Thurstone's Minimalist Maps

L. L. Thurstone: "The scale values represented by the 45 statements [concerning Attitude toward the church are shown in the Figure], the purpose of which is to show that the 45 statements represent a more or less evenly graduated series of scale-values. The upper two horizontal lines constitute the scale proper and between these lines are small cross lines. Each of these cross lines represents the location of one of the 45 opinions. There are 45 such cross lines. The class intervals on the scale and their numerical designations are immediately below." (p.59)

"Having adopted an origin of measurement which is assigned arbitrarily at one end of the series of available opinions, and having a unit of measurement, the equal-appearing interval, we can proceed to ascertain the mean-scale value of all the opinions that any individual indorses." (p.64)

Thurstone, L.L. & Chave, E.J. (1929). The Measurement of Attitude. Chicago: University of Chicago Press.

Thurstone & Chave progressed far towards constructing a linear scale with the method of "equal-appearing" intervals. The scatterplot shows the relationship between the scale values of all 130 of their items (including the 45 above) and the logit values obtained by a Rasch analysis of their data (ibid. p. 33-4). They also advanced toward conjoint measurement. Below is their histogram map (p. 74) of the mean-scale values for two samples. Though both maps use the same scale, they fail to interpret respondent scale position in terms of the item hierarchy.

John Michael Linacre

Thurstone's Minimalist Maps Linacre, J.M. … Rasch Measurement Transactions, 1999, 13:3 p. 699

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Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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