  School bullying victimization is a variable that cannot be measured directly.
Taking into account that this variable has a lower bound, given by the absence
of bullying victimization, this paper proposes IRT logistic models, where the
latent parameter ranges from $0$ to $\infty$ or from $0$ to a positive real
number R, defining the IRT parameters and proposing an empirical anchor
procedure. As the academic abilities and the school bullying victimization can
be explained due to associated factors such as habits, sex, socioeconomic level
and education level of parents, IRT regression models are proposed to make
joint inferences about individual and school characteristic effects. Results
from the application of the proposed models to the Bogot\'a school bullying
dataset are presented. The need for testing based in statistical models
increases in different fields.
