Transforming Parameter Estimates to a Specified Coordinate System

Abstract

All measurement systems have some arbitrariness to them. When length is measured, the size of the unit used is arbitrary. Length units can be chosen from feet, meters, miles, light years, etc. The origin of the length measurements is usually set at true 0 and measurements using different units are typically linear transformations of each other. A common exception is astronomical measurements of distance that are taken from some arbitrary origin such as the Sun or the center of the Milky Way Galaxy. Although measurements of length are much easier to understand than the measurements that result from the applications of IRT models, some of the same concepts can be used for both types of measurements. For example, the concepts of invariance and indeterminacy that are often discussed in the IRT literature also apply to length measurement. The unit of the measurement for length is indeterminate but the length itself is invariant. The length being measured does not change because different units of measurement are used, but there is nothing in the measurement of length that indicates that one unit of measurement is more “correct” than any other unit of measurement. Some units might be more convenient than others such as using Angstroms when measuring things at the atomic level instead of miles, but that does not make them more correct.