Numerous studies of human user behaviours in cybersecurity tasks have used traditional research methods, such as self-reported surveys or empirical experiments, to identify relationships between various factors of interest and user security performance. This work takes a different approach, applying computational cognitive modelling to research the decision-making of cybersecurity users. The model described here relies on cognitive memory chunk activation to analytically simulate the decision-making process of a user classifying legitimate and phishing emails. Suspicious-seeming cues in each email are processed by examining similar, past classifications in long-term memory. We manipulate five parameters (Suspicion Threshold; Maximum Cues Processed; Weight of Similarity; Flawed Perception Level; Legitimate-to-Phishing Email Ratio in long-term memory) to examine their effects on accuracy, email processing time and decision confidence. Furthermore, we have conducted an empirical, unattended study of US participants performing the same task. Analyses on the empirical study data and simulation output, especially clustering analysis, show that these two research approaches complement each other for more insightful understanding of this phishing detection task. The analyses also demonstrate several limitations of this computational model that cannot easily capture certain user types and phishing detection strategies, calling for a more dynamic and sophisticated model construction.