By R. J. Mokken
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Additional info for A theory and procedure of scale analysis with applications in political research
Yet in actual practice such deviations from the deterministic model may well occur. What do these "errors" lead to? 4. I One of the immediate consequences of deviations from the determin istic model in practical applications is, of course, the loss of the property of reproducibilily. No longer does the scale score of any subject predict his response pattern exactly: other "imperfect" patterns with the same score may occur. Still other problems have to be coped with when the deterministic model is used as a guide line for the construction of practical instru ments for measurement.
In the empirical context under consideration, there are typically many possible subjects (n large) and limited possibilities for the use of many items (small k). Therefore, although the formal model is perfectly symmetrical as regards the two sets of subjects and items. in this empirical context we shall have to cope with this asymmetry of a large n relative to k. If we define the scale score(s) of a subject as the number of scale alternatives chosen by a subject from the set of items (the number or ones a subject scores in his response to the k items), we shall see that the subjects are ordered by their scale score, and that this scale score (running from 0 to k) identifies the k + I classes.
Items form a \Ct of C item � for the popular ion. - I. rhe '>calc score::. will �till reproduce the pcrfcc1 pa lle rn which corresponds to it . probability is ;cro). , ib l e (their 38 Theoryand 11/etltod :2. : order of 1 he item difficulties (cS;) will be reflected by that of the population dilli<;ulties of the items ( 7T;). irively to G-item i than to G-item j. 3). 3. : system of the ordered classes is essentially determined by the item dilliculties cS;. The proportions of subjects in these classes are, however.
A theory and procedure of scale analysis with applications in political research by R. J. Mokken