A Gaussian Process Arising from Likert-Type Scaling

Convergence of a sequence of stochastic processes obtained from Likert-Type scaling with increasing number of categories with increasing sample sizes is considered. Conditions are exhibited under which the sequence constructed from cumulative class frequencies by linear interpolation with respect to the class boundaries converges to a Gaussian process in law when the support of latent distribution is a bounded interval. We then extend the result to more general unbounded support. Quadratic variation of the limiting process is derived.