Objective: Existing screening tools for HIV-Associated Neurocognitive Disorders (HAND) may lack the accuracy required for clinical use. We hypothesized that the diagnostic accuracy of the Montreal Cognitive Assessment (MoCA) as a screening tool for HAND might be improved with a stronger scoring methodology. Design: Two hundred HIV-positive participants aged 18-65 years completed the MoCA and a battery of neuropsychological tests. Methods: HAND diagnosis was established according to the Frascati criteria, and an NPZ-8 score was also calculated. Rasch analysis was applied to the MoCA items to create a quantitative score. Results: The optimal cut-off on the quantitative MoCA for detecting impairment as per Frascati criteria yielded a sensitivity of 0.74 and a specificity of 0.68. Overall accuracy was 0.79 (95% CI: 0.73-0.85), an improvement over standard scoring methods. However, whether cognition was quantified with the quantitative MoCA or with NPZ-8, there was substantial overlap between diagnostic categories; several individuals categorized as impaired had better overall cognitive function as assessed by NPZ-8 or quantitative MoCA than those classified as normal using standard criteria. Conclusion: Quantifying performance on MoCA items through Rasch analysis improves its accuracy as a screening tool for HAND, and demonstrates that cognition can be measured as a unidimensional construct in HIV, at least at the level of precision of bedside testing. However, the current categorical diagnostic approach to HAND is poorly aligned with summary measures of cognitive ability. Measuring cognition as a quasi-continuous construct may be more relevant than conventional HAND diagnostic categories for many clinical purposes.