variables or random effects, such as individuals in measurement models or schools in multilevel models and "unit" refers to the elementary entity such as an item in measurement. Cluster-level endogeneity problems can arise in a number of settings, including unobserved confounding of causal effects, measurement error, retrospective sampling, informative cluster sizes, missing data, and heteroskedasticity. Severely inconsistent estimation can result if these challenges are ignored.

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Interrupted time series (ITS) design is commonly used to evaluate the impact of interventions in healthcare settings. Segmented regression (SR) is the most commonly used statistical method and has been shown to be useful in practical applications involving ITS designs. Nevertheless, SR is prone to aggregation bias, which leads to imprecision and loss of power to detect clinically meaningful differences. The objective of this article is to present a weighted SR method, where variability across patients within the healthcare facility and across time points is incorporated through weights. We present the methodological framework, provide optimal weights associated with data at each time point and discuss relevant statistical inference. We conduct extensive simulations to evaluate performance of our method and provide comparative analysis with the traditional SR using established performance criteria such as bias, mean square error and statistical power. Illustrations using real data is also provided. In most simulation scenarios considered, the weighted SR method produced estimators that are uniformly more precise and relatively less biased compared to the traditional SR. The weighted approach also associated with higher statistical power in the scenarios considered. The performance difference is much larger for data with high variability across patients within healthcare facilities. The weighted method proposed here allows us to account for the heterogeneity in the patient population, leading to increased accuracy and power across all scenarios. We recommend researchers to carefully design their studies and determine their sample size by incorporating heterogeneity in the patient population.

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Using statistical identification, we extract a COVID-19-induced shock by exploiting large daily jumps in financial markets caused by news about the pandemic. This shock depresses economic and financial indicators, increases risk and uncertainty measures, has sizeable distributional effects, and hits most harshly those industries relying on face-to-face interactions. Impulse response function analysis across various identification strategies leads us to interpret the statistical COVID-19-induced shock as a structural uncertainty shock.

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This paper examines the role physical activity plays in determining body mass using data from the American Time Use Survey. Our work is the first to address the measurement error that arises when time use during a single day-rather than average daily time use over an extended period-is used as an explanatory variable. We show that failing to account for day-to-day variation in activities results in the effects of time use on a typical day being understated. Furthermore, we account for the possibility that physical activity and body mass are jointly determined by implementing Lewbel's instrumental variables estimator that exploits first-stage heteroskedasticity rather than traditional exclusion restrictions. While averaging 30 min of transportation-related biking or walking per day lowers the BMI of men by 1.5, we find no effect of physically active leisure on the BMI of men in our sample. In contrast, 30 min of per day of either type of physical activity lowers the BMI of women by 1.

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Analyses of preference evidence frequently confuse heterogeneity in the effects of attribute parameters (i.e., taste coefficients) and the scale parameter (i.e., variance). Standard latent class models often produce unreasonable classes with high variance and disordered coefficients because of confounding estimates of effect and scale heterogeneity. In this study, we estimated a scale-adjusted latent class model in which scale classes (heteroskedasticity) were identified using respondents' randomness in choice behavior on the internet panel (e.g., time to completion and time of day). Hence, the model distinctly explained the taste/preference variation among classes associated with individual socioeconomic characters, in which scales are adjusted. Using data from a discrete-choice experiment on US health insurance demand among single employees, the results demonstrated how incorporating behavioral data enhances the interpretation of heterogeneous effects. Once scale heterogeneity was controlled, we found substantial heterogeneity with 4 taste classes. Two of the taste classes were highly premium sensitive (economy class), coming mostly from the low-income group, and the class associated with better educational backgrounds preferred to have a better quality of coverage of health insurance plans. The third class was a highly quality-sensitive class, with a higher SES background and lower self-stated health condition. The last class was identified as stayers, who were not premium or quality sensitive. This case study demonstrates that one size does not fit all in the analysis of preference heterogeneity. The novel use of behavioral data in the latent class analysis is generalizable to a wide range of health preference studies.

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Microdata are required to evaluate the distributive impact of the taxation system as a whole (direct and indirect taxes) on individuals or households. However, in European Union countries this information is usually distributed into two separate surveys: the Household Budget Surveys (HBS), including total household expenditure and its composition, and EU Statistics on Income and Living Conditions (EU-SILC), including detailed information about households' income and direct (but not indirect) taxes paid. We present a parametric statistical matching procedure to merge both surveys. For the first stage of matching, we propose estimating total household expenditure in HBS (Engel curves) using a GLM estimator, instead of the traditionally used OLS method. It is a better alternative, insofar as it can deal with the heteroskedasticity problem of the OLS estimates, while making it unnecessary to retransform the regressors estimated in logarithms. To evaluate these advantages of the GLM estimator, we conducted a computational Monte Carlo simulation. In addition, when an error term is added to the deterministic imputation of expenditure in the EU-SILC, we propose replacing the usual Normal distribution of the error with a Chi-square type, which allows a better approximation to the original expenditures variance in the HBS. An empirical analysis is provided using Spanish surveys for years 2012-2016. In addition, we extend the empirical analysis to the rest of the European Union countries, using the surveys provided by Eurostat (EU-SILC, 2011; HBS, 2010).

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Gene-environment interactions (GxE) can be fundamental in applications ranging from functional genomics to precision medicine and is a conjectured source of substantial heritability. However, unbiased methods to profile GxE genome-wide are nascent and, as we show, cannot accommodate general environment variables, modest sample sizes, heterogeneous noise, and binary traits. To address this gap, we propose a simple, unifying mixed model for gene-environment interaction (GxEMM). In simulations and theory, we show that GxEMM can dramatically improve estimates and eliminate false positives when the assumptions of existing methods fail. We apply GxEMM to a range of human and model organism datasets and find broad evidence of context-specific genetic effects, including GxSex, GxAdversity, and GxDisease interactions across thousands of clinical and molecular phenotypes. Overall, GxEMM is broadly applicable for testing and quantifying polygenic interactions, which can be useful for explaining heritability and invaluable for determining biologically relevant environments.

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In this paper, we propose a new method for testing heteroskedasticity in two-way fixed effects panel data models under two important scenarios where the cross-sectional dimension is large and the temporal dimension is either large or fixed. Specifically, we will develop test statistics for both cases under the conditional moment framework, and derive their asymptotic distributions under both the null and alternative hypotheses. The proposed tests are distribution free and can easily be implemented using the simple auxiliary regressions. Simulation studies and two real data analyses demonstrate that our proposed tests perform well in practice, and may have the potential for wide application in econometric models with panel data.

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It is well known that the standard F test is severely affected by heteroskedasticity in unbalanced analysis of covariance models. Currently available potential remedies for such a scenario are based on heteroskedasticity-consistent covariance matrix estimation (HCCME). However, the HCCME approach tends to be liberal in small samples. Therefore, in the present paper, we propose a combination of HCCME and a wild bootstrap technique, with the aim of improving the small-sample performance. We precisely state a set of assumptions for the general analysis of covariance model and discuss their practical interpretation in detail, since this issue may have been somewhat neglected in applied research so far. We prove that these assumptions are sufficient to ensure the asymptotic validity of the combined HCCME-wild bootstrap analysis of covariance. The results of our simulation study indicate that our proposed test remedies the problems of the analysis of covariance F test and its heteroskedasticity-consistent alternatives in small to moderate sample size scenarios. Our test only requires very mild conditions, thus being applicable in a broad range of real-life settings, as illustrated by the detailed discussion of a dataset from preclinical research on spinal cord injury. Our proposed method is ready-to-use and allows for valid hypothesis testing in frequently encountered settings (e.g., comparing group means while adjusting for baseline measurements in a randomized controlled clinical trial).

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