A Noncentral Lindley Construction Illustrated in an INAR(1) Environment

This paper proposes a previously unconsidered generalization of the Lindley distribution by allowing for a measure of noncentrality. Essential structural characteristics are investigated and derived in explicit and tractable forms, and the estimability of the model is illustrated via the fit of this developed model to real data. Subsequently, this model is used as a candidate for the parameter of a Poisson model, which allows for departure from the usual equidispersion restriction that the Poisson offers when modelling count data. This Poisson-noncentral Lindley is also systematically investigated and characteristics are derived. The value of this count model is illustrated and implemented as the count error distribution in an integer autoregressive environment, and juxtaposed against other popular models. The effect of the systematically-induced noncentrality parameter is illustrated and paves the way for future flexible modelling not only as a standalone contender in continuous Lindley-type scenarios but also in discrete and discrete time series scenarios when the often-encountered equidispersed assumption is not adhered to in practical data environments.

A universal probabilistic spike count model reveals ongoing modulation of neural variability

Neural responses are variable: even under identical experimental conditions, single neuron and population responses typically differ from trial to trial and across time. Recent work has demonstrated that this variability has predictable structure, can be modulated by sensory input and behaviour, and bears critical signatures of the underlying network dynamics and computations. However, current methods for characterising neural variability are primarily geared towards sensory coding in the laboratory: they require trials with repeatable experimental stimuli and behavioural covariates. In addition, they make strong assumptions about the parametric form of variability, rely on assumption-free but data-inefficient histogram-based approaches, or are altogether ill-suited for capturing variability modulation by covariates. Here we present a universal probabilistic spike count model that eliminates these shortcomings. Our method builds on sparse Gaussian processes and can model arbitrary spike count distributions (SCDs) with flexible dependence on observed as well as latent covariates, using scalable variational inference to jointly infer the covariate-to-SCD mappings and latent trajectories in a data efficient way. Without requiring repeatable trials, it can flexibly capture covariate-dependent joint SCDs, and provide interpretable latent causes underlying the statistical dependencies between neurons. We apply the model to recordings from a canonical non-sensory neural population: head direction cells in the mouse. We find that variability in these cells defies a simple parametric relationship with mean spike count as assumed in standard models, its modulation by external covariates can be comparably strong to that of the mean firing rate, and slow low-dimensional latent factors explain away neural correlations. Our approach paves the way to understanding the mechanisms and computations underlying neural variability under naturalistic conditions, beyond the realm of sensory coding with repeatable stimuli.

Reliability of researcher capacity estimates and count data dispersion: a comparison of Poisson, negative binomial, and Conway-Maxwell-Poisson models

Item-response models from the psychometric literature have been proposed for the estimation of researcher capacity. Canonical items that can be incorporated in such models to reflect researcher performance are count data (e.g., number of publications, number of citations). Count data can be modeled by Rasch’s Poisson counts model that assumes equidispersion (i.e., mean and variance must coincide). However, the mean can be larger as compared to the variance (i.e., underdispersion), or b) smaller as compared to the variance (i.e., overdispersion). Ignoring the presence of overdispersion (underdispersion) can cause standard errors to be liberal (conservative), when the Poisson model is used. Indeed, number of publications or number of citations are known to display overdispersion. Underdispersion, however, is far less acknowledged in the literature. In the current investigation the flexible Conway-Maxwell-Poisson count model is used to examine reliability estimates of capacity in relation to various dispersion patterns. It is shown, that reliability of capacity estimates of inventors drops from .84 (Poisson) to .68 (Conway-Maxwell-Poisson) or .69 (negative binomial). Moreover, with some items displaying overdispersion and some items displaying underdispersion, the dispersion pattern in a reanalysis of Mutz and Daniel’s (2018b) researcher data was found to be more complex as compared to previous results. To conclude, a careful examination of competing models including the Conway-Maxwell-Poisson count model should be undertaken prior to any evaluation and interpretation of capacity reliability. Moreover, this work shows that count data psychometric models are well suited for decisions with a focus on top researchers, because conditional reliability estimates (i.e., reliability depending on the level of capacity) were highest for the best researchers.

Aggregating multiple ordinal rankings in engineering design: the best model according to the Kendall’s coefficient of concordance

Aggregating the preferences of a group of experts is a recurring problem in several fields, including engineering design; in a nutshell, each expert formulates an ordinal ranking of a set of alternatives and the resulting rankings should be aggregated into a collective one. Many aggregation models have been proposed in the literature, showing strengths and weaknesses, in line with the implications of Arrow's impossibility theorem. Furthermore, the coherence of the collective ranking with respect to the expert rankings may change depending on: (i) the expert rankings themselves and (ii) the aggregation model adopted. This paper assesses this coherence for a variety of aggregation models, through a recent test based on the Kendall's coefficient of concordance (W), and studies the characteristics of those models that are most likely to achieve higher coherence. Interestingly, the so-called Borda count model often provides best coherence, with some exceptions in the case of collective rankings with ties. The description is supported by practical examples.

Gendered Polarization and Abortion Policymaking in the States

Widening, asymmetric polarization is evident in both the U.S. Congress and state legislatures. Recent work unveils a new dimension to this polarization story: newly elected Republican women are driving this polarization. Women are more likely to legislate on women’s issues than men, yet women’s shared interest in representing women doesn’t preclude their identity as partisans. In this article, we explore the effect of today’s political climate on state legislators’ policy representation of women’s issues. We ask what effect does gendered polarization have on women’s issues? To test this, we evaluate bill sponsorship in the states on the quintessential “women’s issue” of abortion. Our research design focuses on bill introductions and uses on an original dataset of pro- and anti-abortion rights bill introductions, which we analyze using an event count model. We find that overall polarization leads to the introduction of fewer restrictive abortion bills, but as polarization between women lawmakers grows, legislators are more likely to introduce anti-abortion rights legislation. Gender polarization has consequences on the types of bills legislators introduce and for how scholars should study polarization.