The information for the direction of dependence in l1 regression

Fitting a linear regression for a response variable by minimising the sum of absolute deviations, L₁ regression, may be viewed as a maximum likelihood procedure applied to the Laplace distribution. An interesting bivariate case is where the conditional distribution of the response X₂ given X₁ and the marginal distribution of the explanatory variable X₁ are both Laplace. In this context we show there is information to distinguish the direction of dependence between X₁ and X₂ from observations. That is we may distinguish the model in which X₁ is dependent on X₂ from that in which X₂ is dependent on X₁ This is not true for L₂ regression based on the Normal distribution.     

A mixture of experts latent position cluster model for social network data

Social network data represent the interactions between a group of social actors. Interactions between colleagues and friendship networks are typical examples of such data.The latent space model for social network data locates each actor in a network in a latent (social) space and models the probability of an interaction between two actors as a function of their locations. The latent position cluster model extends the latent space model to deal with network data in which clusters of actors exist — actor locations are drawn from a finite mixture model, each component of which represents a cluster of actors.A mixture of experts model builds on the structure of a mixture model by taking account of both observations and associated covariates when modeling a heterogeneous population. Herein, a mixture of experts extension of the latent position cluster model is developed. The mixture of experts framework allows covariates to enter the latent position cluster model in a number of ways, yielding different model interpretations.Estimates of the model parameters are derived in a Bayesian framework using a Markov Chain Monte Carlo algorithm. The algorithm is generally computationally expensive — surrogate proposal distributions which shadow the target distributions are derived, reducing the computational burden.The methodology is demonstrated through an illustrative example detailing relationships between a group of lawyers in the USA.     

Use of a mixture model for the analysis of contraceptive-use duration among long-term users

This paper introduces a mixture model that combines proportional hazards regression with logistic regression for the analysis of survival data, and describes its parameter estimation via an expectation maximization algorithm. The mixture model is then applied to analyze the determinants of the timing of intrauterine device (IUD) discontinuation and long-term IUD use, utilizing 14 639 instances of IUD use by Chinese women. The results show that socio-economic and demographic characteristics of women have different influences on the acceleration or deceleration of the timing of stopping IUD use and on the likelihood of long-term IUD use.     

An Integrative Examination of Peer Conflict: Children's Reported Goals, Emotions, and Behaviors

The primary purpose of the present study was to examine the interrelations among children's typical emotions, goals, and behavior during peer conflict and to examine emotions and goals as joint predictors of behavior. Children (7 to 11 years old) described recent conflicts with peers and were questioned about their emotions, goals, and behaviors. The friendliness of children's reported goals during conflict was associated with low anger intensity and with high intensity of sadness. Children who tended to report nonconstructive behavior also tended to report relatively intense anger and relatively unfriendly goals. Furthermore, in regression analyses, the friendliness of goals uniquely predicted the constructiveness of children's behavior after controlling for the effects of anger intensity, age, gender, provoking event, and friendship with the peer. Although boys and girls reported similar levels of anger and sadness, girls reported friendlier goals and more constructive behavior than did boys. The use of self‐reports of actual events to examine peer conflict during middle childhood is also discussed.