Robustness of normal theory methods in the analysis of linear latent variate models

The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived using properties of cumulants. This is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under non-normality of latent variates are given. Factor analysis, LISREL and other models are discussed as examples.     

Heat and Violence: New Findings from Dallas Field Data, 1980–19811

Research in both laboratory and field settings has suggested a link between thermal stress and violent behavior, and both linear and curvilinear models have been investigated. A dearth of field studies prompted the analysis reported here, which is based on data for some 10,000 aggravated assaults occurring the City of Dallas in 1980 (a summer of severe heat stress) and 1981. This analysis replicates and extends certain aspects of recent work by Anderson and Anderson (1984) relating to the so-called linear and curvilinear hypotheses. Thermal stress is measured in two ways: a Discomfort Index (DI), which takes into account the influence of humidity acting in concert with temperature, and ambient temperature. Regression analyses were performed in two stages. In the first, data for all neighborhoods and all days of the study period were combined into ambient temperature and DI models. At the second stage, models differentiated between the three levels of neighborhood socioeconomic status. With weekend controlled, DI and ambient temperature were significant independent variables in the ‘overall’ model and in medium and low status neighborhoods. However, when linear effects were controlled, the curvilinear measures were never significant. The analysis generally tended to confirm Anderson and Anderson's suggestion that a reduction of aggression with increasing temperature does not appear to occur within the normal range of temperatures. This analysis further suggested that the hypothesized curvilinear effect is weak, if not entirely absent, even during conditions of extreme heat.