Objective measures of speech quality are highly desirable in benchmarking and monitoring the performance of hearing aids (HAs). Existing HA speech quality indices such as the hearing aid speech quality index (HASQI) are intrusive in that they require a properly time-aligned and frequency-shaped reference signal to predict the quality of HA output. Two new reference-free HA speech quality indices are proposed in this paper, based on a model that amalgamates perceptual linear prediction (PLP), hearing loss (HL) modeling, and machine learning concepts. For the first index, HL-modified PLP coefficients and their statistics were used as the feature set, which was subsequently mapped to the predicted quality scores using support vector regression (SVR). For the second index, HL-impacted gammatone auditory filterbank energies and their second-order statistics constituted the feature set, which was again mapped using SVR. Two databases involving HA recordings were collected and utilized for the evaluation of the robustness and generalizability of the two indices. Experimental results showed that the index based on the gammatone filterbank energies not only correlated well with HA quality ratings by hearing impaired listeners, but also exhibited robust performance across different test conditions and was comparable to the full-reference HASQI performance.