Questions and Answers of Categorical Data Analysis

Suppose that P(T = tj) = πj, j = 1 Show that E(mid-P-value) 0.5. [Show that ∑jπj(πj/2 + πj+1 + .....) = (∑jπj)2/2.]
Show that the moment generating function (mgf) for the binomial distribution is m(t) = (1 – π + πet)n, and use it to obtain the first two moments. Show that the mgf for the Poisson distribution
For the multinomial distribution, show thatShow that corr(n1, n2) = €“1 when c = 2. corr (n , n)- -η π.//π1-)Τ1- π).
Suppose that P(Yi = 1) = 1 – P(Yi = 0) = π, i = 1, . . . , n, where {Yi} are independent. Let Y = ∑i Yi).a. What are var(Y) and the distribution of Y?b. When {Yi} instead have pairwise
Why is it easier to get a precise estimate of the binomial parameter π when it is near 0 or 1 than when it is near 1/2?
Table 1.3 contains Ladislaus von Bortkiewicz€™s data on deaths of soldiers in the Prussian army from kicks by army mules (Fisher 1934; Quine and Seneta 1987). The data refer to 10 army
In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. It is desired to estimate π and test H0: π = 0.5 against Ha: π ≠ 0.5. In 20
Refer to the vegetarianism example in Section 1.4.3. For testing H0: π = 0.5 against H0: π ≠ 0.5, show that:a. The likelihood-ratio statistic equals 2[25log(25/12.5)] = 34.7.b. The
Consider the statement, “Please tell me whether or not you think it should be possible for a pregnant woman to obtain a legal abortion if she is married and does not want any more children.” For
In his autobiography A Sort of Life, British author Graham Greene described a period of severe mental depression during which he played Russian Roulette. This “game’s consists of putting a bullet
An experiment studies the number of insects that survive a certain dose of an insecticide, using several batches of insects of size n each. The insects are sensitive to factors that vary among
Each of 100 multiple-choice questions on an exam has four possible answers, one of which is correct. For each question, a student guesses by selecting an answer randomly.a. Specify the distribution
Identify each variable as nominal, ordinal, or interval.a. UK political party preference (Labour, Conservative, Social Democrat)b. Anxiety rating (none, mild, moderate, severe, very severe)c. Patient
Show the normal distribution N(µ, σ2) with fixed σ satisfies family (4.1), and identify the components. Formulate the ordinary regression model as a GLM.
For binary observations, consider the model π(x) = 1/2 + (1/π)tan–1(α + βx). Which distribution has cdf of this form? Explain when a GLM using this curve might be more appropriate than logistic
Consider the value β̂ that maximizes a function L( β). Let β0 denote an initial guess.a. Using L’( β̂.) = L’( β(0) + (β̂ – β(0) L”(β(0)) + ..., argue that for β(0) close to
For n independent observations from a Poisson distribution, show that Fisher scoring gives µ(t + 1) = y̅ for all t > 0. By contrast, what happens with Newton—Raphson?
In a GLM, suppose that var(Y) = υ(µ) for µ = E(Y). Show that the link g satisfying g’(µ.) = [υ(µ)]–1/2 has the same weight matrix W(t) at each cycle. Show this link for a Poisson random
For the 23 space shuttle flights before the challenger mission disaster in 1986, Table 5.12 shows the temperature at the time of the flight and whether at least one primary O-ring suffered thermal
Refer to Table 4.2. Using scores {0, 2, 4, 5) for snoring, fit the logistic regression model. Interpret using fitted probabilities, linear approximations, and effects on the odds. Analyze the
Hastie and Tibshirani described a study to determine risk factors for kyphosis, severe forward flexion of the spine following corrective spinal surgery. The age in months at the time of the operation
Refer to Table 6.11. The Pearson test of independence has X2(I) = 6.88. For equally spaced scores, the Cochran€”Armitage trend test has z2= 6.67 (P = 0.01). Interpret, and explain why
Refer to Table 2.11. Using scores (0, 3, 9.5, 19.5, 37, 55) for cigarette smoking, analyze these data using a logit model. Is the intercept estimate meaningful? Explain.Table 2.11: Disease Group Lung
A study used the 1998 Behavioral Risk Factors Social Survey to consider factors associated with women€™s use of oral contraceptives in the United States. Table 5.13 summarizes effects for a
Refer to Table 2.6. Table 5.14 shows the results of fitting a logit model, treating death penalty as the response (1 = yes) and defendant€™s race (1 = white) and victims€™ race (1
Table 5.15 appeared in a national study of 15-and 16-year-old adoles cent. The event of interest is ever having sexual intercourse, Analyze, including description and inference about the effects of
The National Collegiate Athletic Association studied graduation rates for freshman student athletes during the 1984–1985 academic year. The (sample size, number graduated) totals were (796, 498)
Ina 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
Table 5.17 shows estimated effects for a logistic regression model with squamous cell esophageal cancer (Y = 1, yes; Y = 0, no) as the response. Smoking status (S) equals 1 for at least one pack per
A survey of high school students on Y = whether the subject has driven a motor vehicle after consuming a substantial amount of alcohol (1 = yes), s = gender (1 = female), r = race (1 = black: 0 =
Refer to model (5.2) for the horseshoe crabs using x = width.a. Show that (I) at the mean width (26.3), the estimated odds of a satellite equal 2.07; (ii) at x = 27.3, the estimated odds equal 3.40;
Refer to the prediction equation logit(π̂) = – 10.071 – 0.509c + 0.458x for model (5.13). The means and standard deviations are c̅ = 2.44 and s = 0.80 for color, and x̅ = 26.30 and s = 2.11
Let Y denote a subject’s opinion about current laws legalizing abortion (1 = support), for gender h (h = 1, female; h = 2, male), religious affiliation i (i = 1, Protestant: i = 2, Catholic; i = 3,
For model (5.1), show that ∂π(x)/∂x = βπ(x)[1 – π(x)].
For model (5.1), when π(x) is small, explain why you can interpret exp(β) approximately as π(x + 1)/π(x).
Prove that the logistic regression curve (5.1) has the steepest slope where π(x) = 1/2. Generalize to model (5.8).
The calibration problem is that of estimating x at which π(x) = π0. For the linear logit model, argue that a confidence interval is the set of x values for which |α̂ + β̂x –
A study for several professional sports of the effect of a player’s draft position d (d = 1, 2, 3,...) of selection from the pool of potential players in a given year on the probability π of
Construct the log-likelihood function for the model logit[π(x)] = α + βx with independent binomial outcomes of y0 successes in n1 trials at x = 0 and y1 successes in n1 trials at x = 1. Derive the
Suppose that Y has a bin(n,π ) distribution. For the model, logit(π) = α, consider testing H0: α = 0 (i.e., π = 0.5). Let π̂ = y/n.a. From Section 3.1.6, the asymptotic variance of α̂ =

Showing 500 - 600 of 540

1
2
3
4
5
6