Misleading Statistical Inference Research Articles

Robust density power divergence estimates for panel data models

The panel data regression models have become one of the most widely applied statistical approaches in different fields of research, including social, behavioral, environmental sciences, and econometrics. However, traditional least-squares-based techniques frequently used for panel data models are vulnerable to the adverse effects of data contamination or outlying observations that may result in biased and inefficient estimates and misleading statistical inference. In this study, we propose a minimum density power divergence estimation procedure for panel data regression models with random effects to achieve robustness against outliers. The robustness, as well as the asymptotic properties of the proposed estimator, are rigorously established. The finite-sample properties of the proposed method are investigated through an extensive simulation study and an application to climate data in Oman. Our results demonstrate that the proposed estimator exhibits improved performance over some traditional and robust methods in the presence of data contamination.

Empirical evaluation of overspecified asset pricing models

Empirical asset pricing models with possibly unnecessary risk factors are increasingly common. Unfortunately, they can yield misleading statistical inferences. Unlike previous studies, we estimate the identified set of SDFs and risk prices compatible with a given model’s asset pricing restrictions. We also propose tests that detect problematic situations with economically meaningless SDFs unrelated to the test assets. Empirically, we estimate linear subspaces of SDFs compatible with popular extensions of the traditional and consumption versions of the CAPM, which are typically two-dimensional. Moreover, we often find that all the SDFs in those linear spaces are uncorrelated with the test assets’ returns.

A Monte Carlo Simulation Study to Assess Estimation Methods in CFA on Ordinal Data

Likert-type scale data are ordinal data and are commonly used to measure latent constructs in the educational, social, and behavioral sciences. The ordinal observed variables are often treated as continuous variables in factor analysis, which may cause misleading statistical inferences. Two robust estimators, i.e., unweighted least square (ULS) and diagonally weighted least square (DWLS) have been developed to deal with ordinal data in confirmatory factor analysis (CFA). Using synthetic data generated in a Monte Carlo experiment, we study the behavior of these methods (DWLS and ULS) and compare their performance with normal theory-based ML and GLS (generalized least square) under different levels of experimental conditions. The simulation results indicate that both DWLS and ULS yield consistently accurate parameter estimates across all conditions considered in this study. The Likert data can be treated as a continuous variable under ML or GLS when using at least five Likert scale points to produce trivial bias. However, these methods generally fail to provide a satisfactory fit. Empirical studies in the field of psychological measurement data are reported to present how theoretical and statistical instances have to be taken into consideration when ordinal data are used in the CFA model.Keywords: confirmatory factor analysis, diagonally weighted least square, generalized least square, Likert data, maximum likelihood.

Disentangling the Influence of Data Contamination in Growth Curve Modeling: A Median Based Bayesian Approach

Growth curve models (GCMs), with their ability to directly investigate within-subject change over time and between-subject differences in change for longitudinal data, are widely used in social and behavioral sciences. While GCMs are typically studied with the normal distribution assumption, empirical data often violate the normality assumption in applications. Failure to account for the deviation from normality in data distribution may lead to unreliable model estimation and misleading statistical inferences. A robust GCM based on conditional medians was recently proposed and outperformed traditional growth curve modeling when outliers are present resulting in nonnormality. However, this robust approach was shown to perform less satisfactorily when leverage observations existed. In this work, we propose a robust double medians growth curve modeling approach (DOME GCM) to thoroughly disentangle the influence of data contamination on model estimation and inferences, where two conditional medians are employed for the distributions of the within-subject measurement errors and of random effects, respectively. Model estimation and inferences are conducted in the Bayesian framework, and Laplace distributions are used to convert the optimization problem of median estimation into a problem of obtaining the maximum likelihood estimator for a transformed model. A Monte Carlo simulation study has been conducted to evaluate the numerical performance of the proposed approach, and showed that the proposed approach yields more accurate and efficient parameter estimates when data contain outliers or leverage observations. The application of the developed robust approach is illustrated using a real dataset from the Virginia Cognitive Aging Project to study the change of memory ability.

An Overview of Modern Applications of Negative Binomial Modelling in Ecology and Biodiversity

Negative binomial modelling is one of the most commonly used statistical tools for analysing count data in ecology and biodiversity research. This is not surprising given the prevalence of overdispersion (i.e., evidence that the variance is greater than the mean) in many biological and ecological studies. Indeed, overdispersion is often indicative of some form of biological aggregation process (e.g., when species or communities cluster in groups). If overdispersion is ignored, the precision of model parameters can be severely overestimated and can result in misleading statistical inference. In this article, we offer some insight as to why the negative binomial distribution is becoming, and arguably should become, the default starting distribution (as opposed to assuming Poisson counts) for analysing count data in ecology and biodiversity research. We begin with an overview of traditional uses of negative binomial modelling, before examining several modern applications and opportunities in modern ecology/biodiversity where negative binomial modelling is playing a critical role, from generalisations based on exploiting its Poisson-gamma mixture formulation in species distribution models and occurrence data analysis, to estimating animal abundance in negative binomial N-mixture models, and biodiversity measures via rank abundance distributions. Comparisons to other common models for handling overdispersion on real data are provided. We also address the important issue of software, and conclude with a discussion of future directions for analysing ecological and biological data with negative binomial models. In summary, we hope this overview will stimulate the use of negative binomial modelling as a starting point for the analysis of count data in ecology and biodiversity studies.

Robust Bayesian growth curve modelling using conditional medians

Growth curve models have been widely used to analyse longitudinal data in social and behavioural sciences. Although growth curve models with normality assumptions are relatively easy to estimate, practical data are rarely normal. Failing to account for non-normal data may lead to unreliable model estimation and misleading statistical inference. In this work, we propose a robust approach for growth curve modelling using conditional medians that are less sensitive to outlying observations. Bayesian methods are applied for model estimation and inference. Based on the existing work on Bayesian quantile regression using asymmetric Laplace distributions, we use asymmetric Laplace distributions to convert the problem of estimating a median growth curve model into a problem of obtaining the maximum likelihood estimator for a transformed model. Monte Carlo simulation studies have been conducted to evaluate the numerical performance of the proposed approach with data containing outliers or leverage observations. The results show that the proposed approach yields more accurate and efficient parameter estimates than traditional growth curve modelling. We illustrate the application of our robust approach using conditional medians based on a real data set from the Virginia Cognitive Aging Project.

Black swan models for the entertainment industry with an application to the movie business

Success in popular entertainment is highly unpredictable. Yet it is the high-impact low-probability events—known as ‘black swans’—that drive entertainment industry profitability because success is highly concentrated on a small number of winners. In this research, we apply recently developed statistical tools to model motion-picture success; these tools explicitly account for rare extreme events while permitting valid statistical inferences to be made on how product attributes are associated with product success. The specific empirical application relates the attributes of a film and its theatrical release to the distribution of worldwide cumulative box-office revenue. A regression model with skew-stable random disturbances is applied to a large sample of motion pictures to quantify the correlates of film success while explicitly accounting for skewness and heavy tails. The skew-stable estimates are compared to estimates obtained from symmetric-stable regression, ordinary least-squares regression, and several alternative robust-to-outliers regression models. Failure to control explicitly for heavy tails and skewness generates misleading statistical inferences, particularly regarding the impact of production budget, opening week screens, and star power on a film’s success at the box-office.

The Spike-and-Slab Lasso regression modeling with compositional covariates: An application on Brazilian children malnutrition data.

There are considerable challenges in analyzing large-scale compositional data. In this paper, we introduce the Spike-and-Slab Lasso linear regression in the presence of compositional covariates for parameter estimation and variable selection. We consider the well-known isometric log-ratio (ilr) coordinates to avoid misleading statistical inference. The separable and non-separable (adaptative) Spike-and-Slab Lasso penalties are compared to verify the advantages of each approach. The proposed method is illustrated on simulated and on real Brazilian child malnutrition data.

A single-level random-effects cross-lagged panel model for longitudinal mediation analysis.

Cross-lagged panel models (CLPMs) are widely used to test mediation with longitudinal panel data. One major limitation of the CLPMs is that the model effects are assumed to be fixed across individuals. This assumption is likely to be violated (i.e., the model effects are random across individuals) in practice. When this happens, the CLPMs can potentially yield biased parameter estimates and misleading statistical inferences. This article proposes a model named a random-effects cross-lagged panel model (RE-CLPM) to account for random effects in CLPMs. Simulation studies show that the RE-CLPM outperforms the CLPM in recovering the mean indirect and direct effects in a longitudinal mediation analysis when random effects exist in the population. The performance of the RE-CLPM is robust to a certain degree, even when the random effects are not normally distributed. In addition, the RE-CLPM does not produce harmful results when the model effects are in fact fixed in the population. Implications of the simulation studies and potential directions for future research are discussed.

Finite Sample Sizes of the GRS Test in the Presence of Dynamic Correlation and Conditional Heteroskedasticity

This paper investigates the finite sample properties of the widely-used Gibbons, Ross, Shanken (1989) (GRS) test in the presence of both conditional correlation and conditional heteroskedasticity. It finds that the GRS test exhibits serious size distortions resulting in potentially misleading statistical inferences. The correct critical values, as reported in the study, are considerably larger than suggested by the GRS test.

Perceived accessibility, mobility, and connectivity of public transportation systems

Although public transportation is considered effective at reducing the external cost of driving private vehicles, many urbanites do not use public transportation. This study develops measures employing accessibility, mobility, and seamless connectivity for an entire public transportation service chain as indicators for evaluating public transport services, prioritizes underperforming scenarios from the perspective of urban travelers, and derives various market segmentation strategies that consider different socio-demographic characteristics. A conceptual model is set up herein to assess these latent constructs that describe unobservable and immeasurable characteristics. As a Likert ordinal scale can generate misleading statistical inferences, the Rasch model is used to eliminate bias generated by an ordinal scale when measuring these three latent constructs separately. The Rasch model compares person parameters with item parameters, which are then subjected to logarithmic transformation along a logit scale so as to recognize specific difficulties of service scenarios that cannot be easily eliminated by certain urban travelers. The multidimensional Rasch model also measures the perceptions of urban travelers in terms of the interactions between accessibility, mobility, and seamless connectivity of this public transportation system. While comparing urban travelers of two large cities in Taiwan, Taipei and Kaohsiung, the empirical results demonstrate that perceived accessibility, mobility, and seamless connectivity differ based on travelers’ age, frequency of weekly sports activities, and environmental awareness. This paper also advances appropriate improvement strategies and provides policy suggestions for urban planners, public transportation service operation agencies, and policy makers when they seek to create user-friendly public transportation services. The proposed approach can be generalized in other cities by considering their local context uniqueness and further evaluating their public transport services.

A skew-normal random effects model for longitudinal ordinal categorical responses with missing data

Missing values are common in longitudinal data studies. The missing data mechanism is termed non-ignorable (NI) if the probability of missingness depends on the non-response (missing) observations. This paper presents a model for the ordinal categorical longitudinal data with NI non-monotone missing values. We assumed two separate models for the response and missing procedure. The response is modeled as ordinal logistic, whereas the logistic binary model is considered for the missing process. We employ these models in the context of so-called shared-parameter models, where the outcome and missing data models are connected by a common set of random effects. It is commonly assumed that the random effect follows the normal distribution in longitudinal data with or without missing data. This can be extremely restrictive in practice, and it may result in misleading statistical inferences. In this paper, we instead adopt a more flexible alternative distribution which is called the skew-normal distribution. The methodology is illustrated through an application to Schizophrenia Collaborative Study data [19] and a simulation.

Likelihoods for fixed rank nomination networks.

Many studies that gather social network data use survey methods that lead to censored, missing, or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence of other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare Bayesian parameter estimates obtained from a likelihood for complete binary networks with those obtained from likelihoods that are derived from the FRN scheme, and therefore accommodate the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, particularly for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

Evaluating bicycle-transit users’ perceptions of intermodal inconvenience

Bicycles and transit systems are considered to be the pinnacle of green transportation. The combined use of the two could provide a competitive alternative for an integrated, green, and seamless service, yet relatively few studies have investigated the multimodal integration problems of the entire service chain from the perspective of users. Users’ perceived inconvenience during travel can be regarded as a latent construct that describes an unobservable and immeasurable characteristic. Nevertheless, the traditional Likert method in an ordinal scale causes a misleading statistical inference. The Rasch model eliminates such bias generated by an ordinal scale through a logistic linear transformation, and it compares person parameters with item parameters, which are then subjected to a logarithmic transformation along a logit scale to clearly identify which service items’ inconvenience cannot be easily overcome by certain users. This empirical study demonstrates that perceived inconveniences differ based on the users’ sex, riding frequency, trip purpose, and environmental awareness. The differential item functioning analysis that was adopted in this study can identify the critical factors leading to the differences in perceived inconvenience. Our empirical results suggest that a male cyclist who is a commuter with a high monthly riding frequency and who is environmentally conscious has a better ability than their counterpart to overcome perceived inconveniences during travel using a bicycle-transit service. To effectively mitigate users’ perceived inconvenience, the Rasch analytical results suggest that the improvement of the intra-transit system factors in the short term and the improvement of external environmental factors in the long term will be successful. The information herein proves useful for transportation planners and policy makers when considering the special travel needs of certain groups to create a user-friendly bicycle-transit travel environment that promotes its usage.

The Early Adoption of Stock Option Compensation Expense

I examine the likelihood of firms adopting the fair value based method of accounting for stock option compensation cost in 2002 and 2003. To examine this issue, I use two matched sample methodologies: (1) a size and book-to-market matching method typically employed in empirical accounting and finance research; and (2) a Propensity Score matching method typically used in the life sciences. I create a profile of firms that elected to expense employee stock option compensation when it was not yet required by Statement on Financial Standards No. 123 (Revised): Share-Based Payment (SFAS 123(R)). I find support for the general hypothesis that increasing switching costs from disclosure to recognition lowers the likelihood for stock option expense adoption in 2002 and 2003. More specifically, the likelihood of expensing stock options decreases when the magnitude of (implied) stock option expense increases and the value of options awarded to the firm's executives increases in relation to their total compensation. I find that the likelihood of expensing stock options increases when the interest coverage ratio increases and when the number of options awarded to the firm's executives increases in relation to the number of stock options awarded to all employees. I also find weak evidence that the likelihood of expensing is highest in the healthcare industry. Although these results hold under both matched sample approaches, the Propensity Score approach helps to prevent misleading statistical inference by reducing the bias inherent in traditional size and book-to-market matched sampling.

Unit roots versus other types of time heterogeneity, parameter time dependence and superexogeneity

AbstractThis paper stresses the restrictive nature of the standard unit root/cointegration assumptions and examines a more general type of time heterogeneity, which might characterize a number of economic variables, and which results in parameter time dependence and misleading statistical inference. We show that in such cases ‘operational’ models cannot be obtained, and the estimation of time‐varying parameter models becomes necessary. For instance, economic processes subject to endemic change can only be adequately modelled in a state space form. This is a very important point, because unstable models will break down when used for forecasting purposes. We also discuss a new test for the null of cointegration developed by Quintos and Phillips (1993), which is based on parameter constancy in cointegrating regressions. Finally, we point out that, if it is possible to condition on a subset of superexogenous variables, parameter instability can be handled by estimating a restricted system. Copyright © 2002 John Wiley & Sons, Ltd.

Estimating medical costs with censored data

Incompleteness of follow-up data is a common problem in estimating medical costs. Naive analysis using summary statistics on the collected data can result in severely misleading statistical inference. This paper focuses on the problem of estimating the mean medical cost from a sample of individuals whose medical costs may be right censored. A class of weighted estimators which account appropriately for censoring are introduced. Our estimators are shown to be consistent and asymptotically normal with easily estimated variances. The efficiency of these estimators is studied with the goal of finding as efficient an estimator for the mean medical cost as is feasible. Extensive simulation studies are used to show that our estimators perform well in finite samples, even with heavily censored data, for a variety of circumstances. The methods are applied to a set of cost data from a cardiology trial conducted by the Duke University Medical Center. Extensions to other censored data problems are also discussed.

Regression Analysis with Missing Covariate Data Using Estimating Equations

In regression analysis, missing covariate data has been among the most common problems. Frequently, practitioners adopt the so-called complete-case analysis, i.e., performing the analysis on only a complete dataset after excluding records with missing covariates. Performing a complete-case analysis is convenient with existing statistical packages, but it may be inefficient since the observed outcomes and covariates on those records with missing covariates are not used. It can even give misleading statistical inference if missing is not completely at random. This paper introduces a joint estimating equation (JEE) for regression analysis in the presence of missing observations on one covariate, which may be thought of as a method in a general framework for the missing covariate data problem proposed by Robins, Rotnitzky, and Zhao (1994, Journal of the American Statistical Association 89, 846-866). A generalization of JEE to more than one such covariate is discussed. The JEE is generally applicable to estimating regression coefficients from a regression model, including linear and logistic regression. Provided that the missing covariate data is either missing completely at random or missing at random (in addition to mild regularity conditions), estimates of regression coefficients from the JEE are consistent and have an asymptotic normal distribution. Simulation results show that the asymptotic distribution of estimated coefficients performs well in finite samples. Also shown through the simulation study is that the validity of JEE estimates depends on the correct specification of the probability function that characterizes the missing mechanism, suggesting a need for further research on how to robustify the estimation from making this nuisance assumption. Finally, the JEE is illustrated with an application from a case-control study of diet and thyroid cancer.