Censored Scales
Abstract:
Discrete scales are often issued to record responses concerning characteristics which really vary along a continuum. Examples in attitudinal measurement are most prevalent where respondents are given several choices (e.g., a 6-point agreement scale) which are used to capture attitudes that fall along a continuum. Number of units consumed (e.g., glasses of beer), or demographic characteristics, such as age or income, are also obtained by splitting a measurement continuum into several discrete intervals. Respondents are then instructed to check the scale position or interval which most accurately describes their intended response. Quite often the discrete measurements of consumption or demographics are characterized by open-ended intervals at the scale extremes. "More than 20 glasses" or "over 65 years of age" are examples of open-ended upper bounds on scale for beer consumption and age, respectively. "Under $10,000 a year" reflects the open-ended nature of a lower bound on income. This paper addresses some issues which arise when discrete scales with open-ended extremes are used to measure characteristics which really vary along a continuum.
