A theory and procedure of scale analysis with applications by R. J. Mokken PDF

By R. J. Mokken

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Additional info for A theory and procedure of scale analysis with applications in political research

Sample text

System of the ordered classes is essentially determined by the item dilliculties cS;. The proportions of subjects in these classes are, however. dependent on the population distribution. J. A set of k items forms a perfect scale for a population if and only if, given the ordering of the items, the error cell in the corresponding (2 x 2)-table has zero probability for every pair in the set, that is. if it is impossible for any subject drawn from the population to score I on any item and 0 on any less difficult item in the set.

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.

For instance, a subject with the value ()2 will s c ore I on items 4. 3 and 2. and 0 on item I. thus producing the pattern {0, I, I, I}. As a matter of fact any \uhject "ith a 6-value in the interval (Be. o,) will do this. The four G-item'> therefore divide the 0-axis into five intervals. 0. ); 0 < 5,: {0. 0. 0. 0}; (seeOs). The c are the .. perfect'' response patterns. The only information the respondent gives about his 0-value is that it i-. within one of these intervals: he indicates by his answer.

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A theory and procedure of scale analysis with applications in political research by R. J. Mokken


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