Age-related hearing loss (HL) reduces speech intelligibility (SI) in older adults (OAs). However, deficits in central and cognitive processing also substantially impact SI. Understanding these contributions is essential for explaining individual differences and developing effective assistive hearing strategies. This study presents a framework that distinguishes peripheral HL from central and cognitive influences on SI. This framework uses the Wakayama University Hearing Impairment Simulator (WHIS), and the Gammachirp Envelope Similarity Index (GESI), an objective measure of intelligibility. First, speech-in-noise tests were conducted with young, normal-hearing listeners (YNHs) using WHIS to simulate the audiogram of a target OA. The target OA achieved SI scores comparable to or higher than those of YNHs with simulated HL, suggesting contributions beyond peripheral hearing function. Then, GESI was used to predict SI scores for YNHs and OAs across different hearing levels. The prediction accuracy was comparable for both groups. Interestingly, many OAs' subjective SI scores were higher than those predicted using parameters derived from YNHs' experiments. This finding is inconsistent with previous research indicating that speech perception ability declines with age. This issue will be discussed. There was no significant correlation between the average hearing levels and the residual differences between the subjective and predicted SI scores. This suggests that GESI effectively absorbed the effects of peripheral HL. Thus, the proposed framework may facilitate systematic examination and comparison of central and cognitive factors beyond peripheral HL among individual YNHs and OAs with and without HL.