Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Importance, Cohesion and Structural Equivalence in the Evolving Citation Network of the International Journal of Research in Marketing

The citation network of the International Journal of Research in Marketing (IJRM) is examined from 1981 to 1995. We propose a model that contains log-linear and logmultiplicative terms to estimate simultaneously the importance, cohesion, and structural equivalence of journals in the network across time. Our findings show that the overall importance of IJRM in its network is low but growing. The importance of psychology journals in the network appears to be decreasing. Clear cohesive and structurally equivalent groups of core marketing, methodology, managerial and psychology journals with distinct functions in the network are identified. Recommendations for future citation research are offered.Citation analysis;social networks;log-multiplicative models