Predictive models from statistically nonconforming databases

Data sets in civil and structural engineering are often statistically challenging. This is because the data are from one-of-a-kind systems such as buildings and other large facilities, as opposed to replicated systems as found in most other fields of engineering. Special care is required in developing predictive models from such data. Herein a database of building natural period and damping is used to provide a rich context for analyzing one-of-a-kind systems. The database is statistically nonconforming in three ways. The data are nested, where measurements from different excitation sources are obtained for each building; the data set is unbalanced with measurements unevenly distributed among different building categories; and the variability is nonuniform. Furthermore, the number of possibly relevant building parameters is large. The goal is to develop a relatively simple, yet general approach for deriving predictive models based on such statistically nonconforming data sets. The approach is based on the statistical framework of generalized linear models and is structured in a manner to allow for engineering insights into the model. In the companion paper, it is shown how this approach can be applied to develop comprehensive models for building natural period and damping.