Mathematical models that capture patient-specific information can enable personalised mechanical ventilation, improving care for patients in the intensive care unit (ICU). A nonlinear autoregressive (NARX) model that uses pressure dependent elastance, and multiple time dependent resistance coefficients has been fit to 25 patient data sets containing increasing PEEP steps. This model was more successful than a well-accepted first order model (FOM) at describing the shape of the airway pressure curve. In this study, the NARX model and FOM were identified on the first 20% and last 20% of the available data (IDD40). The parameterized model was then interpolated over the evaluation data (EVD) that consisted of the middle 60% of the data. The model-data residuals were compared to the result of identification using 100% of the data (IDD100). There were significant differences between the average root mean square (RMS) residuals for most IDD100, IDD40, and EVD combinations (p < 0.05). However, the magnitude of the differences was small in a clinical sense. Importantly, the NARX model was able to provide consistent results across all 25 patients. In contrast the FOM interpolation results were worse when the patient suffered over-distension in the high PEEP IDD40 data. The results suggest the NARX model could be suitable for use in the ICU, to estimate behaviour when data is not available, allowing clinicians to make informed decisions regarding ventilator PEEP settings