We investigate the impact of pubertal development, age, and its interaction on female substance use behaviour. An extended latent transition model with two latent variables is used to reflect the dependency of adolescent substance use on pubertal development and age. A sample of females in grades 7-12 is analysed using maximum-likelihood estimation. Analyses indicate that experiencing puberty is related to increased substance use for all age groups. Among females aged 12-15, those who have experienced puberty are more likely to advance in substance use compared to their late-maturing counterparts. Particularly, among 12-year old non-substance users, those who have experienced puberty are approximately three times more likely to advance towards substance use than those who have not experienced puberty. In addition, among older females, those whose puberty is in progress are more prone to advance in substance use compared to those whose puberty has not occurred.

It is well known that most commonly used discrete distributions fail to belong to the domain of maximal attraction for any extreme value distribution. Despite this negative finding, C. W. Anderson showed that for a class of discrete distributions including the negative binomial class, it is possible to asymptotically bound the distribution of the maximum. In this paper we extend Anderson's result to discrete-valued processes satisfying the usual mixing conditions for extreme value results for dependent stationary processes. We apply our result to obtain bounds for the distribution of the maximum based on negative binomial autoregressive processes introduced by E. McKenzie and Al-Osh and Alzaid. A simulation study illustrates the bounds for small sample sizes.

No abstract