Learning from
Principal Components Analysis of Residuals

A COMET Presentation by
J. Michael Linacre on 4-22-1999,
MESA Psychometric Laboratory
MESA Research Note #7

The Rasch model extracts from observational data the linear dimension best supported by those data. But each observation, to some degree, contains its own characteristic features. These contradict the dimension. The responses idiosyncratic characteristics are manifested as the differences between what the Rasch model predicts and what is observed, i.e., the observation residuals. Principal components analysis of these residuals identifies characteristics shared in common among items. These are often indications of secondary structures or sub-dimensions within the data.

In this presentation, an analysis of an Attitudes to Recreational Drugs survey is performed. This identifies "for" and "against" statements. Further, it confirms an earlier finding about that "for" and "against" are not always perceived as opposite. More subtle sub-dimensions are also identified in the instrument.

In this example, the power and utility of Principal Components analysis of Rasch residuals is demonstrated.

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