AStA Advances in Statistical Analysis

This paper proposes a hierarchical Bayes estimator for a panel data random coefficient model with heteroskedasticity to assess the contribution of R&D capital to total factor productivity. Based on Hall (1993) data for 323 US firms over 1976–1990, we find that there appear to have substantial unobserved heterogeneity and heteroskedasticity across firms and industries that support the use of our Bayes inference procedure. We find much higher returns to R&D capital and a more pronounced downswing for the 1981–1985 period, followed by a more pronounced upswing than those yielded by the conventional feasible generalized least squares estimators or other estimates. The estimated elasticities of R&D capital are 0.062 for 1976–1980, 0.036 for 1981–1985 and 0.081 for 1986–1990, while the estimated elasticities of ordinary capital are much more stable over these periods.

Multinomial choice models are used for the analysis of unordered, mutually exclusive choice alternatives. Conventionally used multinomial choice models are the multinomial logit, nested logit, multinomial probit and random parameters logit models. This paper develops multinomial choice models based on Archimedean copulas. In contrast to the multinomial logit and nested logit models, no independence of irrelevant alternatives property is implied. Moreover, copula-based multinomial choice models are more parsimonious than the multinomial probit and random parameters logit models, which makes them attractive from a computational point of view and makes them particularly suitable for prediction purposes. When the number of alternatives becomes large, additional complexity can be introduced using nested Archimedean copulas. Nested structures can often be motivated from individual behavior. The paper also considers an empirical application to travel mode choice. It is found that copula-based multinomial choice models provide a good compromise between fit and parsimony.

The analysis of time-indexed categorical data is important in many fields, e.g., in telecommunication network monitoring, manufacturing process control, ecology, etc. Primary interest is in detecting and measuring serial associations and dependencies in such data. For cardinal time series analysis, autocorrelation is a convenient and informative measure of serial association. Yet, for categorical time series analysis an analogous convenient measure and corresponding concepts of weak stationarity have not been provided. For two categorical variables, several ways of measuring association have been suggested. This paper reviews such measures and investigates their properties in a serial context. We discuss concepts of weak stationarity of a categorical time series, in particular of stationarity in association measures. Serial association and weak stationarity are studied in the class of discrete ARMA processes introduced by Jacobs and Lewis (J. Time Ser. Anal. 4(1):19–36, 1983).

We find that existing multiple imputation procedures that are currently implemented in major statistical packages and that are available to the wide majority of data analysts are limited with regard to handling incomplete panel data. We review various missing data methods that we deem useful for the analysis of incomplete panel data and discuss, how some of the shortcomings of existing procedures can be overcome. In a simulation study based on real panel data, we illustrate these procedures’ quality and outline fruitful avenues of future research.

Partially rank-ordered set (PROS) sampling is a generalization of ranked set sampling in which rankers are not required to fully rank the sampling units in each set, hence having more flexibility to perform the necessary judgemental ranking process. The PROS sampling has a wide range of applications in different fields ranging from environmental and ecological studies to medical research and it has been shown to be superior over ranked set sampling and simple random sampling for estimating the population mean. We study Fisher information content and uncertainty structure of the PROS samples and compare them with those of simple random sample (SRS) and ranked set sample (RSS) counterparts of the same size from the underlying population. We study uncertainty structure in terms of the Shannon entropy, Rényi entropy and Kullback–Leibler (KL) discrimination measures.

The objective of advanced topic modeling is not only to explore latent topical structures, but also to estimate relationships between the discovered topics and theoretically relevant metadata. Methods used to estimate such relationships must take into account that the topical structure is not directly observed, but instead being estimated itself in an unsupervised fashion, usually by common topic models. A frequently used procedure to achieve this is the method of composition, a Monte Carlo sampling technique performing multiple repeated linear regressions of sampled topic proportions on metadata covariates. In this paper, we propose two modifications of this approach: First, we substantially refine the existing implementation of the method of composition from the R package stm by replacing linear regression with the more appropriate Beta regression. Second, we provide a fundamental enhancement of the entire estimation framework by substituting the current blending of frequentist and Bayesian methods with a fully Bayesian approach. This allows for a more appropriate quantification of uncertainty. We illustrate our improved methodology by investigating relationships between Twitter posts by German parliamentarians and different metadata covariates related to their electoral districts, using the structural topic model to estimate topic proportions.

The problem of testing for the parametric form of the conditional variance is considered in a fully nonparametric regression model. A test statistic based on a weighted $$L_2$$ -distance between the empirical characteristic functions of residuals constructed under the null hypothesis and under the alternative is proposed and studied theoretically. The null asymptotic distribution of the test statistic is obtained and employed to approximate the critical values. Finite sample properties of the proposed test are numerically investigated in several Monte Carlo experiments. The developed results assume independent data. Their extension to dependent observations is also discussed.

Quantile regression models are typically used for modeling non-Gaussian outcomes, and such models allow quantile-specific inference. While there exists a vast literature on conditional quantile regression (where the model parameters are estimated precisely for one prefixed quantile level), relatively less work has been reported on joint quantile regression. The challenge in joint quantile regression is to avoid quantile crossing while estimating multiple quantiles simultaneously. In this article, we propose a semi-parametric approach of handling non-Gaussian zero-inflated and incomplete longitudinal outcomes. We use a two-part model for handling the excess zeros, and propose a dynamic joint quantile regression model for the nonzero outcomes. A multinomial probit model is used for modeling the missingness. We develop a Bayesian joint estimation method where the model parameters are estimated through Markov Chain Monte Carlo. The unknown distribution of the outcome can be constructed based on the estimated quantiles. We analyze data from the health and retirement study and model the out-of-pocket medical expenditure through the proposed joint quantile regression method. Simulation studies are performed to assess the practical usefulness and efficiency of the proposed approach compared to the existing methods.