Influence analysis for the factor analysis model with ranking data

Abstract

Influence analysis is an important component of data analysis, and the local influence approach has been widely applied to many statistical models to identify influential observations and assess minor model perturbations since the pioneering work of Cook (1986). The approach is often adopted to develop influence analysis procedures for factor analysis models with ranking data. However, as this well-known approach is based on the observed data likelihood, which involves multidimensional integrals, directly applying it to develop influence analysis procedures for the factor analysis models with ranking data is difficult. To address this difficulty, a Monte Carlo expectation and maximization algorithm (MCEM) is used to obtain the maximum-likelihood estimate of the model parameters, and measures for influence analysis on the basis of the conditional expectation of the complete data log likelihood at the E-step of the MCEM algorithm are then obtained. Very little additional computation is needed to compute the influence measures, because it is possible to make use of the by-products of the estimation procedure. Influence measures that are based on several typical perturbation schemes are discussed in detail, and the proposed method is illustrated with two real examples and an artificial example.

Bayesian Thurstonian models for ranking data using JAGS

“…Several researchers have proposed limited-information methods using the ranking of pairs or triples of choices (Brady, 1989;Chan & Bentler, 1998;Maydeu-Olivares, 1999). Others have proposed fullinformation maximum likelihood methods using Monte Carlo expectation-maximization algorithms (Poon & Lu, 2009;Xu, Poon, & Lee, 2008). Yao and Böckenholt (1999) and Yu (2000) showed that Bayesian Thurstonian ranking models are amenable to Markov chain Monte Carlo (MCMC) algorithms by using data augmentation with Gibbs sampling (Gelfand & Smith, 1990;Tanner & Wong, 1987).…”

Effect of Influential Data in 3 ω Fixed Factorial Designs

“…Por lo tanto, el análisis de la influencia es considerado como un componente importante en el análisis de un diseño experimental 3 ω . Aunque el análisis de la influencia ha sido durante mucho tiempo un tema importante en varios modelos estadísticos (véase, [3], [4], [2], [5], [6], [7], [8], [9], [10], [11], [12], [13]), se ha trabajado muy poco en los diseños factoriales simétricos, y en particular, en los diseños 3 ω .…”

On the modelling and estimation of attribute rankings with ties in the Thurstonian framework

“…Analysis of ranking data in the Thurstonian framework has received much attention in the behavioural science literature. See Arbuckle and Nugent (1973) for a general parameter estimation procedure, Böckenholt (1992) for a multivariate partial ranking model, Yao and Böckenholt (1999) and Yu (2000) for a Bayesian approach with Gibbs sampler, Brady (1989), Chan and Bentler (1996, 1998), and Yu, Lam, and Lo (2005) for factor analysis models, and Poon and Chan (2002) and Xu, Poon, and Lee (2008) for influence analysis. Moreover, relating the choice of a set of alternatives to the underlying subjective values is a commonly used modelling approach in marketing: see, for example, Currim (1982), Kamakura and Srivastava (1984), Carroll, Soete, and DeSarbo (1990), Harlam and Lodish (1995), Huber and Zwerina (1996) and Sinha and DeSarbo (1998).…”