British Journal of Mathematical and Statistical Psychology

A note on residual M‐distances for identifying aberrant response patterns

Early View

Although a statistical model might fit well to a large proportion of the individuals of a random sample, some individuals might give ‘unusual’ responses that are not well explained by the hypothesized model. If individual responses are given as continuous response vectors, M‐distances can be used to produce real valued indicators of how well an individual's response vector corresponds to a covariance structure implied by a psychometric model. In this note, we focus on the so‐called one‐factor model. Two M‐distances, dsi and dri, which are sensitive to different aspects of the assumed factor model, have been proposed. While one of the M‐distances, dri, has been derived based on Bartlett factor scores, in this note we show that the second M‐distance, dsi, can be derived in an analogous fashion based on Thomson factor scores.

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