An Introduction To Categorical Data Analysis 2nd Edition Alan Agresti - Solutions

Table 3.9, based on a study with British doctors conducted by R. Doll and A. Bradford Hill, was analyzed by N. R. Breslow in A Celebration of Statistics, Berlin: Springer, 1985.a. For each age, compute the sample coronary death rates per 1000 person-years, for nonsmokers and smokers. To compare
For rate data, a GLM with identity link isμ/t = α + βx Explain why you could fit this model using t and tx as explanatory variables and with no intercept or offset terms.
True, or false?a. An ordinary regression (or ANOVA) model that treats the response Y as normally distributed is a special case of a GLM, with normal random component and identity link function.b. With a GLM, Y does not need to have a normal distribution and one can model a function of the mean of Y
A study used logistic regression to determine characteristics associated with Y = whether a cancer patient achieved remission (1 = yes). The most important explanatory variable was a labeling index (LI) that measures proliferative activity of cells after a patient receives an injection of tritiated
Refer to the previous exercise. Using information from Table 4.9:a. Conduct aWald test for the LI effect. Interpret.b. Construct aWald confidence interval for the odds ratio corresponding to a 1-unit increase in LI. Interpret.c. Conduct a likelihood-ratio test for the LI effect. Interpret.d.
In the first nine decades of the twentieth century in baseball’s National League, the percentage of times the starting pitcher pitched a complete game were: 72.7(1900–1909), 63.4, 50.0, 44.3, 41.6, 32.8, 27.2, 22.5, 13.3(1980–1989)(Source: GeorgeWill, Newsweek, April 10, 1989).a. Treating the
Consider the snoring and heart disease data of Table 3.1 in Section 3.2.2.With scores {0, 2, 4, 5} for snoring levels, the logistic regression ML fit is logit(πˆ ) = −3.866 + 0.397x.a. Interpret the sign of the estimated effect of x.b. Estimate the probabilities of heart disease at snoring
For the 23 space shuttle flights before the Challenger mission disaster in 1986, Table 4.10 shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress.a. Use logistic regression to model the effect of temperature on the probability of
Refer to Exercise 3.9. Use the logistic regression output reported there to (a)interpret the effect of income on the odds of possessing a travel credit card, and conduct a (b) significance test and (c) confidence interval about that effect.
Hastie and Tibshirani (1990, p. 282) described a study to determine risk factors for kyphosis, which is severe forward flexion of the spine following corrective spinal surgery. The age in months at the time of the operation for the 18 subjects for whom kyphosis was present were 12, 15, 42, 52, 59,
For the horseshoe crab data (Table 3.2, available at www.stat.ufl.edu/∼aa/intro-cda/appendix.html), fit the logistic regression model for π = probability of a satellite, using weight as the predictor.a. Report the ML prediction equation.b. Find ˆπ at the weight values 1.20, 2.44, and 5.20 kg,
For the horseshoe crab data, fit a logistic regression model for the probability of a satellite, using color alone as the predictor.a. Treat color as nominal scale (qualitative). Report the prediction equation, and explain how to interpret the coefficient of the first indicator variable.b. For the
An international poll quoted in an Associated Press story (December 14, 2004)reported low approval ratings for President GeorgeW. Bush among traditional allies of the United States, such as 32% in Canada, 30% in Britain, 19% in Spain, and 17% in Germany. Let Y indicate approval of Bush’s
Moritz and Satariano (J. Clin. Epidemiol., 46: 443–454, 1993) used logistic regression to predict whether the stage of breast cancer at diagnosis was advanced or local for a sample of 444 middle-aged and elderly women.A table referring to a particular set of demographic factors reported the
Exercise 2.33 mentioned a study in Florida that stated that the death penalty was given in 19 out of 151 cases in which a white killed a white, in 0 out of 9 cases in which a white killed a black, in 11 out of 63 cases in which a black killed a white, and in 6 out of 103 cases in which a black
Refer to (d) in the previous exercise. The Cochran–Mantel–Haenszel test statistic for this hypothesis equals 7.00.a. Report the null sampling distribution of the statistic and the P-value.b. Under H0, find the expected count for the cell in which white defendants who had black victims received
Refer to the results that Table 4.5 shows for model (4.5) fitted to the data from the AZT and AIDS study in Table 4.4.a. For black veterans without immediateAZT use, use the prediction equation to estimate the probability of AIDS symptoms.b. Construct a 95% confidence interval for the conditional
Table 4.12 refers to ratings of agricultural extension agents in North Carolina.In each of five districts, agents were classified by their race and by whether they qualified for a merit pay increase.a. Conduct the Cochran–Mantel–Haenszel test of the hypothesis that the merit pay decision is
Table 4.13 shows the result of cross classifying a sample of people from the MBTI Step II National Sample (collected and compiled by CPP, Inc.) on whether they report drinking alcohol frequently (1 = yes, 0 = no) and on the four binary scales of the Myers–Briggs personality
Refer to the previous exercise. Table 4.14 shows the fit of the model with only E/I and T/F as predictors.a. Find ˆπ for someone of personality type introverted and feeling.b. Report and interpret the estimated conditional odds ratio between E/I and the response.c. Use the limits reported to
A study used the 1998 Behavioral Risk Factors Social Survey to consider factors associated with American women’s use of oral contraceptives. Table 4.15 summarizes effects for a logistic regression model for the probability of using oral contraceptives. Each predictor uses an indicator variable,
A sample of subjects were asked their opinion about current laws legalizing abortion (support, oppose). For the explanatory variables gender (female, male), religious affiliation (Protestant, Catholic, Jewish), and political party affiliation (Democrat, Republican, Independent), the model for the
Table 4.16 shows results of an eight-center clinical trial to compare a drug to placebo for curing an infection. At each center, subjects were randomly assigned to groups.a. Analyze these data, describing and making inference about the group effect, using logistic regression.b. Conduct the
In a study designed to evaluate whether an educational program makes sexually active adolescents more likely to obtain condoms, adolescents were randomly assigned to two experimental groups. The educational program, involving a lecture and videotape about transmission of the HIV virus, was provided
Refer to model (4.11) with width and color effects for the horseshoe crab data.Using the data at www.stat.ufl.edu/∼aa/intro-cda/appendix.html:a. Fit the model, treating color as nominal-scale but with weight instead of width as x. Interpret the parameter estimates.b. Controlling for weight,
Table 4.18 shows estimated effects for a fitted logistic regression model with squamous cell esophageal cancer (1 = yes, 0 = no) as the response variable Y . Smoking status (S) equals 1 for at least one pack per day and 0 otherwise, alcohol consumption (A) equals the average number of alcoholic
Table 4.19 shows results of a study about Y = whether a patient having surgery with general anesthesia experienced a sore throat on waking (1 = yes) as a function of D = duration of the surgery (in minutes) and T = type of device used to secure the airway (0 = laryngeal mask airway, 1 = tracheal
For model (4.11) for the horseshoe crabs with color and width predictors, add three terms to permit interaction between color and width.a. Report the prediction equations relating width to the probability of a satellite, for each color. Plot or sketch them, and interpret.b. Test whether the
Model (4.11) for the probability π of a satellite for horseshoe crabs with color and width predictors has fit logit(πˆ ) = −12.715 + 1.330c1 + 1.402c2 + 1.106c3 + 0.468x Consider this fit for crabs of width x = 20 cm.a. Estimate π for medium-dark crabs (c3 = 1) and for dark crabs (c1 = c2 =c3
The prediction equation for the horseshoe crab data using width and quantitative color (scores 1, 2, 3, 4) is logit(πˆ ) = −10.071 − 0.509c + 0.458x. Color has mean = 2.44 and standard deviation = 0.80, and width has mean = 26.30 and standard deviation = 2.11.a. For standardized versions of
For recent General Social Survey data, a prediction equation relating Y =whether attended college (1 = yes) to x = family income (thousands of dollars, using scores for grouped categories), m = whether mother attended college (1 = yes, 0 = no), f = whether father attended college (1 = yes, 0 = no),
Table 4.20 appeared in a national study of 15- and 16-year-old adolescents.The event of interest is ever having sexual intercourse. Analyze these data and summarize in a one-page report, including description and inference about the effects of both gender and race.
The US National Collegiate Athletic Association (NCAA) conducted a study of graduation rates for student athletes who were freshmen during the 1984–1985 academic year. Table 4.21 shows the data. Analyze and interpret in a one-page report, including description and inference.
Refer to Table 7.3, treating marijuana use as the response variable. Analyze these data. Prepare a one-page report summarizing your descriptive and inferential results.
See http://bmj.com/cgi/content/full/317/7153/235 for a meta analysis of studies about whether administering albumin to critically ill patients increases or decreases mortality. Analyze the data for the three studies with burn patients using logistic regression methods. Summarize your analyses in a
Fowlkes et al. (J. Am. Statist. Assoc., 83: 611–622, 1988) reported results of a survey of employees of a large national corporation to determine how satisfaction depends on race, gender, age, and regional location. The data are at www.stat.ufl.edu/∼aa/cda/cda.html. Fowlkes et al. reported
For the model, logit[π(x)] = α + βx, show that eα equals the odds of success when x = 0. Construct the odds of success when x = 1, x = 2, and x = 3. Use this to provide an interpretation of β. Generalize these results to the multiple logistic regression model (4.10).
The slope of the line drawn tangent to the probit regression curve at a particular x value equals (0.40)β exp[−(α + βx)2/2].a. Show this is highest when x = −α/β, where it equals 0.40β. At this point,π(x) = 0.50.b. The fit of the probit model to the horseshoe crab data using x = width is
When β > 0, the logistic regression curve (4.1) has the shape of the cdf of a logistic distribution with mean μ = −α/β and standard deviation σ =1.814/β. Section 4.1.3 showed that the horseshoe crab data with x = width has fit, logit[ ˆ π(x)] = −12.351 + 0.497x.a. Show that the curve
For data from Florida on Y = whether someone convicted of multiple murders receives the death penalty (1 = yes, 0 = no), the prediction equation is logit(πˆ ) = −2.06 + .87d − 2.40v, where d and v are defendant’s race and victims’ race (1 = black, 0 = white). The following are

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