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Local structural equation models (LSEM) are structural equation models that study model parameters as a function of a moderator. This article reviews and extends LSEM estimation methods and discusses the implementation in the R package sirt. In previous studies, LSEM was fitted as a sequence of models separately evaluated as each value of the moderator variables. In this article, a joint estimation approach is proposed that is a simultaneous estimation method across all moderator values and also allows some model parameters to be invariant with respect to the moderator. Moreover, sufficient details on the main estimation functions in the R package sirt are provided. The practical implementation of LSEM is demonstrated using illustrative datasets and an empirical example. Moreover, two simulation studies investigate the statistical properties of parameter estimation and significance testing in LSEM. [ABSTRACT FROM AUTHOR]

This paper deals with a new Bayesian approach to the one-sample test for proportion. More specifically, let x = (x 1 , ... , x n) be an independent random sample of size n from a Bernoulli distribution with an unknown parameter θ. For a fixed value θ 0 , the goal is to test the null hypothesis H 0 : θ = θ 0 against all possible alternatives. The proposed approach is based on using the well-known formula of the Kullback–Leibler divergence between two binomial distributions chosen in a certain way. Then, the difference of the distance from a priori to a posteriori is compared through the relative belief ratio (a measure of evidence). Some theoretical properties of the method are developed. Examples and simulation results are included. [ABSTRACT FROM AUTHOR]