The Hearing-Aid Speech Perception Index version 2 (HASPI v2) is a speech intelligibility metric derived by fitting subject responses scored as the proportion of complete sentences correct. This paper presents an extension of HASPI v2, denoted by HASPI w2, which predicts proportion keywords correct for the same datasets used to derive HASPI v2. The results show that the accuracy of HASPI w2 is nearly identical to that of HASPI v2. The values produced by HASPI w2 and HASPI v2 also allow the comparison of proportion words correct and sentences correct for the same stimuli. Using simulation values for speech in additive noise, a model of context effects for words combined into sentences is developed and accounts for the loss of intelligibility inherent in the impaired auditory periphery. In addition, HASPI w2 and HASPI v2 have a small bias term at poor signal-to-noise ratios; the model for context effects shows that the residual bias is reduced in converting from proportion keywords to sentences correct but is greatly magnified when considering the reverse transformation.