Misspecified Discrete Choice Models and Huber-White Standard Errors

BackgroundLog-binomial and robust (modified) Poisson regression models are popular approaches to estimate risk ratios for binary response variables. Previous studies have shown that comparatively they produce similar point estimates and standard errors. However, their performance under model misspecification is poorly understood.MethodsIn this simulation study, the statistical performance of the two models was compared when the log link function was misspecified or the response depended on predictors through a non-linear relationship (i.e. truncated response).ResultsPoint estimates from log-binomial models were biased when the link function was misspecified or when the probability distribution of the response variable was truncated at the right tail. The percentage of truncated observations was positively associated with the presence of bias, and the bias was larger if the observations came from a population with a lower response rate given that the other parameters being examined were fixed. In contrast, point estimates from the robust Poisson models were unbiased.ConclusionUnder model misspecification, the robust Poisson model was generally preferable because it provided unbiased estimates of risk ratios.

In random-effects models, hierarchical linear models, or multilevel models, it is typically assumed that the variances within higher-level units are homoscedastic, meaning that they are equal across these units. However, this assumption is often violated in research. Depending on the degree of violation, this can lead to biased standard errors of higher-level parameters and thus to incorrect inferences. In this article, we describe a resampling technique for obtaining standard errors—Zitzmann’s jackknife. We conducted a Monte Carlo simulation study to compare the technique with the commonly used delete-1 jackknife, the robust standard error in Mplus, and a modified version of the commonly used delete-1 jackknife. Findings revealed that the resampling techniques clearly outperformed the robust standard error in rather small samples with high levels of heteroscedasticity. Moreover, Zitzmann’s jackknife tended to perform somewhat better than the two versions of the delete-1 jackknife and was much faster.

Research studying robustness of maximum likelihood (ML) statistics in covariance structure analysis has concluded that test statistics and standard errors are biased under severe non-normality. An estimation procedure known as asymptotic distribution free (ADF), making no distributional assumption, has been suggested to avoid these biases. Corrections to the normal theory statistics to yield more adequate performance have also been proposed. This study compares the performance of a scaled test statistic and robust standard errors for two models under several non-normal conditions and also compares these with the results from ML and ADF methods. Both ML and ADF test statistics performed rather well in one model and considerably worse in the other. In general, the scaled test statistic seemed to behave better than the ML test statistic and the ADF statistic performed the worst. The robust and ADF standard errors yielded more appropriate estimates of sampling variability than the ML standard errors, which were usually downward biased, in both models under most of the non-normal conditions. ML test statistics and standard errors were found to be quite robust to the violation of the normality assumption when data had either symmetric and platykurtic distributions, or non-symmetric and zero kurtotic distributions.

The consistency of propensity score (PS) estimators relies on correct specification of the PS model. The PS is frequently estimated using main-effects logistic regression. However, the underlying model assumptions may not hold. Machine learning methods provide an alternative nonparametric approach to PS estimation. In this simulation study, we evaluated the benefit of using Super Learner (SL) for PS estimation. We created 1,000 simulated data sets (n = 500) under 4 different scenarios characterized by various degrees of deviance from the usual main-term logistic regression model for the true PS. We estimated the average treatment effect using PS matching and inverse probability of treatment weighting. The estimators' performance was evaluated in terms of PS prediction accuracy, covariate balance achieved, bias, standard error, coverage, and mean squared error. All methods exhibited adequate overall balancing properties, but in the case of model misspecification, SL performed better for highly unbalanced variables. The SL-based estimators were associated with the smallest bias in cases of severe model misspecification. Our results suggest that use of SL to estimate the PS can improve covariate balance and reduce bias in a meaningful manner in cases of serious model misspecification for treatment assignment.

Discrete Choice Modeling for the Quantification of Health States: The Case of the EQ-5D

Computing the mean square error of unobserved components extracted by misspecified time series models

Discrete choice models are a group of models that are used to analyze choice data basically because they accommodate the nature of the process that generates the data. The most common types of discrete models include the logit, probit, multinomial logit, nested logit, mixed logit and most recently the generalized multinomial logit. Discrete choice models have been mostly used in the area economics, transportation, energy, psychology, etc. Prediction in these models isn\\'t uncommon, in contexts such as engineering, marketing, and production, discrete choice models are mostly used to forecast demand. Unfortunately, for out-of-sample prediction at the individual level for complex models such as mixed logit, which involves predicting the random effects/parameters, there isn\\'t any work found in literature. Thus, in this is work we propose a method for this scenario in mixed logit discrete models using the nearest neighbour concept. We carry out various simulations and then apply on two types of real-life data. We find that the prediction accuracy of this new method is better than the rudimentary method of using the population parameters especially when the model fitted isn\\'t the very best.

This paper analyzes and synthesizes the fundamentals of discrete choice models. This paper alsodiscusses the basic concept and theory underlying the econometrics of discrete choice, specific choicemodels, estimation method, model building and tests, and applications of discrete choice models. Thiswork highlights the relationship between economic theory and discrete choice models: how economictheory contributes to choice modeling and vice versa.
 Keywords: Discrete choice models; Random utility maximization; Decision makers; Utility function;Model formulation

Previous work has documented that ignoring product stockouts in estimating discrete choice models of demand leads to biased estimates of the taste parameters. We investigate the relation between the taste bias and the economic primitives of the choice environment. In a setting with vertically differentiated products, we simulate choice data under limited product availability and estimate two econometric specifications, one that incorrectly assumes alternatives are unconstrained and the second one that incorporates the data on the exhaustion of alternatives. Assuming all products are always available leads to a taste coefficient bias that can be as large as 100 % of the true parameter. The taste coefficient is underestimated, and the bias decreases (in magnitude) with the number of alternatives and increases with the severity of the constraints and product differentiation. Moreover, when capacity constraints are severe, we find a tradeoff between bias and precision: the misspecified model is more precise but biased, while the correct model is unbiased but less precise. The tradeoff vanishes as constraints relax, even though exhaustions remain possible.

This study investigates the interconnections among sustainability reporting, social performance, and firm value across the BRICS nations (Brazil, Russia, India, China, and South Africa). Employing a quantitative research design, the study utilizes firm-level data from the Refinitiv database, covering 862 firms operating in the BRICS countries from 2017 to 2022. The analysis begins with Ordinary Least Squares (OLS) regression and extends to models incorporating year-fixed effects and firm-fixed effects to account for heterogeneity and omitted variable bias. Robustness checks are conducted using OLS regression with robust standard errors, fixed effects regression with Driscoll–Kraay standard errors, and an instrumental variable approach to address potential endogeneity concerns. To examine the moderating role of sustainability reporting, interaction terms are incorporated into the regression models and margin plots are used for visualization. The findings reveal that social performance positively impacts firm value, underscoring the role of social responsibility in driving financial performance. Furthermore, sustainability reporting strengthens this relationship, indicating that firms with well-established reporting frameworks can effectively leverage social initiatives to enhance market valuation. Therefore, this study contributes to the literature by providing empirical evidence on the moderating effect of sustainability reporting in emerging markets. The findings offer valuable implications for policymakers, investors, and corporate leaders seeking to optimize CSR strategies and enhance firm value in dynamic economic environments.

When the multivariate normality assumption is violated in structural equation modeling, a leading remedy involves estimation via normal theory maximum likelihood with robust corrections to standard errors. We propose that this approach might not be best for forming confidence intervals for quantities with sampling distributions that are slow to approach normality, or for functions of model parameters. We implement and study a robust analog to likelihood-based confidence intervals based on inverting the robust chi-square difference test of Satorra (2000). We compare robust standard errors and the robust likelihood-based approach versus resampling methods in confirmatory factor analysis (Studies 1 & 2) and mediation analysis models (Study 3) for both single parameters and functions of model parameters, and under a variety of nonnormal data generation conditions. The percentile bootstrap emerged as the method with the best calibrated coverage rates and should be preferred if resampling is possible, followed by the robust likelihood-based approach.

Of the Jewish inhabitants of Amsterdam 25.9% survived the Holocaust. However, different cultural and socio-economic groups within the Jewish community may have had different social resources and different chances of survival. To determine social resources by studying a random sample of 7,665 Jews living in Amsterdam on the eve of the destruction of Dutch Jewry. Binary logistic regression models are used to test several hypotheses and express odds ratios. As some types of social resources may be interrelated, multivariable analyses are used. There were basically two ways of avoiding deportation to the death camps: going into hiding or acquiring protected status. The latter option was open chiefly to Jews having German nationality. In the analyses a higher survival rate correlates with holding German nationality, however is not significant when job status is included. Survival correlates strongly with having relations with non-Jews. The results were controlled for marital status, number of children, age below 15 years and gender. Standard errors and P-values were adjusted for family relationship by using robust standard error analyses. Survival correlates most strongly with having close social ties with non-Jews. Although Jews could sometimes acquire protected status, this was no more than temporary. In order to survive, Jews needed someone who was a non-Jew to hide them and provide support.

This study examines the effect of Research and Development (R&D) intensity on firm value in Southeast Asia, with a focus on the moderating role of business strategy. Panel regression was applied to unbalanced data from non-financial companies listed on Southeast Asian stock exchanges during 2017-2024, analyzed using OLS with robust standard errors in STATA 17. The results indicate that R&D intensity positively and significantly influences firm value. Both cost leadership and product differentiation strategies significantly moderate this relationship, strengthening the impact of innovation investment on market value. Robustness tests using cluster-robust standard errors and one-year lag regression reinforce the findings and confirm their regional relevance. The main contribution lies in integrating business strategy as a moderator, enriching the literature on innovation and strategy in enhancing firm value. Practical implications emphasize the importance of aligning R&D management with appropriate business strategies to optimize competitiveness and market value. Policy support through fiscal incentives, intellectual property protection, and innovation capacity building is essential to foster the successful implementation of these strategies. Thus, firms can develop innovative, efficient, and sustainable business ecosystems in the digital and global era.

In many African countries, burn injuries often lead to chronic disability, psychological trauma and socio-economic hardship. These consequences have a long-term impact on people’s well-being and livelihoods. It is argued that the contributions of selected socio-structural determinants to burns are an important focus especially for population prevention measures. Therefore, this study examines the contribution of key socio-structural determinants to the non-fatal burden of burn injuries in Africa, with a focus on social inequality, informal housing and access to clean cooking energy technologies. The study applies the panel correlated standard errors regression, ordinary least squares regression with robust standard errors with adjusted predictions and marginal effects plots, and the least squares dummy variables analysis using panel data of all five regions of Africa for the period 2000–2022. The study finds that social inequality and informal housing exacerbate the burden of burn injuries in Africa. Conversely, access to clean cooking energy technology reduces this burden. The findings are confirmed by robustness checks. In this regard, the study recommends policies that lower structural inequities to reduce the risk of burns for vulnerable populations. This involves concretizing strategies to reduce poverty and providing more appropriately targeted social safety nets. There is also a need for region-specific strategies that tackle inequality, improve energy accessibility, and enhance housing conditions as a means of mitigating burn-related hazards across Africa.

Robust standard errors are of central importance in confirmatory factor models. In calculating these statistics a central ingredient is the inverse of the asymptotic covariance matrix of second-order moments calculated under the assumption of normality. Currently, two ways of estimating this matrix are employed in software packages. One approach uses the sample covariance matrix, the other the model-implied covariance matrix. Previous research based on a small confirmatory factor model demonstrated that the latter approach yielded a slight improvement in standard error performance. The present study argues theoretically that the discrepancy between the two approaches increases in models where there are few model parameters relative to , where is the number of observed variables. We present simulation results that support this claim, in both small and large correctly specified models, across a large variety of non-normal conditions. We recommend the model-implied covariance matrix for robust standard error computation.