Can the US general schedule (GS) scale be mapped to academic rank?

There are a number of US government jobs that are in essentially academic research labs that are unaffiliated with a university (e.g., the NIH and the national laboratories). The salary for some of these jobs are based on the General Schedule (GS) salary scale. Is it possible to roughly map a GS grade to an academic rank? For example, GS-11 requires a Masters degree and GS-12 requires a PhD so presumably step one as a GS-12 would be a new post-doc, but how do GS-13, GS-14, and GS-15 fit into the mix? Is it fair to say a GS-13 is like an assistant professor, GS-14 is like an associate, and GS-15 is like a full professor?