Second-Order Covariance Matrix Formula for Heteroskedastic Generalized Linear Models

For the first time, we provide a matrix formula for second-order covariances of maximum likelihood estimates in heteroskedastic generalized linear models, thus generalizing the results of Cordeiro (2004 Cordeiro , G. M. ( 2004 ). Second-order covariance matrix of maximum likelihood estimates in generalized linear models . Statist. Probab. Lett. 66 : 153 – 160 .[Crossref], [Web of Science ®] , [Google Scholar]) and Cordeiro et al. (2006 Cordeiro , G. M. , Barroso , L. P. , Botter , D. A. (2006). Covariance matrix formula for generalized linear models with unknown dispersion. Commun. Statist. Theor. Meth. 35:113–120.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) related to the generalized linear models with known and unknown dispersion parameter, respectively. The covariance matrix formula does not involve cumulants of log-likelihood derivatives and can be easily obtained using simple matrix operations. We apply our main result to a simple model. Some simulations show that the second-order covariances can be quite pronounced in small to moderate samples. The usual covariances of the maximum likelihood estimates can be corrected by these second-order covariances.     

Peer and family influences on adolescent anger expression and the acceptance of cross-gender aggression

Past research has examined the relative impact of family and peers on adolescent behavior, but very little research has examined it in relation to youth dating violence. Eight hundred and sixty-five adolescents, primarily urban Latino youth, completed self-administered surveys at school. Multivariate analyses indicated that exposure to prior family violence was not significantly associated with adolescents' aggressive expression of anger or their acceptance of cross-gender aggression. However, current conflict--either family or peer--was associated with adolescent behavior and attitudes, with the exception that current peer conflict was not significantly associated with adolescents' acceptance of male on female aggression. Parental monitoring and attachment were not found to be moderators of these relationships. Implications for dating violence interventions and future directions for research are explored.