Questions and Answers of Categorical Data Analysis

9. Consider the following hierarchical changepoint model for the number of occurrences Yi of some event during time interval i:Yi ∼% Poisson(θ), i = 1,...,k Poisson(λ), i = k + 1,...,nθ ∼
8. Repeat the analysis of the previous problem in WinBUGS. Do your answers agree? List two advantages and two disadvantages of MCMC methods relative to noniterative MC methods.
7. Actually perform the point and interval estimation of the age corresponding to minimum property tax in the previous problem using a
6. In the previous problem, suppose that instead of the intercept β0, the parameter of interest is the age corresponding to minimum tax under this model. Describe how you would modify the above
5. Use quadratic regression to analyze the data in Table 3.4, which relate property taxes and age for a random sample of 19 homes. The response variable Y is property taxes assessed on each home (in
4. Suppose we have a sample {θ1,...,θN } from a posterior p1(θ|y), and we want to see the effect of changing the prior from π1(θ) to π2(θ).Describe how the weighted bootstrap procedure could
3. Show that the probability of accepting a given θj candidate in the rejection sampling is c/M, where c = L(θ)π(θ)dθ, the normalizing constant for the posterior distribution h(θ).
2. Suppose that f(y|θ) = n i=1 f(yi|θ). Describe how equation (3.1) could be used to investigate the effect of single case deletion (i.e., removing xi from the dataset, for i = 1,...,n) on the
1. Use Theorem 3.1 to obtain a first-order approximation to the Bayes factor BF, given in equation (2.19). Is there any computational advantage in the case where the two models are nested, i.e., θ1
23. Refer to Example 2.18.(a) Repeat the analysis of the stack loss data assuming a slightly generalized model where we letπj iid∼ Bernoulli(θ) , where θ ∼ Unif(0, 1). That is, allow prior
22. Refer to Example 2.16. Repeat the exact “leave one out” analysis of the stack loss data using the BRugs language. Here we would avoid the“trickery” of the fully WinBUGS solution given in
21. Refer to Example 2.15. Repeat the analysis of the MAC treatment data assuming a model having(a) three sets of random effects ri, Wi, and β1i, adding clinic-specific treatment effect
20. The following are increased hours of sleep for 10 patients treated with soporific B compared with soporific A (Cushny and Peebles, presented by Fisher in Statistical Methods for Research
19. The data in Table 2.11 come from a 1980 court case (Reynolds v. Sheet Metal Workers) involving alleged applicant discrimination. Perform a Bayesian analysis of these data. Is there evidence of
18. For the Dirichlet process prior described in Section 2.6, use the properties of the Dirichlet distribution to show that for any measurable set B,(a) E[G(B)] = G0(B)(b) V ar[G(B)] = G0(B)(1 −
17. Consider the two-stage binomial problem wherein θ ∼ G, and Xi|θ iid∼Bernoulli(θ), i = 1,...,n.(a) Find the joint marginal distribution of Xn = (X1,...,Xn).(b) Are the components
15. Suppose that Y |θ ∼ G(1, θ) (i.e., the exponential distribution with meanθ), and that θ ∼ IG(α, β).(a) Find the posterior distribution of θ.(b) Find the posterior mean and variance of
14. Refer to Example 2.10. Compare pD and DIC for the two prior distributions considered for the error terms, namely, the Gamma(.1, .1) prior on the error precision τ, and the Unif(.01, 100) prior
13. The classic Behrens-Fisher problem is that of estimating normal means from independent populations with unknown (and thus possibly unequal) variances. Here we consider this problem in the context
12. Consider www.biostat.umn.edu/~brad/data/land_data.txt, for which a few records are shown in Table 2.9. Here, Y represents log-transformed?
11. In a pediatric clinical study carried out to see how effective aspirin is in reducing temperature, n = 12 five-year-old children suffering from influenza had their temperature taken immediately
9. Show that the Jeffreys prior based on the binomial likelihoodf(x|θ) = n xθx(1 − θ)n−x is given by the Beta(.5, .5) distribution.10. Suppose that in the situation of Example 2.3 we adopt
8. Suppose that f(x|θ, σ) is normal with mean θ and standard deviation σ.(a) Suppose that σ is known, and show that the Jeffreys prior (2.12) forθ is given by p(θ)=1, θ ∈ .(b) Next, suppose
7. Let θ be a univariate parameter of interest, and let γ = g(θ) be a 1-1 transformation. Use (2.12) and (2.13) to show that (2.14) holds, i.e., that the Jeffreys prior is invariant under
6. For the following densities from Appendix A, state whether each represents a location family, scale family, location-scale family, or none of these. For any of the first three situations, suggest
6. For the following densities from Appendix A, state whether each represents a location family, scale family, location-scale family, or none of these. For any of the first three situations, suggest
5. For each of the following densities from Appendix A, provide a conjugate prior distribution for the unknown parameter(s), if one exists:(a) X ∼ Bin(n, θ), n known(b) X ∼ NegBin(r, θ), r
4. Let θ be the height of the tallest individual currently residing in the city where you live. Elicit your own prior density for θ by(a) a histogram approach(b) matching an appropriate
3. Confirm expression (2.11) for the conditional posterior distribution of σ2 given θ in the conjugate normal model. If your random number generator could produce only χ2 random variates, how
2. Confirm expression (2.3) for the conditional posterior distribution of θgiven σ2 in the conjugate normal model, and show that the precision in this posterior is the sum of the precisions in the
1. Let Y1, Y2.... be a sequence of random variables (not necessarily independent) taking on the values 0 and 1. Let Sn = Y1 + ...Yn.(a) Represent P(Yn+1 = 1|Sn = s) in terms of the joint distribution
8. In analyzing data from a Bin(n, θ) likelihood, the MLE is ˆθMLE = Y /n, which has MSE = Ey|θ(ˆθMLE −θ)2 = V ary|θ(ˆθMLE) = θ(1−θ)/n. Find the MSE of the estimator ˆθBayes = (Y +
7. In the basic diagnostic test setting, a disease is either present (D = 1)or absent (D = 0), and the test indicates either disease (T = 1) or no disease (T = 0). Represent P(D = d|T = t) in terms
6. In the Normal/Normal example of Subsection 1.5.1, let σ2 = 2, μ = 0, and τ 2 = 2.(a) Suppose we observe y = 4. What are the mean and variance of the resulting posterior distribution? Sketch the
5. Here is an example in a vein similar to that of Example 1.2, and originally presented by Berger and Berry (1988). Consider a clinical trial established to study the effectiveness of vitamin C in
4. For predictive distributions of survival time associated with two medical treatments, propose treatment selection criteria that are meaningful to you (or if you prefer, to society).
3. Assume you have developed predictive distributions of the length of time it takes to drive to work, one distribution for Route A and one for Route B. What summaries of these distributions would
2. Repeat the journal publication thought problem from Subsection 1.2.1 for the situation where(a) you have won a lottery on your first try.(b) you have correctly predicted the winner of the first
1. Let θ be the true proportion of men in your community over the age of 40 with hypertension. Consider the following “thought experiment”:(a) Though you may have little or no expertise in this
=+What types of uncontrolled variables or covariates might be operating in each of these situations?
=+5. Describe some data analysis situations in which MANOVA and MANCOVA would be appropriate in your areas of interest.
=+ How would you design a study to ensure adequate power?
=+4. How is statistical power affected by statistical and research design decisions?
=+dependent variables; and (c) examination of the discriminant functions. Describe the practical advantages and disadvantages of each of these approaches.
=+is computed after eliminating the effects of the previous
=+contrast procedures; (b) stepdown analysis, which is similar to stepwise regression in that each successive F statistic
=+3. Besides the overall, or global, significance, at least three approaches to follow-up tests include (a) use of Scheffé
=+What would a significant interaction tell you?
=+What are the different sources of variance in your experiment?
=+2. Design a two-way factorial MANOVA experiment.
=+1. What are the differences between MANOVA and discriminant analysis? What situations best suit each multivariate technique?
=+• Is the direct distribution system always preferred over the indirect system across the customer groups of X1?
=+• Do the two distribution systems show differences for customers of 5 years or more?
=+• Is the direct distribution system more effective for newer customers?
=+3. What is the relationship between the distribution system and these relationships with customers in terms of the purchase outcomes?
=+2. Is HBAT establishing better relationships with its customers over time, as reflected in customer satisfaction and other purchase outcomes?
=+1. What differences are present in customer satisfaction and other purchase outcomes between the two channels in the distribution system?
=+ Describe the purpose of multivariate analysis of covariance (MANCOVA).
=+ Interpret interaction results when more than one independent variable is used in MANOVA.
=+ Describe the purpose of post hoc tests in ANOVA and MANOVA.
=+ Discuss the different types of test statistics that are available for significance testing in MANOVA.
=+ State the assumptions for the use of MANOVA.
=+ Discuss the advantages of a multivariate approach to significance testing compared to the more traditional univariate approaches.
=+ Explain the difference between the univariate null hypothesis of ANOVA and the multivariate null hypothesis of MANOVA.
=+5. Why is it important to examine the results of a measurement model before proceeding to test a structural model?
=+4. How is the validity of a SEM model estimated?
=+3. What is the distinguishing characteristic of a nonrecursive SEM model?
=+item be incorporated into a SEM model?
=+2. How can a measured variable represented with a single
=+for a measurement model differ from that of a SEM model?
=+the way a SEM model is tested? How does the visual diagram
=+What implications do these differences have for
=+1. In what ways is a measurement theory different from a structural theory?
=+ Diagnose problems with the SEM results
=+ Test a structural model using SEM.
=+ Depict a model with dependence relationships using a path diagram.
=+ Describe the similarities between SEM and other multivariate techniques.
=+Distinguish a measurement model from a structural model.
=+result. Does the model show evidence of adequate construct validity? Explain.
=+8. Find an article in a business journal that reports a CFA
=+7. Is it possible to establish precise cutoffs for CFA fit indices? Explain.
=+6. What is a Heywood case, and how is it treated using SEM?
=+5. How is the order condition of identification verified?
=+Why do they represent the properties of good measurement?
=+4. What are the properties of a congeneric measurement model?
=+3. What are the steps in developing a new construct measure?
=+2. List and define the components of construct validity.
=+1. How does CFA differ from EFA?
=+ Understand the concept of model fit as it applies to measurement models and be able to assess the fit of a confirmatory factor analysis model.
=+ Understand the basic principles of statistical identification and know some of the primary causes of CFA identification problems.
=+ Know how to represent a measurement model using a path diagram.
=+ Assess the construct validity of a measurement model.
=+Distinguish between exploratory factor analysis and confirmatory factor analysis (CFA).
=+expected to be related negatively to the endogenous construct.
=+each measured by five items and the endogenous construct is measured by four items. Both exogenous constructs are
=+11. Draw a path diagram with two exogenous constructs and one endogenous construct. The exogenous constructs are
=+from poor fit across all situations?
=+10. Why are no magic values available to distinguish good fit
=+9. How does sample size affect structural equation modeling?
=+8. What is the difference between an absolute and a relative fit index?

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