1. Th e productivity of a scholar is often judged by the number of articles he or she publishes in..

1. Th e productivity of a scholar is often judged by the number of articles he or she publishes in scholarly journals. Th is productivity may be aff ected by factors, such as sex, marital status, number of young children, prestige of the graduate program and the number of articles published by the scholar’s mentor. Since the number of articles published is a fi nite number, with many scholars producing a small a number of articles and a few publishing a relatively large number of articles, it seems the number of articles published may follow the Poisson distribution. Th erefore, we can

»1. Th e productivity of a scholar is often judged by the number of articles he or she publishes in scholarly journals. Th is productivity may be aff ected by factors, such as sex, marital status, number of young children, prestige of the graduate program and the number of articles published by the scholar’s mentor. Since the number of articles published is a fi nite number, with many scholars producing a small a number of articles and a few publishing a relatively large number of articles, it seems the number of articles published may follow the Poisson distribution. Th erefore, we can estimate the following Poisson regression model: 12 3 4 5 6 (| ) exp{ 5 } i ii i i E Y XB B B fem B mar B kid B phd B ment P imwhere = E(Y | XB) = the average number of articles published by a scholar in the last three years of a PhD. fem = gender, taking a value of 1 for female and 0 for male mar = marital status, 1 if married, 0 if single kid5 = number of children under the age of 5 phd = prestige of the graduate program, on a scale of 1 to 5 ment = number of articles published by the mentor of the scholar in the last three years. To see if the Poisson regression model fi ts the data, you can obtain data from Table 12.7 on the companion website.11 Th e data are for 915 scholars. In the sample, the number of articles published by the scholars ranged from 0 to 19 and the number of articles published by the mentors ranged from 0 to 77. (a) Interpret the coeffi cients of the estimated model. im (b) What is the expected change in for a unit change in fem, mar, kid5, phd, and ment, respectively? (c) What are your prior expectations of the impact of the regressors on the average productivity of a scholar? (d) Which of the regressors are individually statistically signifi cant? Which test do you use? (e) How would you judge the overall signifi cance of the estimated model? (f) Test whether the assumption of proportional odds model is valid in the present case (g) If the assumption of the proportional odds model is not tenable in the present example, what alternative(s) would you consider? Obtain the results from the chosen alternative and interpret them.

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