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SAS/ETS 9.22 User's Guide 57

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SAS/Ets 9.22 User's Guide 57. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 552 F Chapter 10 The COUNTREG Procedure 70 as follows e 0.99-2.09 .20 20 years 1 _ _ e 0.99-2.09 .20 0.64 e 0.99-2.09 .50 50 years 1 _ _ e 0.99-2.09 .50 0.49 e 0.99-2.09 .70 70 years 1 _ _ e 0.99-2.09 .70 0.38 That is the estimated probability of belonging to the low-risk group is about 0.64 for a 20-year-old individual 0.49 for a 50-year-old individual and only 0.38 for a 70-year-old individual. This supports the suspicion that older individuals are more likely to have a positive number of doctor visits. Alternative models to account for the overdispersion are the negative binomial and the zero-inflated negative binomial models which can be fit using the DIST NEGBIN and DIST ZINB options respectively. Example 10.2 ZIP and ZINB Models for Data Exhibiting Extra Zeros In the study by Long 1997 of the number of published articles by scientists see the section Getting Started COUNTREG Procedure on page 519 the observed proportion of scientists who publish no articles is 0.3005. The following statements use PROC FREQ to compute the proportion of scientists who publish each observed number of articles. Output 10.2.1 shows the results. proc freq data long97data table art out obs run Example 10.2 ZIP and ZINB Models for Data Exhibiting Extra Zeros F 553 Output 10.2.1 Proportion of Scientists Who Publish a Certain Number of Articles The FREQ Procedure art Frequency Percent Cumulative Frequency Cumulative Percent 0 275 30.05 275 30.05 1 246 26.89 521 56.94 2 178 19.45 699 76.39 3 84 9.18 783 85.57 4 67 7.32 850 92.90 5 27 2.95 877 95.85 6 17 1.86 894 97.70 7 12 1.31 906 99.02 8 1 0.11 907 99.13 9 2 0.22 909 99.34 10 1 0.11 910 99.45 11 1 0.11 911 99.56 12 2 0.22 913 99.78 16 1 0.11 914 99.89 19 1 0.11 915 100.00 PROC COUNTREG is then used to fit Poisson and negative binomial models to the data. For each model the PROBCOUNT option computes the probability that the number of published articles is m for m 0 to 10.The following statements compute the estimates for Poisson and .