## 2 Modeling Procedure
### Secondary Data Modeling
Additionally, a validation procedure relying on correlation analysis was performed for a semi-physical identification method resulting in residual errors within confidence bounds. The autocorrelation for behavior and cross-correlation for different lags between behavior and each of the following variables are shown in Figure 3, where:  
* \"Co-usage\"\(\Leftrightarrow\)\"skills training\" corresponds to the daily number of glances at the application. * \"Sumusa\" is \"sum of application usage\"\(\Leftrightarrow\)\"observed behavior\" is the total length of time (in seconds) per day the application was glanced at. * \"Weather\"\(\Leftrightarrow\)\"perceived barriers\" means the environmental condition in which the subject is influenced to engage in physical activity or not. * \"Weekend\"\(\Leftrightarrow\)\"environmental context\" indicates whether the date of measurement falls or does not fall during the weekend. Lag refers to a time delay or temporal shift between two variables. Therefore, when calculating correlation with lag, the relationship between the two variables was analyzed with a certain time delay to see if there was any significant correlation between them at that specific moment. Figure 3: Model validation via correlation analysis for the semi–physical identification procedure. The areas highlighted in blue represent the confidence bounds [9]. Figure 2: Comparison between estimated behavior (i.e., \(\eta_{4}\)) (number of steps) using semi–physical identification (simulated data) vs. real experimental data (male adult participant number 115) [9]. Correlation analysis is a statistical method that measures the strength and direction of the relationship between two variables. It uses the correlation coefficient, with the amplitude ranging from \(-1\) to \(1\), where \(-1\) indicates a perfect negative correlation, \(0\) indicates no correlation, and \(1\) indicates a perfect positive correlation. To confirm the predictive ability of the model [9], it was expected that the amplitude of autocorrelation would be equal to \(1\) at zero lag and would take any value within the confidence interval for other lags, if the model is reliable. Moreover, the values within the confidence bounds depicted in Figure 3 in the cross-correlation plots validate the reliability of the model [19]. Although the percentage fit was relatively low, the model developed in [9] is able to follow some of the dynamic characteristics of the system (i.e., amplitude and frequency variations of the signal \(\eta_{4}\) over time), even though it was derived from secondary data. Nevertheless, the model has limited applicability for the required purpose since it does not support the implementation of behavioral interventions using external cues or reinforcement through outcome expectancy. As a result of the previous analysis, internal parameters for the secondary data SCT model were obtained [9]. For the intervention design, this SCT model needs to be expanded to include additional input variables directly associated with the required behavior change intervention. Thus, the secondary data model was expanded with parameters obtained from different experiments where preliminary validated models were obtained using primary data [11; 20].