For researchers who are interested in quantitative change over time rather than (rank order) stability, the measurements need to be made on a common scale that achieves at least an interval level of measurement over time. This property characterizes many physical measurements such as height, blood pressure, or counts of behaviors. However, this property often does not characterize psychological measures of attitudes and traits. Attempts to measure abilities, attitudes, or traits usually rely on the collective strength of responses to individual items within instruments. In the measurement of psychological traits, the response to each item is typically assessed by either using a dichotomous response (e.g., "I enjoy parties"—true or false) or a Likert-
type response scale that is essentially ordinal (e.g., "How much do you like parties?" rated on a 5-point scale from "not at all" to "very much"). In current research practice the same instrument is administered at each measurement wave, and the total scale score at each wave is used to model change. However, this practice involves several important untested assumptions: (a) the scale is unidimensional, (b) the total scores yields interval level measurements, (c) the same total score would indicate the same construct level over time, and (d) there is measurement invariance over time. These assumptions are seldom checked or addressed.
If the measurements are not made on an interval scale, equal differences in scores over time at different levels of the construct may not mean the same amount of change in the construct. The measurement unit stretches or shrinks as a function of the level that is measured—the rubber ruler problem. Desirable interval scale properties can usually be achieved through careful scale construction and through successfully applying measurement models.
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