Consider a generalized linear model with a canonical link function, containing both fixed and random effects. In this paper, we consider inference about the fixed effects based on a conditional likelihood function. It is shown that this conditional likelihood function is valid for any distribution of the random effects and, hence, the resulting inferences about the fixed effects are insensitive...

The analysis of non-Gaussian time series has been studied extensively and has many applications. Many successful models can be viewed as special cases or variations of the generalized autoregressive moving average (GARMA) models of Benjamin et al. (2003), where a link function similar to that used in generalized linear models is introduced and the conditional mean, under the link function, assu...

The usual definition of R (variance of the predicted values divided by the variance of the data) has a problem for Bayesian fits, as the numerator can be larger than the denominator. We propose an alternative definition similar to one that has appeared in the survival analysis literature: the variance of the predicted values divided by the variance of predicted values plus the variance of the e...

The Com-Poisson (CMP) model is one of the most popular discrete generalized linear models (GLMS) that handles both equi-, overand under-dispersed data. In longitudinal context, an integer-valued autoregressive (INAR(1)) process that incorporates covariate specification has been developed to model longitudinal CMP counts. However, the joint likelihood CMP function is difficult to specify and thu...

The present paper investigates the word order alternation of English transitive phrasal verbs such as, e.g., to pick up the book versus to pick the book up. It builds on traditional monofactorial analyses, but argues that previously used methods of analysis are grossly inadequate to describe, explain and predict the word order choice by native speakers. A hypothesis integrating virtually all re...

Data with an array structure are common in statistics, and the design or regression matrix for analysis of such data can often be written as a Kronecker product. Factorial designs, contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models. In such a setting, we develop an arithmetic of arrays which allows us to define the expectation of...