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Unformatted text preview: EdPsych/Psych/Soc Spring 2009 C.J. Anderson Midterm 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. Be sure to report any tests and/or models that you fit to the data to justify your answer. A vaccination is “effective” if either it decreases the probability of becoming sick or given that an individual gets sick, they have a milder case of the disease. The data given here allows us to look at the benefit of vaccination for smallpox leading to a nonfatal versus a fatal case of smallpox. To examine this, I used logistic regression to model the probability of dying from smallpox as a function of • Having been vaccinated in infancy or not (2 levels, nominal). • The age classification of the person (5 leveles, nominal). While age is an ordinal variable, I choose to treat it nominally, becuase I was not certain of the proper scores for the categories and was not even sure that “correct” order in this case was the natural order. Not: When age is treated it numerically and the scores correspond to the natural order of age leads to a poorly fitting model. The model fit to the data: logit( π i j ) = α + β Vaccination 1 i + β AgeClass 2 j This model fits very well: Global Fit Statistic Value df pvalue Deviance, G 2 1.6081 4 .81 Pearson Chisquare, X 2 1.0433 4 .90 The fit statistics are not significant indicating the model fits the data. 1 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 missfit. • 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 missfit). (next page). – All of the observations except for 1 (vaccinated, 0 4) are within 95% confidence intervals/bands. (plot not given) 2 The estimated parameters are Analysis Of Parameter Estimates Standard Wald 95% Confidence Parameter DF Estimate Error Limits Intercept 1 0.2133 0.46350.6952 1.1218 age 04 10.4105 0.53451.4582 0.6372 age 0514 12.4261 0.62583.65261.1996 age 1529 11.9968 0.53253.04050.9531 age 3049 10.1158 0.50221.1000 0.8684 age >50 0.0000 0.0000 0.0000 0.0000 vac yes 13.3171 0.35484.01252.6216 vac no 0.0000 0.0000 0.0000 0.0000 3 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 chisquares, we see that for the individual parameter estimates Analysis Of Parameter Estimates Parameter Pr > ChiSq Intercept 0.6454 age...
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 Spring '08
 Hong
 Likelihood function, Pearson's chisquare test, Likelihoodratio test, Parameter Estimates Standard

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