Mean-parametrized Conway-Maxwell-Poisson regression models for dispersed counts

Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to directly model the mean of counts, making them not compatible with nor comparable to competing count regression models, such as the log-linear Poisson, negative-binomial or generalized Poisson regression models. This note illustrates how CMP distributions can be parametrized via the mean, so that simpler and more easily-interpretable mean-models can be used, such as a log-linear model. Other link functions are also available, of course. In addition to establishing attractive theoretical and asymptotic properties of the proposed model, its good finite-sample performance is exhibited through various examples and a simulation study based on real datasets. Moreover, the MATLAB routine to fit the model to data is demonstrated to be up to an order of magnitude faster than the current software to fit standard CMP models, and over two orders of magnitude faster than the recently proposed hyper-Poisson model.Comment: To appear in Statistical Modelling: An International Journa

Estimating and explaining efficiency in a multilevel setting: A robust two-stage approach

Various applications require multilevel settings (e.g., for estimating fixed and random effects). However, due to the curse of dimensionality, the literature on non-parametric efficiency analysis did not yet explore the estimation of performance drivers in highly multilevel settings. As such, it lacks models which are particularly designed for multilevel estimations. This paper suggests a semi-parametric two-stage framework in which, in a first stage, non-parametric a effciency estimators are determined. As such, we do not require any a priori information on the production possibility set. In a second stage, a semiparametric Generalized Additive Mixed Model (GAMM) examines the sign and significance of both discrete and continuous background characteristics. The proper working of the procedure is illustrated by simulated data. Finally, the model is applied on real life data. In particular, using the proposed robust two-stage approach, we examine a claim by the Dutch Ministry of Education in that three out of the twelve Dutch provinces would provide lower quality education. When properly controlled for abilities, background variables, peer group and ability track effects, we do not observe differences among the provinces in educational attainments.Productivity estimation; Multilevel setting; Generalized Additive Mixed Model; Education; Social segregation

Nonparametric estimation of mean and dispersion functions in extended generalized linear models.

In this paper the interest is in regression analysis for data that show possibly overdispersion or underdispersion. The starting point for modeling are generalized linear models in which we no longer admit a linear form for the mean regression function, but allow it to be any smooth function of the covariate(s). In view of analyzing overdispersed or underdispersed data, we additionally bring in an unknown dispersion function. The mean regression function and the dispersion function are then estimated using P-splines with difference type of penalty to prevent from overfitting. We discuss two approaches: one based on an extended quasi-likelihood idea and one based on a pseudo-likelihood approach. The choices of smoothing parameters and implementation issues are discussed. The performance of the estimation method is investigated via simulations and its use is illustrated on several data, including continuous data, counts and proportions.Double exponential family; Extended quasi-likelihood; Modeling; Overdispersion; Pseudo likelihood; P-splines; Regression; Variance estimation; Underdispersion;

Strong succession in arbuscular mycorrhizal fungal communities.

The ecology of fungi lags behind that of plants and animals because most fungi are microscopic and hidden in their substrates. Here, we address the basic ecological process of fungal succession in nature using the microscopic, arbuscular mycorrhizal fungi (AMF) that form essential mutualisms with 70-90% of plants. We find a signal for temporal change in AMF community similarity that is 40-fold stronger than seen in the most recent studies, likely due to weekly samplings of roots, rhizosphere and soil throughout the 17 weeks from seedling to fruit maturity and the use of the fungal DNA barcode to recognize species in a simple, agricultural environment. We demonstrate the patterns of nestedness and turnover and the microbial equivalents of the processes of immigration and extinction, that is, appearance and disappearance. We also provide the first evidence that AMF species co-exist rather than simply co-occur by demonstrating negative, density-dependent population growth for multiple species. Our study shows the advantages of using fungi to test basic ecological hypotheses (e.g., nestedness v. turnover, immigration v. extinction, and coexistence theory) over periods as short as one season