  Air pollution is a great concern because of its impact on human health and on
the environment. Statistical models play an important role in improving
knowledge of this complex spatio-temporal phenomenon and in supporting public
agencies and policy makers. We focus on the class of hierarchical models that
provides a flexible framework for incorporating spatio-temporal interactions at
different hierarchical levels. The challenge is to choose a model that is
satisfactory in terms of goodness of fit, interpretability, parsimoniousness,
prediction capability and computational costs. In order to support this choice,
we propose a comparison approach based on a set of criteria summarized in a
table that can be easily communicated to non-statisticians. Our proposal -
simple in principle but articulated in practice - holds true for many
environmental phenomena where a hierarchical structure is suitable, a
large-scale trend is included and a spatio-temporal covariance function has to
be chosen. We illustrate the details of our proposal through a case study
concerning particulate matter concentrations in Piemonte region (Italy) during
the cold season October 2005-March 2006. From the evaluation of the proposed
criteria for our case study we draw some conclusions. First, a model with a
complex hierarchical structure is globally preferable to one with a complex
spatio-temporal covariance function. Moreover, in the absence of suitable
computational resources, a model simple in structure and with a simple
covariance function can be chosen, since it shows good prediction performance
at reasonable computational costs.
