Peaked-spectrum (PS) sources exhibit turnover characteristics in their broad radio spectra. However, the mechanism underlying this phenomenon remains elusive. The two most common hypotheses are synchrotron self-absorption (SSA) and free–free absorption (FFA). By incorporating multiple absorption scenarios, we propose a multimechanism hybrid model, which aligns well with current observational data and provides a good physical explanation. Using data from the GLEAM survey, we identified a sample of 4315 sources with peak frequencies between approximately 72 and 3000 MHz, most of which are MHz-peaked-spectrum sources. Our analysis shows that FFA rather than SSA is the dominant mechanism in producing the spectral turnover for most of the sources in this sample. The index of the optically thick spectrum α_thick has a lower boundary due to FFA, and the steeper α_thick indicates a complex multiabsorption mechanism. In particular, the external FFA produces substantial α_thick, which exhibits a weak correlation with the peak frequency. Future ultralong-wavelength observations would also provide data on the spectrum of these sources at even lower frequencies. Determining the absorption mechanism that shaped the spectrum of these sources would be a crucial part of understanding their nature.