Weighting Schemes and Incomplete Data: A Generalized Bayesian Framework for Chance-Corrected Interrater Agreement

Van Oest (2019) developed a framework to assess interrater agreement for nominal categories and complete data. We generalize this framework to all four situations of nominal or ordinal categories and complete or incomplete data. The mathematical solution yields a chance-corrected agreement coefficient that accommodates any weighting scheme for penalizing rater disagreements and any number of raters and categories. By incorporating Bayesian estimates of the category proportions, the generalized coefficient also captures situations in which raters classify only subsets of items; that is, incomplete data. Furthermore, this coefficient encompasses existing chance-corrected agreement coefficients: the S-coefficient, Scott’s pi, Fleiss’ kappa, and Van Oest’s uniform prior coefficient, all augmented with a weighting scheme and the option of incomplete data. We use simulation to compare these nested coefficients. The uniform prior coefficient tends to perform best, in particular, if one category has a much larger proportion than others. The gap with Scott’s pi and Fleiss’ kappa widens if the weighting scheme becomes more lenient to small disagreements and often if more item classifications are missing; missingness biases play a moderating role. The uniform prior coefficient usually performs much better than the S-coefficient, but the S-coefficient sometimes performs best for small samples, missing data, and lenient weighting schemes. The generalized framework implies a new interpretation of chance-corrected weighted agreement coefficients: These coefficients estimate the probability that both raters in a pair assign an item to its correct category without guessing. Whereas Van Oest showed this interpretation for unweighted agreement, we generalize to weighted agreement.

Coefficients estimate for a subclass of holomorphic mappings on the unit polydisk in Cn

The aim of this paper is to obtain the sharp solutions of Fekete-Szeg? problems of high dimensional version for family of holomorphic mappings that are normalized on the unit polydisk Un in Cn. The main results unify some recent works, which are closely related to the starlike mappings. Moreover, some previous results are improved.

On Certain Class of Bazilevič Functions Associated with the Lemniscate of Bernoulli

Making use of the principle of subordination, we introduce a certain class of multivalently Bazilevi c ˘ functions involving the Lemniscate of Bernoulli. Also, we obtain subordination properties, inclusion relationship, convolution result, coefficients estimate, and Fekete–Szegö problem for this class.

Some properties of univalent log-harmonic mappings

We determine the representation theorem, distortion theorem, coefficients estimate and Bohr?s radius for log-harmonic starlike mappings of order ?, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of 1-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch?s norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained.

Model-averaged regression coefficients have a straightforward interpretation using causal conditioning

Model-averaged regression coefficients have been criticized for averaging over a set of models with parameters that have different meanings from model to model. This criticism arises because of confusion between two different parameters estimated by the coefficients of a statistical model.Ever since Fisher, the textbook definition of a coefficient (a “differences in conditional means”) takes its meaning from probabilistic conditioning (P(Y|X)). Because the parameter estimated with probabilistic conditioning is conditional on a specific set of covariates, its meaning varies from model to model.The coefficients in many applied statistical models, however, take their meaning from causal conditioning (P(Y|do(X))) and these coefficients estimate causal effect parameters (or simply, causal effects or Average Treatment Effects). Causal effect parameters are also differences in conditional expectations, but the event conditioned on is not the set of covariates in a statistical model but a hypothetical intervention. Because an effect parameter takes its meaning from causal and not probabilistic conditioning, it is the same from model to model, and an averaged coefficient has a straightforward interpretation as an estimate of a causal effect.Because an effect parameter is the same from model to model, the estimates of the parameter will generally be biased. By contrast, with probabilistic conditioning, the coefficients are consistent estimates of their parameter in every model, but the parameter differs from model to model. Confounding and omitted variable bias, which are central to explanatory modeling, are meaningless in statistical modeling as mere description.The argument developed here only addresses the “different parameters” criticism of model-averaged coefficients and is not advocating model averaging more generally.