Small Sample Bias Research Articles

A unified model-implied instrumental variable approach for structural equation modeling with mixed variables

The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal . We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.

Estimation of Causal Effects with Small Data in the Presence of Trapdoor Variables

Abstract We consider the problem of estimating causal effects of interventions from observational data when well-known back-door and front-door adjustments are not applicable. We show that when an identifiable causal effect is subject to an implicit functional constraint that is not deducible from conditional independence relations, the estimator of the causal effect can exhibit bias in small samples. This bias is related to variables that we call trapdoor variables. We use simulated data to study different strategies to account for trapdoor variables and suggest how the related trapdoor bias might be minimized. The importance of trapdoor variables in causal effect estimation is illustrated with real data from the Life Course 1971–2002 study. Using this data set, we estimate the causal effect of education on income in the Finnish context. Bayesian modelling allows us to take the parameter uncertainty into account and to present the estimated causal effects as posterior distributions.

Thermotherapy for knee osteoarthritis: A protocol for systematic review.

Background:Osteoarthritis of the knee is one of the leading causes of pain and disability among adults. Thermotherapy has been widely used to treat knee osteoarthritis. But its efficiency has not been scientifically and methodically evaluated. The aim of this study is to assess the benefits of thermotherapy for people with osteoarthritis of the knee, in terms of pain, stiffness, and physical dysfunction.Methods:Eight databases will be searched from their inception to September 2020. They are as follows: PubMed, Embase, Cochrane Library, ClinicalTrials.gov, China Knowledge Resource Integrated Database (CNKI), Weipu Database for Chinese Technical Periodicals (VIP), Chinese Biomedical Literature Database (CBM), and Wanfang Database. Two researchers will independently select studies, collect data, and assess the methodology quality by the Cochrane risk of bias tool.Results:The systematic review will provide high-quality evidence to assess the benefits and harms of thermotherapy for people with osteoarthritis of the knee, in terms of pain, stiffness, and dysfunction of knee joint, and quality of life, as well as adverse events.Conclusion:The systematic review will provide evidence to assess the effectiveness and safety of thermotherapy for knee osteoarthritis patients.INPLASY registration number:INPLASY202140038.

Pandemic-induced fear and stock market returns: Evidence from China

We construct a pandemic-induced fear (PIF) index to measure fear of the COVID-19 pandemic using Internet search volumes of the Chinese local search engine and empirically investigate the impact of fear of the pandemic on Chinese stock market returns. A reduced-bias estimation approach for multivariate regression is employed to address the issue of small-sample bias. We find that the PIF index has a negative and significant impact on cumulative stock market returns. The impact of PIF is persistent, which can be explained by mispricing from investors' excessive pessimism. We further reveal that the PIF index directly predicts stock market returns through noise trading. Investors' Internet search behaviors enhance the fear of the pandemic, and pandemic-induced fear determines future stock market returns, rather than the number of cases and deaths caused by the COVID-19 pandemic.

Theoretical framework for industrial energy consumption revisited: The role of demographics

A vast number of studies have considered economic aspects of industrial energy consumption, whereas, to the best of our knowledge, very few studies have considered demographic aspects, and none of them provided a theoretical foundation for the demographic variables employed. Studying the effect of demographic factors on industrial energy consumption is also important because of the reasons found in the literature. This motivated us to develop a theoretical framework using features of production function and the labor market, in which industrial energy consumption is linked to both economic and demographic factors. We then empirically tested the reliability of the developed framework. To produce robust results, various unit root and cointegration tests, long-run estimation methods, small sample bias corrections, as well as two functional forms and two measures of the demographics were employed in the empirical analysis. The results are theoretically and empirically coherent: demographic and economic indicators have statistically significant long- and short-run impacts on industrial electricity consumption. Further analysis showed that the demographic indicators also exert statistically significant and theoretically coherent impacts on other energy types used in industry within this new framework. We concluded that the suggested framework can be used to examine the role of both demographic and economic factors in the industrial consumption of electricity and other energy types.

Small-sample inference for cluster-based outcome-dependent sampling schemes in resource-limited settings: Investigating low birthweight in Rwanda.

The neonatal mortality rate in Rwanda remains above the United Nations Sustainable Development Goal 3 target of 12 deaths per 1000 live births. As part of a larger effort to reduce preventable neonatal deaths in the country, we conducted a study to examine risk factors for low birthweight. The data were collected via a cost-efficient cluster-based outcome-dependent sampling (ODS) scheme wherein clusters of individuals (health centers) were selected on the basis of, in part, the outcome rate of the individuals. For a given data set collected via a cluster-based ODS scheme, estimation for a marginal model may proceed via inverse-probability-weighted generalized estimating equations, where the cluster-specific weights are the inverse probability of the health center's inclusion in the sample. In this paper, we provide a detailed treatment of the asymptotic properties of this estimator, together with an explicit expression for the asymptotic variance and a corresponding estimator. Furthermore, motivated by the study we conducted in Rwanda, we propose a number of small-sample bias corrections to both the point estimates and the standard error estimates. Through simulation, we show that applying these corrections when the number of clusters is small generally reduces the bias in the point estimates, and results in closer to nominal coverage. The proposed methods are applied to data from 18 health centers and 1 district hospital inRwanda.

Forecasting the U.S. Dollar in the 21st Century

The level of the (log of) the exchange rate seems to have strong forecasting power for dollar exchange rates against major currencies post-2000 at medium- to long-run horizons of 12-, 36- and 60-months. We find that this is true using conventional asymptotic statistics correcting for serial correlation biases. But correcting for small-sample bias using simulation methods, we find little evidence to reject a random walk. This small sample bias arises because of near-spurious correlation when the predictor variable is persistent and the horizon for exchange rate forecasts is long. Similar problems of spurious correlation may arise when other persistent variables are used to forecast changes in the exchange rate. We find, in fact, using asymptotic statistics, the level of the exchange rate provides better forecasts than economic measures of “global risk”, and the measures of global risk do not improve the (possibly spurious) forecasting power of the level of the exchange rate.

Bias in Local Projections

<ns3:p>Local projections (LPs) are a popular tool in macroeconomic research. We show that LPs are often used with very small samples in the time dimension. Consequently, LP point estimates can be severely biased. We derive simple expressions for this bias and propose a way to bias-correct LPs. Small sample bias can also lead autocorrelation-robust standard errors to dramatically understate sampling uncertainty. We argue they should be avoided in LPs like the ones we study. Using identified monetary policy shocks, we demonstrate that the bias in point estimates can be economically meaningful and the bias in standard errors can affect inference.</ns3:p>

Arbitrage Pricing Theory, the Stochastic Discount Factor and Estimation of Risk Premia from Portfolios

The arbitrage pricing theory (APT) attributes differences in expected returns to exposure to systematic risk factors, which are typically assumed to be strong. In this paper we consider two aspects of the APT. Firstly we relate the factors in the statistical factor model to a theoretically consistent set of factors defined by their conditional covariation with the stochastic discount factor (mt) used to price securities within inter-temporal asset pricing models. We show that risk premia arise from non-zero correlation of observed factors with mt; and the pricing errors arise from the correlation of the errors in the statistical factor model with mt: Secondly we compare estimates of factor risk premia using portfolios with the ones obtained using individual securities, and show that the identification conditions in terms of the strength of the factor are the same and that, in general, no clear cut ranking of the small sample bias of the two estimators is possible.

Comparison of the New Estimators: The Semi-Parametric Likelihood Estimator, SPW, and the Conditional Weighted Pseudo Likelihood Estimator, WPCE

The analysis of sample-based studies involving sampling designs for small sample size, is challenging because the sample selection probabilities (as well as the sample weights) is dependent on the response variable and covariates. The study has focused on using systems of weighted regression estimating equations, using different modified weights, to estimate the coefficients of Weighted Likelihood Estimators. Usually, the design-consistent (Weighted) estimators are obtained by solving (sample) weighted estimating equations. They are then used to construct estimates which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A. The purpose of our study is to compare derived Estimators of the weighted regression estimating equations for estimating the coefficients of Weighted Likelihood Estimators, the Semi-Parametric Weighted Likelihood Estimator, SPW and the Weighted Conditional Pseudo Likelihood Estimator, WCPE with the conventional Horvitz-Thompson Weighted Likelihood Estimator, using relative efficiency, sample bias and Standard Error for small sample size. The constructed estimates from the system of weighted regression estimating equations, using different modified weights, are actually the Weighted Likelihood Estimators. The study compared the two new estimators, the Semi-parametric weighted estimator, SPW and the Weighted Conditional Pseudo Likelihood estimator, WCPE, for both the unmodified and modified Weights, which were found to have better relative efficiency and smaller finite small sample bias than the estimates from conventional Horvitz-Thompson Weighted Estimator, for both generated and for real data. The outcome of the tests show strong similarity in performance to those obtained using the simulated data. Estimates were constructed which have better relative efficiencies and smaller finite small sample bias than the estimates from the Horvitz-Thompson Weighted Estimator with unmodified weight, option A.

Predicting the Oil Market

We study the performance of many traditional and novel, text-based variables for in-sample and out-of-sample forecasting of oil spot, futures, and energy company stock returns, and changes in oil volatility, production, and inventories. After controlling for small-sample biases, we find evidence of in-sample predictability. Our text measures, derived using energy news articles, hold their own against traditional variables. While we cannot identify ex-ante rules for selecting successful out-of-sample forecasters, an analysis of all possible two-variable models reveals out-of-sample performance above that expected under random variation. Our findings provide new directions for identifying robust forecasting models for oil markets, and beyond.

Output and Expected Returns in Central and Eastern European Countries

<p><strong>Theoretical background</strong>: Although some controversy remains, some aspects of the predictability of aggregate stock market returns in the United States and other industrialized countries appear to be relatively well established. Intertemporal asset pricing models based on the paradigm of investor rationality and market efficiency imply that various macro variables describing the state of the economy may forecast future returns on the aggregate stock market.</p><p><strong>Purpose of the article</strong>: The aim of the article is to present the results of a preliminary study which set out to determine whether the ratio of the stock index to the aggregate output in the economy and future rates of return in the aggregate stock markets in Central and Eastern Europe are significantly related to each other over different time horizons.</p><p><strong>Research methods</strong>: Heteroskedasticity and autocorrelation-consistent estimators with a small sample degrees of freedom adjustment were used in regressions to track overlapping data problem and small sample bias.</p><p><strong>Main findings</strong>: The analysis of the key market indices has shown that they explain much of the variation in the long-horizon future cumulative returns, as well as in cumulative excess returns.</p>

Instruments with Heterogeneous Effects: Bias, Monotonicity, and Localness

Abstract In Instrumental Variables (IV) estimation, the effect of an instrument on an endogenous variable may vary across the sample. In this case, IV produces a local average treatment effect (LATE), and if monotonicity does not hold, then no effect of interest is identified. In this paper, I calculate the weighted average of treatment effects that is identified under general first-stage effect heterogeneity, which is generally not the average treatment effect among those affected by the instrument. I then describe a simple set of data-driven approaches to modeling variation in the effect of the instrument. These approaches identify a Super-Local Average Treatment Effect (SLATE) that weights treatment effects by the corresponding instrument effect more heavily than LATE. Even when first-stage heterogeneity is poorly modeled, these approaches considerably reduce the impact of small-sample bias compared to standard IV and unbiased weak-instrument IV methods, and can also make results more robust to violations of monotonicity. In application to a published study with a strong instrument, the preferred approach reduces error by about 19% in small (N ≈ 1, 000) subsamples, and by about 13% in larger (N ≈ 33, 000) subsamples.

The relationship between advanced glycation end products and gestational diabetes: A systematic review and meta-analysis.

Gestational Diabetes Mellitus (GDM) is a condition in which women without history of diabetes experience hyperglycemia during pregnancy, especially at the second and third trimesters. In women who have had GDM, an elevated body mass index (BMI) may have a substantial impact for persistent hyperglycemia in their lives after gestation. Beyond hyperglycemia, increased local oxidative stress directly promotes the formation of Advanced Glycation End-products (AGEs). Hence, this systematic review and meta-analysis was aimed to determine the relationship between the level of AGEs and/or related metabolic biomarkers with GDM. Literature search was carried out through visiting electronic databases, indexing services, and directories including PubMed/MEDLINE (Ovid®), EMBASE (Ovid®), google scholar and WorldCat to retrieve studies without time limit. Following screening and eligibility evaluation, relevant data were extracted from included studies and analyzed using Rev-Man 5.3 and STATA 15.0. Inverse variance method with random effects pooling model was used for the analysis of outcome measures at 95% confidence interval. Hedge's adjusted g statistics was applied to calculate the standardized mean difference (SMD) to consider the small sample bias. Besides, meta-regression, meta-influence, and publication bias analyses were conducted. The protocol has been registered on PROSPERO with ID: CRD42020173867. A total of 16 original studies were included for the systematic review and meta-analysis. Compared with women with pregnant controls, the level of AGE was significantly higher in women with GDM (SMD [95% CI] = 2.26 [1.50‒3.02], Z = 5.83, P < 0.00001; I2 = 97%, P< 0.0001). The BMI was also significantly higher in women with GDM (SMD [95% CI] = 0.97 [0.33‒1.62], Z = 2.98, P = 0.003) compared to controls. Regarding specific and related metabolic biomarkers, there was higher level of HOMA-IR (SMD [95% CI] = 0.39 [0.22-0.55], Z = 4.65, P < 0.0001, after sensitivity analysis) and HbA1c (SMD [95% CI] = 0.58 [0.03‒1.12], Z = 2.07, P = 0.04, after sensitivity analysis) in gestational diabetic women. Subgroup analyses indicated that studies conducted in Asia and Europe, at third trimester of pregnancy and blood/plasma AGE samples showed a significant difference in AGE level among women with GDM compared to pregnant controls. What is more, meta-regression with the sample size (regression coefficient (Q) = -0.0092, P = 0.207) and year of publication (Q = 0.0035, P = 0.984) suggested that the covariates had no significant effect on the heterogeneity. The study indicated that there was a strong relationship between AGE and GDM. Besides, the BMI and other specific biomarkers showed a significant difference between the two groups indicating the high risk of developing long-standing type 2 diabetes and its complications in gestational diabetic women. Early detection of these biomarkers may play a pivotal role in controlling postpartum diabetic complications.

Reducing the effect of sample bias for small data sets with double‐weighted support vector transfer regression

AbstractSmall data sets are an extremely challenging problem in the machine learning (ML) realm, and in specific, in regression scenarios, as the lack of relevant data can lead to ML models that have large bias. However, there are many applications for which a purely data‐driven procedure would be advantageous, but a large amount of data are not available. This article proposes a novel regression‐based transfer learning (TL) model to address this challenge, where TL is defined as knowledge transfer from a large, relevant data set (source domain data) to a small data set (target domain data). The proposed TL model is termed double‐weighted support vector transfer regression (DW‐SVTR), which couples least squares support vector machines for regression (LS‐SVMR) with two weight functions. The first weight function uses kernel mean matching (KMM) to reweight the source domain data such that the mean values of the source and target domain data in a reproduced kernel Hilbert space (RKHS) are close. In this way, the source domain data points relevant to the target domain points have a larger weight than irrelevant source domain points. The second weight is a function of estimated residuals, which aims to further reduce the negative interference of irrelevant source domain points. The proposed approach is assessed and validated via simulated data and by enhanced shear strength prediction of nonductile columns based on limited availability of nonductile column data. Specifically, the results for the latter show that the proposed DW‐SVTR can reduce the root mean square error (RMSE) by 34% and enhance the coefficient of determination (R2) by 229%. These numerical results demonstrate that the DW‐SVTR significantly reduces the effect of small sample bias and improves prediction performance compared to standard ML methods.

Dynamic interactive links among sustainable energy investment, air pollution, and sustainable development in regional China

This research investigates the dynamic interactive associations among sustainable investment in the energy sector, air pollution, and sustainable development. To this end, it employs a "one-step" system-generalized method of moments (GMM) and "one-step" differential-GMM estimators, covering the period between 1996 and 2017. In this context, it utilizes the simultaneous equations of the dynamic panel data model for panel data of 27 Chinese provinces and municipalities. We have developed a new model of sustainable development, which incorporates sustainable investment in the energy sector and air pollution to offer a robust theoretical foundation for considering the underlying relations. The system-GMM estimator is used for the full data set; however, differential-GMM is utilized for the subsets of data, in order to tackle the small sample bias problem. The empirical outcomes provide several vital insights in that they yield mixed findings for the aggregated sample and subsets of data. For example, a two-way causal relationship occurs for all the panels, except the central part (medium development regions), between sustainable investment in the energy sector and sustainable development. Contrary to this, causality runs from air pollution to sustainable investment in the energy sector in a full data set and the central part (medium dev.). Nevertheless, the opposite is true in the case of the eastern part (most developed regions) of China. Still, the same relationship runs in either direction in the case of the western part (least developed regions). On the other way around, the feedback hypothesis of causality is confirmed, across all the samples, between air pollution and sustainable development. Hence, sustainable development and air pollution are overwhelmingly interdependent, in the country as well as the province and municipality level of the Chinese economy.

On maximum likelihood estimation of competing risks using the cause-specific semi-parametric Cox model with time-varying covariates – An application to credit risk

Credit-granting institutions need to estimate the probability of loan default, which represents the chance a customer fails to make repayments as promised. Critically this estimation is intertwined with the competing risk a customer fully repays their loan while also having key predictive drivers with values that change over time. A conventional model in this setting is a competing risks Cox Model with time-varying covariates. However partial likelihood estimation of this model has two shortcomings: (1) the baseline hazard is not estimated, so calculating probabilities requires a further estimation step; and (2) a covariance matrix for both regression coefficients and the baseline hazard is not produced. This paper caters for these shortcomings by devising a maximum likelihood technique to jointly estimate regression coefficients and the cause-specific baseline hazards using constrained optimisation to ensure the latter’s non-negativity. We show via simulation our technique produces regression coefficients estimates with lower bias in small samples with heavy censoring. When applied to a real-world credit risk dataset consisting of home loan data our Maximum Likelihood approach produces a smoother estimate of the cause-specific baseline hazards for default and redemption than those obtained using the Partial Likelihood and Breslow approach. This provides better clarity of the shape of these functions through both a less volatile central estimate as well as quantifying the error of this central estimate. We implement our method in R.

Self-determination theory interventions for health behavior change: Meta-analysis and meta-analytic structural equation modeling of randomized controlled trials.

We conducted a meta-analysis of randomized controlled trials (RCTs) to promote health behavior change based on self-determination theory (SDT). The review aimed to (a) quantify the impact of SDT interventions on health behaviors, (b) test mediation by theoretically specified variables (autonomous motivation and perceived competence), and (c) identify moderators of intervention effectiveness. Computerized searches and additional strategies identified 56 articles that yielded 65 independent tests of SDT interventions. Random effects meta-analysis and metaregressions were conducted via STATA; meta-analytic structural equation modeling (MASEM) was used to test mediation. The sample-weighted average effect size for SDT interventions was d+ = .23, and there were significant effects for physical activity, sedentary behavior, diet, alcohol consumption, and smoking cessation (.16 ≥ d+ ≥ .29). Effect sizes exhibited both publication bias and small sample bias but remained significantly different from zero, albeit of smaller magnitude, after correction for bias (d+ ≥ .15). MASEM indicated that autonomous motivation and perceived competence mediated intervention effects on behavior. Metaregression analyses indicated that features of the sample, intervention, or methodology generally did not moderate effect sizes. The present review indicates that SDT interventions have a significant but small effect on health behavior change and suggests several directions for future research. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

SARS-CoV-2 Testing, Prevalence, and Predictors of COVID-19 in Patients with Inflammatory Bowel Disease in Northern California

SARS-CoV-2 Testing, Prevalence, and Predictors of COVID-19 in Patients with Inflammatory Bowel Disease in Northern California

News Shocks across Countries: An Empirical Investigation

We estimate the role of news shocks to total factor productivity, foreign interest rates and commodity terms of trade in explaining the variance of output and other macro aggregates in a large sample of countries. To correct for the small-sample bias of the variance decomposition estimates we develop a Bootstrap-after-Bootstrap method. We find that the mean difference of variance share of output explained by news shocks between developing and developed countries is: I) Negligible for news shocks to total factor productivity. II) Positive for news shocks to foreign interest rates (6 p.p.) and to commodity terms of trade (8.3 p.p.). Using cross-sectional data, we find that countries with less financial development have a larger share of output variance explained by news shocks to foreign interest rates, and countries with higher total trade of commodities to output ratio and less developed financial markets exhibit a larger share of output variance explained by news shocks to commodity terms of trade. These results suggest that to study the role of news shocks in the economy, one-sector models with only shocks to total factor productivity are not adequate, and that there must be a structural distinction regarding financial markets' development when modeling developing countries as opposed to developed in a general equilibrium framework.