For any positive integer n, let SL(n) denotes the least positive integer k such that L(k) ≡ 0 (mod n), where L(k) denotes the Least Common Multiple of all integers from 1 to k. The main purpose of this paper is to study the properties of the Smarandache LCM function SL(n), and give an asymptotic formula for its mean value.

Previous work by the author used Markov Latent Class Analysis (MLCA) to make aggregate estimates of the underreporting of household expenditure by category (e.g. clothes, furniture, and electricity) by exploiting the four interview, rotating panel design of the Consumer Expenditure Interview Survey (CE). This analysis collapsed a few years of the CE into a pooled single panel. Estimates from th...

This paper addresses the issue of classification uncertainty in latent class analysis. It proposes a new bootstrap-based approach for quantifying the level of classification uncertainty at both the individual and the aggregate level. The procedure is illustrated by means of two applications.

We inspect digit stroke sets in LCM UpWrite space.

The Linguistic Category Model (LCM) was developed as a manual coding scheme for quantifying abstract mindsets in human language. Previous attempts to computationally automate the LCM have relied primarily on pre-coded semantic features, which fail to incorporate important contextual information integral to the LCM coding scheme. In this paper, we introduce Syntax-LCM, a novel method for automat...

Latent class and the Grade of Membership (GoM) models are two examples of latent structure models. Latent class models are discrete mixture models. The GoM model has been originally developed as an extension of latent class models to a continuous mixture. This note describes a constrained latent class model which is equivalent to the GoM model, and provides a detailed proof of this equivalence....

The purpose of this dissertation is to present a new psychometric model that combines a Mixture Rasch model with a diagnostic model. We refer to this model as a diagnostic classification mixture Rasch model (DCMixRM). The motivation for the development of the DCMixRM is twofold. First, the DCMixRM is designed to provide rigorous explanation as to factors that are potentially causing the latent ...

In this paper two scales of a personality questionnaire, extraversion and neuroticism, are analyzed using a family of latent trait latent class models. The items are responded to in one of three categories: “yes”, “?”, or “no”. The results show that one single measurement model does not suffice in describing the data. More specifically, the meaning of the “?” response category is not invariant ...