A ligand that acts on a target receptor to activate particular multiple signalling pathways with activity that is distinct from other ligands is termed ligand bias. Quantification of ligand bias is based on applying the operational model to each pathway separately and subsequent calculation of the ligand bias metric (ΔΔlogR). This approach implies independence among different pathways and causes propagation of error in the calculation. Here, we propose a semi-mechanism-based model which allows for receptor selectivity across all the pathways simultaneously (termed the 'intact operational model'). The power of the intact model for detecting ligand bias was evaluated via stochastic simulation estimation studies. It was also applied to two examples: (1) opposing effects of Gi/Gs signalling of α2-adrenergic receptors and (2) simultaneous measurement of arachidonic acid release and inositol phosphate accumulation following 5-HT2C receptor activation. The intact operational model demonstrated greater power to detect ligand bias in the simulation. In the applications, it provided better precision of estimation and identified biased ligands that were missed by analysis of traditional methods. Issues identified in both examples might lead to different interpretations of the data. The intact operational model may elucidate greater understanding of the underlying mechanisms of functional selectivity.