midterm09_key - EdPsych\/Psych\/Soc Spring 2009 C.J Anderson Mid-term Exam Answer Key All the work must be your own If you have any questions ask Carolyn

midterm09_key - EdPsych/Psych/Soc Spring 2009 C.J...

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EdPsych/Psych/Soc Spring 2009 C.J. Anderson Mid-term Exam Answer Key All the work must be your own. If you have any questions ask Carolyn. 1.It is widely believed that immunity from smallpox vaccination declines rapidly.Analyze these data to determine whether the data provide evidence for this belief. Besure to report any tests and/or models that you fit to the data to justify your answer. 1
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Further evidence that the model fits: The residuals are all pretty small and approximately normaly distributed (I used SAS/INSIGHT to examine them). Furthermore, there is not systematic miss-fit. Graphical displays: Plot of predicted probabilities versus observed proportions are all clustered around 45 o line. (below) Plot of observed and predicted by Age Classification with separate symbol or line for whether vacinated or not shows the closeness bewteen observed and predictied (and no systematic miss-fit). (next page). All of the observations except for 1 (vaccinated, 0 - 4) are within 95% confidence intervals/bands. (plot not given) 2
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The estimated parameters are Analysis Of Parameter Estimates Standard Wald 95% Confidence Parameter DF Estimate Error Limits Intercept 1 0.2133 0.4635 -0.6952 1.1218 age 0-4 1 -0.4105 0.5345 -1.4582 0.6372 age 05-14 1 -2.4261 0.6258 -3.6526 -1.1996 age 15-29 1 -1.9968 0.5325 -3.0405 -0.9531 age 30-49 1 -0.1158 0.5022 -1.1000 0.8684 age >50 0 0.0000 0.0000 0.0000 0.0000 vac yes 1 -3.3171 0.3548 -4.0125 -2.6216 vac no 0 0.0000 0.0000 0.0000 0.0000 3
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All of the effects are significant based on the likelihood ratio tests: LR Statistics For Type 3 Analysis Chi- Source DF Square Pr > ChiSq age 4 50.09 <.0001 vac 1 103.00 <.0001 From the Wald chi-squares, we see that for the individual parameter estimates Analysis Of Parameter Estimates Parameter Pr > ChiSq Intercept 0.6454 age 0-4 0.4425 age 5-14 0.0001 age 15-29 0.0002 age 30-49 0.8177 age >50 . vac yes <.0001 vac no . In words, the parameter estimates for age classes 0–4 and 30–49 are not significantly different from zero. So while I didn’t expect anyone to do this, a slightly “better” model as follows. Define a new nominal age variable with three levels: age * = 1 if age 5 - - 14
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  • Spring '08
  • Hong
  • Likelihood function, Pearson's chi-square test, Likelihood-ratio test, Parameter Estimates Standard

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