In a hierarchical or fixed-order regression analysis, the independent variables are entered into the regression equation in a prespecified order. Such an analysis is often performed when the extra amount of variance accounted for in a dependent variable by a specific independent variable is the main focus of interest (e.g., Cohen & Cohen, 1983). For example, in the area of reading achievement, ...

We introduce permissive nominal terms. Nominal terms extend first-order terms with binding. They lack properties of firstand higher-order terms: Terms must be reasoned on in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; and it is not always possible to ‘alpha-convert a bound variable symbol’. Permissive nominal terms reco...

In this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language L, then, clearly, any definable subset S ⊂ M (i.e., a subset S = {a | M |= φ(a)} defined by some formula φ) is invariant under all automorphisms of ...

A positive rst-order formula is bounded if the sequence of its stages converges to the least xed point of the formula within a xed nite number of steps independent of the input structure. The boundedness problem for a fragment L of rst-order logic is the following decision problem: given a positive formula in L, is it bounded? In this paper, we investigate the boundedness problem for two-variab...

E-matching is the most commonly used technique to handle quantifiers in SMT solvers. It works by identifying characteristic subexpressions of quantified formulae, named triggers, which are matched during proof search on ground terms to discover relevant instantiations of the quantified formula. E-matching has proven to be an efficient and practical approach to handle quantifiers, in particular ...

let f, g and h be all entire functions of several complex variables. in this paper we would like to establish some inequalities on the basis of relative order and relative lower order of f with respect to g when the relative orders and relative lower orders of both f and g with respect to h are given.

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are hidden. The currently most efficient algorithm for learning HLC models can deal with only a few dozen observed variables. While this is sufficient for some applications, more efficient algorithms are needed for domains with, e.g., hundreds of observed variables. Wi...

We consider a semi-nonparametric specification for the density of latent variables in Generalized Linear Latent Variable Models (GLLVM). This specification is flexible enough to allow for an asymmetric, multi-modal, heavy or light tailed smooth density. The degree of flexibility required by many applications of GLLVM can be achieved through the semi-nonparametric specification with a finite num...

We then went on to introduce mean field variational inference, in which the variational distribution over latent variables is assumed to factor as a product of functions over each latent variable. In this sense, the joint approximation is made using the simplifying assumption that all latent variables are independent. Alternatively, we can use approximations in which only groups of variables ar...