Mixture structure analysis using the Akaike Information Criterion and the bootstrap

Given i.i.d. observations x1,x2,x3,...,xn drawn from a mixture of normal terms, one is often interested in determining the number of terms in the mixture and their defining parameters. Although the problem of determining the number of terms is intractable under the most general assumptions, there is hope of elucidating the mixture structure given appropriate caveats on the underlying mixture. This paper examines a new approach to this problem based on the use of Akaike Information Criterion (AIC) based pruning of data driven mixture models which are obtained from resampled data sets. Results of the application of this procedure to artificially generated data sets and a real world data set are provided.     

Robust models in probability sampling

In the estimation of a population mean or total from a random sample, certain methods based on linear models are known to be automatically design consistent, regardless of how well the underlying model describes the population. A sufficient condition is identified for this type of robustness to model failure; the condition, which we call 'internal bias calibration', relates to the combination of a model and the method used to fit it. Included among the internally bias-calibrated models, in addition to the aforementioned linear models, are certain canonical link generalized linear models and nonparametric regressions constructed from them by a particular style of local likelihood fitting. Other models can often be made robust by using a suboptimal fitting method. Thus the class of model-based, but design consistent, analyses is enlarged to include more realistic models for certain types of survey variable such as binary indicators and counts. Particular applications discussed are the estimation of the size of a population subdomain, as arises in tax auditing for example, and the estimation of a bootstrap tail probability.     

A Comparison of Three-level Orthogonal Arrays in the Presence of a Possible Correlation in Observations

When we want to compare two designs we usually assume the standard linear model with uncorrelated observations. In this paper we use the comparison method proposed by Ghosh & Shen (2006) to compare three level orthogonal arrays with 18, 27 and 36 runs under a possible presence of correlation in observations.     

Model-based clustering for social networks

Summary.  Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the latent position cluster model , under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model.     

Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference

This paper discusses recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite. An algorithm for detecting such cases and characterizing the divergence of the parameter estimates is presented. A method for fitting the remaining parameters is also presented . All of these methods rely only on sufficient statistics rather than less aggregated quantities, as required for inference according to the method of Kolassa & Tanner (1994). These results are applied to approximate conditional inference via saddlepoint methods. Specifically, the double saddlepoint method of Skovgaard (1987) is adapted to the case when the solution to the saddlepoint equations exists as a point at infinity