By R. J. Mokken
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Extra info for A theory and procedure of scale analysis with applications in political research
Trca-. , ( rr,) of item i. a dif l'crcnl \jJI'Cad. , in thc population di�tribution or. what may amount 10 Ihe same thing. which prop0rtic� ar0 roughly preserved wi 1 h di trerent <,ample� or �ubjects. ch. 1960). ,e problem-. crved when the/.. 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;).
In our model each subject compares his own position on this continuum with the item content as related to the au ribute. yes". W e can imagine respondents of all possible heights distributed along the horizontal axis. A respondent of a certain height (the degree. positive" answer (scale alternative) with a probability depending on that degree or value. Assuming that with all subjects of the same height. the -;ame probabil ity exists that they will do so, we can measure the probability of a positive answer (scale alternative) and plot this probability as a function of the "underlying" or "latent" attribute or height.
Aliitude. urcd by 0, in the sense that for perfect scale� these proportion'>. though dependent on the particular item distribution. will renect perfectly the order of the 01: for 0, that proportion i� smaller than that for()� becau�e o, < o�. >. Apart from the fact that the quality of our sampling from the universe is unknown. >C k. the number of item-.. idcration. It i-. a virtue of the model that it teaches us to be modest concerning the preci... ion of the measurements which we base on �calcs.