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legal research analysis

Questions and Answers of Legal Research Analysis

Each of 100 multiple-choice questions on an exam has four possible answers but one correct response. For each question, a student randomly selects one response as the answer.a. Specify the
Which scale of measurement is most appropriate for the following variables —nominal or ordinal?a. UK political party preference (Labour, Liberal Democrat, Conservative, other)b. Highest educational
In the following examples, identify the natural response variable and the explanatory variables.a. Attitude toward gun control (favor, oppose), gender (female, male), mother’s education (high
Project: Go to a site with large data files, such as the UCI Machine Learning Repository (archive.ics.uci.edu/ml) or Yahoo! Webscope (webscope.sandbox.yahoo.com). Find a data set of interest to you
Using the spam data set at the website web.stanford.edu/~hastie/ElemStatLearn for Hastie et al. (2009), use two methods presented in this chapter to select explanatory variables to classify whether a
For the myocardial infarction example in Section 11.5.6, use the FDR method to test significance, with α = 0.10. Compare results to the Bonferroni method.
For the Students data file, model y = whether you are a vegetarian, with the 13 other explanatory variables used in Section 11.5.3. For ordinary logistic regression, show that this model fits better
For the data analyzed in Sections 5.3.4, 5.4.2, and 5.4.4 on risk factors for endometrial cancer, compare the results shown there with those you obtain with the lasso by selecting λ using
For the horseshoe crab data set, plot the satellite count against the crab’s weight.Also plot a curve based on smoothing the data using a generalized additive model, assuming a Poisson response and
For the horseshoe crab data set, plot the binary response of the satellite presence against the crab’s weight. Also plot a curve based on smoothing the data using a generalized additive model,
Conduct a cluster analysis for the complete Elections data file at the text website.Show the two-cluster solution and interpret.
Refer to the Presidential elections cluster analysis in Section 11.3.3.a. The observations were the same for New Jersey and Pennsylvania as llinois, and the same for North Carolina as Virginia.
A classification tree predicted whether, over a one-year period, elderly subjects participating in an assisted-living program disenroll from the program to enter a nursing home.9 The sample consisted
Refer to the previous exercise. Use the classification tree method with all four explanatory variables, treating color and spine condition as quantitative. Explain how you pruned the tree, interpret
Consider the horseshoe crab classification tree in Figure 11.1.a. Sketch a plot of width against color. Based on the information at the terminal nodes, show the rectangular regions for which yˆ = 1.
For the Crabs data file with y = whether a female horseshoe crab has at least one satellite, conduct a linear discriminant analysis. Use all four explanatory variables, treating color and spine
Refer to the use of linear discriminant analysis by R.A. Fisher in 1936 for Iris flower data, as discussed in the article “Iris flower data set” at Wikipedia. Conduct a linear discriminant
Fit a logistic-normal random intercept model to the carcinoma ratings of Table 10.7 in the Carcinoma data file. (Note: The data file must be re-constructed to have 7 lines of observations for each
Refer to Table 9.1 on opinions about legalized abortion in three situations. Using the Abortion2 data file at the text website that shows the three responses for each subject on a single line, fit
For the smoking prevention study analyzed in Section 10.4.2, fit the multilevel model that allows interaction between SC and TV. Interpret effects. Compare results to those for the ordinary logistic
Refer to the cereal diet and cholesterol study of Table 6.10. Analyze these data with an ordinal GLMM. Summarize results in a short report, showing edited software output as an appendix.
For Table 8.13 on premarital and extramarital sex, a cumulative logit model with a random intercept has βˆ = 4.134 with SE = 0.330 and σˆ = 2.076 for the random effects. The corresponding
Table 10.11 reports results of a study of fish hatching under three environments.Eggs from seven clutches were randomly assigned to three treatments, and the response was whether an egg hatched by
A crossover study compares two drugs on a binary response variable. The study classifies subjects by age as under 60 or over 60. In a GLMM, these two age groups have the same effect comparing the
Analyze Table 9.4 with age and maternal smoking as predictors using (a) a logisticnormal model, (b) a marginal model, (c) a transitional model. Summarize your analyses in a short report. Explain how
For Table 5.2 on admissions decisions for Florida graduate school applicants, let yig = 1 denote a subject in department i of gender g (1 = females, 0 = males) being admitted. The model logit[P(Yig =
Refer to Exercise 9.4 and the Depression data file. Now let yit denote observation t for subject i. Fit the model logit[P(Yit = 1)] = ui + α + β1s + β2d + β3t + β4(d × t).Interpret effects and
For the crossover study summarized in Exercise 9.6, fit the model logit[P(Yi(k)t = 1)] = ui(k) + αk + βt, where {ui(k)} are independent N(0, σ2). Interpret {βˆt} and σˆ. Compare
For Table 7.1, let yit = 1 when student i used substance t (t = 1, cigarettes; t = 2, alcohol; t = 3, marijuana). Fit the model, logit[P(Yit = 1)] = ui + α + βt.a. Report and interpret the
For 10 coins, let πi denote the probability of a head for coin i. You flip each coin 5 times. The sample numbers of heads are (2, 4, 1, 3, 3, 5, 4, 2, 3, 1).a. Report the sample proportion estimates
Table 10.10 shows results of a teratology experiment, available in the Teratology data file at the text website. Female rats on iron-deficient diets were assigned to four groups. Group 1 received
For Table 8.9, which asked subjects whether they believe in heaven and whether they believe in hell, fit model (10.2). If your software uses numerical integration, report βˆ, σˆ, and their
True or false? For repeated measurement data, under an assumption of independent observations, the ML estimates are valid but their ordinary standard errors are usually too large for within-subject
Give an example of a scenario in which data would likely (a) be missing at random but not missing completely at random, (b) not be missing at random.
What is wrong with this statement?: “For a first-order Markov logistic regression model, Yt is independent of Yt−2.”
Analyze Table 9.4 from Section 9.4.2 using a transitional model with two previous responses. Given that yt−1 is in the model, does yt−2 provide additional predictive power? How does the maternal
For the insomnia study (Table 9.2), the transitional model (9.1) compared treatments while controlling for initial time to fall asleep.a. Add an interaction term to model (9.1). Summarize how the
Refer to the cereal diet and cholesterol study of Table 6.10 (Exercise 6.16). Analyze these data with ordinal marginal models. Summarize results in a short report, showing edited software output as
Analyze the 3×3×3×3 table on government spending in Table 7.16 with a marginal cumulative logit model. Interpret effects and show how to test marginal homogeneity.
Table 9.7 is from a longitudinal study of coronary risk factors in school children. A sample of children aged 10–13 were classified by gender and by relative weight (O =obese, N = not obese) at the
A Kansas State University survey6 of 262 pig farmers asked “What are your primary sources of veterinary information?” The farmers were asked to select all relevant categories from (A)
Table 9.6 refers to a three-period crossover trial to compare placebo (treatment A), a low-dose analgesic (B), and a high-dose analgesic (C) for relief of primary dysmenorrhea. Subjects were divided
Refer to the previous exercise. Analyze the Depression data file at the text website using GEE, assuming exchangeable correlation and with the time scores (1, 2, 4).Interpret model parameter
Table 9.5 refers to a clinical trial comparing a new drug (d = 1) with a standard drug(d = 0) for subjects suffering mental depression. Initial severity of depression was recorded as mild (s = 0) or
For Table 7.8, in fitting marginal models to describe main effects of race, gender, and substance type on whether a subject had used that substance, we find evidence of an interaction between gender
Analyze Table 9.4 using a marginal model with age and maternal smoking as explanatory variables. Report the prediction equation and compare interpretations to the Markov logistic model of Section
Refer to Table 7.1 on high school students’ use of alcohol, cigarettes, and marijuana.Consider the data as matched triplets.a. Construct the marginal distribution for each substance. Specify a
True or false: With positively correlated dependent samples, the estimator of the difference of marginal probabilities is more precise than with independent samples of the same size.
When the Bradley–Terry model holds, explain why it is not possible that A could be preferred to B (i.e., ΠAB > 1 2 ) and B could be preferred to C, yet C could be preferred to A.
Women’s tennis data for Exercise 8.15.Loser Winner Kerber Halep Pliskova S. Williams V. Williams Kerber – 5 4 1 1 Halep 3 – 5 2 4 Pliskova 3 2 – 1 1 S. Williams 3 5 2 – 3 V. Williams 2 2 1
Table 8.16 summarizes results of tennis matches for several women professional players between January 2014 and June 2017.a. Fit the Bradley–Terry model. Report the parameter estimates and rank the
A sample of psychology graduate students at the University of Florida made blind, pairwise preference tests of three cola drinks. For 49 comparisons of Coke and Pepsi, Coke was preferred 29 times.
On their TV show, Chicago film critics Gene Siskel and Roger Ebert portrayed themselves as adversarial, with quite different opinions. During a two-year period, the counts of (positive, mixed,
Table 8.15 displays diagnoses of multiple sclerosis for two neurologists. The categories are (1) Certain multiple sclerosis, (2) Probable multiple sclerosis, (3) Possible multiple sclerosis, (4)
For Table 8.5 on choice of coffee brand on two occasions, show that the quasiindependence model fits dramatically better than the ordinary independence model.Interpret.
Table 8.14 is from a General Social Survey. Subjects were asked whether danger to the environment was caused by car pollution and/or by a rise in the world’s temperature caused by the greenhouse
Table 8.13 is from a General Social Survey. Subjects were asked their opinion about a man and a woman having sex relations before marriage and a married person having sexual relations with someone
Table 8.12, from the 2016 General Social Survey, reports region of residence now and at age 16 for residents of the US.a. Test marginal homogeneity by comparing fits of two models.b. Fit the
Table 8.11, from the 2016 General Social Survey, reports religious affiliation now and at age 16 for US residents, with categories (1) Protestant, (2) Catholic, (3) Jewish,(4) None or Other.a. Fit
Explain the following analogy: The McNemar test is to binary response variables as the paired-difference t test is to normally distributed response variables.
Section 8.1.1 presented the large-sample z and chi-squared McNemar test for comparing dependent proportions. The exact P-value uses the binomial distribution. For Table 8.1, consider Ha: P(Y1 = 1) >
Table 8.10 shows results from a matched case-control study. A study of acute myocardial infarction (MI) among Navajo Indians matched 144 victims of MI according to age and gender with 144 individuals
Explain the difference between βˆ for marginal model (8.2) and βˆ for subject-specific model (8.3). Illustrate with Table 8.1 on helping the environment.
A recent General Social Survey asked subjects whether they believed in heaven and whether they believed in hell. Table 8.9 shows the results.a. Test the hypothesis that the population proportions
Apply the McNemar test to Table 8.3 on smoking and birthweight. Interpret.
A recent General Social Survey asked subjects how many times they had sexual intercourse in the previous month. The sample means were 5.9 for males and 4.3 for females; the sample variances were 54.8
For the Crabs data file at the text website, let y = number of satellites and x = weight.Fit the Poisson and negative binomial (NB) loglinear models. For each model, report the prediction equation
Consider Table 7.11 on survival of lung cancer patients.a. Fit the more complex model that allows interaction between stage and time. Analyze whether it provides a significantly improved fit.b. Fit
True or false?a. With a single categorical response variable, logistic regression models are more appropriate than loglinear models.b. To model the association and interaction structure among several
Table 7.17 comes from a General Social Survey. Subjects were asked whether methods of birth control should be available to teenagers and how often they attend religious services.a. Fit the
For the substance use data in Table 7.8, consider loglinear model (AC, AM, CM, AG, AR, GM, GR).a. Explain why the AM conditional odds ratio is unchanged by collapsing over race, but it is not
Refer to Exercise 7.7 with Table 7.16 and the Spending data file.a. Beginning with the homogeneous association model, show that backward elimination yields (CE, CL, EH, HL). Interpret its fit.b.
For loglinear model (WXZ,W Y Z), draw its independence graph and identify variables that are conditionally independent.
For a multiway contingency table, when is a logistic model more appropriate than a loglinear model? When is a loglinear model more appropriate?
For a three-way contingency table, consider the independence graph, X Z Y Write the corresponding loglinear model. Which pairs of variables are conditionally independent? Which pairs of variables
The data in Table 7.16, from a General Social Survey, are in the Spending data file at the text website. Subjects were asked about government spending on the environment (E), health (H), assistance
Table 7.15, from a General Social Survey, relates responses on R = religious service attendance (1 = at most a few times a year, 2 = at least several times a year), P = political views (1 = liberal,
Refer to the auto accident injury data shown in Table 7.5.a. Explain why the fitted odds ratios in Table 7.7 for model (GL, GS, LS, GI, LI, SI) suggest that the most likely case for injury is
At the website www.stat.ufl.edu/~aa/intro-cda/data for the second edition of this book, the MBTI data file cross-classifies the MBTI Step II National Sample on four binary scales of the
Table 7.14 is based on automobile accident records supplied by the state of Florida Department of Highway Safety and Motor Vehicles. Subjects were classified by whether they were wearing a seat belt,
For Table 2.9, let D = defendant’s race, V = victims’ race, and P = death penalty verdict. Table 7.13 shows the output for fitting loglinear model (DV, DP, PV ).a. Report the estimated
For the recent General Social Survey data on X = gender (males, females) and Y =belief in an afterlife (no, yes), Table 7.12 shows results of fitting the independence loglinear model.a. The deviance
True, or false?a. One reason it is usually wise to treat an ordinal variable with methods that use the ordering is that in tests about effects, chi-squared statistics have smaller df values and tend
Table 6.12, from the Accidents data file at the text website, is an expanded version of data that Section 7.2.7 analyzes about a sample of auto accidents. The response categories are (1) not injured,
A response scale has the categories (strongly agree, mildly agree, mildly disagree, strongly disagree, don’t know). Describe a way to model this response variable simultaneously using two models.
The output in Table 6.11 shows sequential-logit modeling of data from a developmental toxicity study.14 Rodent studies are commonly used to test and regulate substances posing a potential danger to
Table 6.10 refers to a study that randomly assigned subjects to a control group or a treatment group. Daily during the study, treatment subjects ate cereal containing psyllium. The purpose of the
For Table 6.2 on belief in an afterlife, fit a model using (a) cumulative logits,(b) adjacent-categories logits, and (c) sequential logits. Prepare a short report, summarizing your analyses and
Table 6.9 shows cell counts from the 2010 General Social Survey that compare Republicans and Democrats when asked whether claims about environmental threats are exaggerated. Fit a multinomial model
Using the output in Section 6.2.2 for the cumulative logit model fitted to the political ideology data, find Pˆ(Y ∗2 > Y ∗1 ) for comparing strong Republicans with strong Democrats on the
Refer to the previous two exercises. Fit the main-effects cumulative probit model.Interpret the SES effect. Find and interpret the estimated R2 and multiple correlation for the corresponding latent
Refer to the previous exercise and the Mental data file.a. For the main effects fit, summarize the life events effect with probability interpretations for P(Y = 1) analogous to those given in the
For the mental impairment example (Section 6.3.4), when we add an interaction term, we obtain the fit logit[Pˆ(Y ≤ j)] = ˆαj − 0.420x1 + 0.371x2 + 0.181x1x2.The coefficient 0.181 of x1x2 has
A cumulative logit model is fitted to data from a General Social Survey, with Y =political ideology (very liberal to very conservative) and x = religious preference(Protestant, Catholic, Jewish,
Table 6.8 results from a clinical trial for the treatment of small-cell lung cancer.Patients were randomly assigned to two treatment groups. The sequential therapy administered the same combination
Refer to the previous exercise. Table 6.7 shows output for a cumulative logit model with scores (1, 2, 3) for the income categories.a. Explain advantages of this model over the baseline-category
shows the output for a baseline-category logit model with Table 6.6 Software output on modeling happiness for Exercise
Is marital happiness associated with family income? For a General Social Survey, counts in the happiness categories (not, pretty, very) were (6, 43, 75) for a below average income, (6, 113, 178) for
For a recent General Social Survey, a prediction equation relating Y = job satisfaction (4 ordered categories; 1 = least satisfied) to the subject’s report of x1 = earnings compared to others with
For the belief in an afterlife example (Section 6.1.5), describe the gender effect by reporting and interpreting the estimated conditional odds ratio for the (a) undecided and no pair of response

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