He studied mental rotation, and was an inventor of non-metric multidimensional scaling, a method for representing certain kinds of statistical data in a graphical form that can be comprehended by humans.

[4] Shepard obtained his Ph.D. in psychology at Yale University in 1955 under Carl Hovland,[5] and completed post-doctoral training with George Armitage Miller at Harvard.

[7] His students include Lynn Cooper, Leda Cosmides, Rob Fish, Jennifer Freyd, George Furnas, Carol L. Krumhansl, Daniel Levitin, Michael McBeath, and Geoffrey Miller.

He reports, "This led to the development of the methods now known as non-metric multidimensional scaling – first by me (Shepard, 1962a, 1962b) and then, with improvements, by my Bell Labs mathematical colleague Joseph Kruskal (1964a, 1964b).

"[3] According to the American Psychological Association, "nonmetric multidimensional scaling .. has provided the social sciences with a tool of enormous power for uncovering metric structures from ordinal data on similarities.

Awarding Shepard its Rumelhart Prize in 2006, the Cognitive Science Society called non-metric multidimensional scaling a "highly influential early contribution," explaining that:[7]This method provided a new means of recovering the internal structure of mental representations from qualitative measures of similarity.

"[14]) The early experiments, in collaboration with Jacqueline Metzler, used perspective drawings of very abstract objects: "ten solid cubes attached face-to-face to form a rigid armlike structure with exactly three right-angled 'elbows,'" to quote their 1971 paper, the first report of this research.

Reviewing that work in 1983, Michael Kubovy assessed its importance:[18]Up to that day in 1968 [Shepard's dream about rotating objects], mental transformations were no more accessible to psychological experimentation than were any other so-called private experiences.

He began his research on auditory illusions during his years at Bell Labs, where his colleague Max Mathews was experimenting with computerized music synthesis (Mind Sights, page 30.)