Unfinished and drafts posts from 2012.

Unidimensional scaling

(July 2012)

This summer, I was reading Unidimensional scaling, by John P. McIver and Edward G. Carmines (Sage Publications, 1981). This is a concise introduction to the construction of unidimensional scales, by means of different “historical” scaling models, namely Thurstone, Likert, Guttman, as well as unfolding theory.

Basically, scaling models may be used to scale persons, stimuli, or both. Likert scaling falls in the first category, and as such it is considered a subject or person-centered approach. Thurstone dedicated a fair amount of his work on how to measure psychological stimuli and how they can be compared with one another. (The counterpart of this approach for physical stimuli is the basis for most psychophysics methods.) The response approach is concerned with scaling subjects and stimuli, where “the task set for the subject is to respond to a stimulus on the basis of the position of the stimulus in relation to the subject’s own position with respect to the attribute.” (This is basically what modern psychometrics intend to do with IRT modeling.)

Thurstone scaling

Thurstone is well known for his law of comparative judgment whereby each individual makes a discrimination or response involving a judgment as to the relative degree of prestige of each occupation, where we assume that the distribution of all discriminal processes aroused by any stimulus will be normal wrt. modal discriminal process on the psychological continuum. For more information, see Thurstone, L.L. (1994). A law of comparative judgment. Psychological Review, 101(2), 266-270.

According to this law, the degree to which any two stimuli can be discriminated is a direct function of the difference in their status as regards the attribute in question. For instance,

This has led to developing three distinct methods of scaling: paired comparisons, successive intervals, and equal-appearing intervals.

Here is Edwards’s list of desirable characteristics for attitude items:

1. Avoid statements that refer to the past rather than to the present.
2. Avoid statements that are factual or capable of being interpreted as factual.
3. Avoid statements that may be interpreted in more than one way.
4. Avoid statements that are irrelevant to the psychological object under consideration.
5. Avoid statements that are likely to be endorsed by almost everyone or by almost no one.
6. Select statements that are believed to cover the entire range of the affective scale of interest.
7. Keep the language of the statements simple, clear, and direct.
8. Each statement should contain only one complete thought.
9. Statements containing universals such as all, always, none, and never often introduce ambiguity and should be avoided.
10. Words such as only, just, merely, and others of a similar nature should be used with care and moderation in writing statements.
11. Whenever possible, statements should be in the form of simple sentences rather than in the form of compound or complex sentences.

(Edwards, A. (1957). Techniques of attitude scale construction. Englewood Cliffs, NJ: Prentice-Hall.)

Likert scaling

Guttman model

Contrary to Likert scaling, the purpose of Guttman scaling is to scale both respondents and questionnaire items, in relation to a given attitude.

Unfolding theory

Pyschoco and JSS

(June 2012)

Last year I posted a note on the Psychoco conference. The official website is here. There is now a special issue in the Journal of Statistical Software about this project: Psychoco: Psychometric Computing in R. Here is a quick review.

Clinical prediction models

(May 2012)

• Cochrane Prognosis Methods Group
• Reporting of prognostic markers: current problems and development of guidelines for evidence-based practice in the future
• Reporting of prognostic studies of tumour markers: a review of published articles in relation to REMARK guidelines
• Rules of evidence for cancer molecular-marker discovery and validation
• Primer: an evidence-based approach to prognostic markers