# Condition Rating Prediction Using an Interactive Deterioration Model Development Package
## 5 Effect of Using Weighted LASSO
### Selection of Explanatory Variables  
To investigate the efficacy of the weighted LASSO, we identified the lists of explanatory variables for the deck, superstructure, and substructures using the inspection data from a single year (existing method) and the previous eight years (proposed method), as indicated in Tables 2-4, which show the index numbers of the candidate variables defined in Table 1. In general, more consistent results were observed when the proposed method was applied to the selection of explanatory variables. For the deck elements identified using the proposed method, the type of wearing surface, which had an index number of 23, was generally considered to be the most significant, followed by the structure length, which had an index number of 19, whereas this ranking was inconclusive when only the single year inspection data were used. The inspection records for a single year can possibly be affected by specific conditions including human error, natural disasters, and maintenance actions across the entire state whether they are recorded. The expansion of inspection data to include previous years helps to diminish such biased effects. Similar results were observed for the other elements; therefore, the proposed method identifies the top-ranked explanatory variables with superior consistency compared to the existing method.  
These explanatory variable sets determined by LASSO are used to divide the bridge data into multiple groups using a classification tree and to develop deterioration models, the performances of which were evaluated by the normalized prediction error defined in Equation (5). The number of classification tree levels was set to three and logistic regression was applied to estimate the transition probability matrices. For example, Figures 4 and 5 illustrate the specific classification trees for the deck element based on the inspection data from a single year (2013) and from multiple years (2006 to 2013), respectively. The minimum number of bridge  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Year** & \multicolumn{4}{c}{**Single-Year Inspection**} & \multicolumn{4}{c}{**Eight-Year Inspection**} \\ \hline
2009 & 10 & 20 & 23 & 22 & 21 & 10 & 20 & 21 & 22 & 23 \\
2010 & 20 & 10 & 23 & 22 & 1 & 10 & 20 & 22 & 23 & 21 \\
2011 & 20 & 23 & 10 & 22 & 1 & 10 & 20 & 23 & 22 & 1 \\
2012 & 23 & 10 & 20 & 5 & 4 & 10 & 20 & 23 & 22 & 1 \\
2013 & 23 & 20 & 10 & 5 & 22 & 10 & 23 & 22 & 20 & 1 \\
2014 & 23 & 10 & 20 & 5 & 26 & 23 & 20 & 10 & 22 & 5 \\
2015 & 23 & 10 & 20 & 5 & 22 & 23 & 10 & 20 & 5 & 22 \\
2016 & 23 & 10 & 20 & 22 & 5 & 23 & 10 & 20 & 5 & 22 \\
2017 & 10 & 23 & 22 & 20 & 5 & 23 & 10 & 20 & 22 & 5 \\
2018 & 10 & 22 & 26 & 20 & 5 & 10 & 23 & 22 & 20 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: List of explanatory variables for substructure since 2009 using LASSO with and without weights.  
Figure 4: Classification tree for Wyoming bridges using explanatory variables from a single year (2013) of inspection data for deck elements.  
Logistic regression was utilized to develop the deterioration models. Then, the normalized prediction errors for the 2014 to 2018 inspection data were compared, as shown in Figure 6, in which it can be observed that the normalized error generally increased with increasing prediction year. Although the normalized error decreased by an average of only 1.6% over all prediction periods, this was still a remarkable improvement considering the large number of bridges and inspection data points. Using the inspection data from multiple years reduced the chance of selecting explanatory variables that would only exhibit high correlation with a particular year. This provided additional benefits to bridge owners for more effectively managing their bridge assets.