Questions and Answers of Categorical Data Analysis

11.10 For the model described in Problem 11.9, suppose that the variance of U0j(i.e., τ0 2) is estimated to be 0.2.a. Interpret this value in the context of this model and variables.b. How does this
11.9 For the data set described in Problem 11.6, suppose that you obtain the following results for a random intercept model, where πij is the predicted probability of proficiency, AGEc is
11.8 For the model described in Problem 11.7, suppose that the variance of U0j(i.e., τ0 2) is estimated to be 0.4.a. Interpret this value in the context of this model and variables.b. How does this
11.7 For the data set described in Problem 11.6, suppose that you obtain the following results for the random intercept model, where πij is the predicted probability of proficiency and AGEc is
11.6 Suppose that you are analyzing a data set consisting of a random sample of patients who were selected from a random sample of clinics, and you would like to predict whether a given patient will
11.5 For the model described in Problem 11.4, suppose that the variance of U0j(i.e., τ0 2) is estimated to be 0.2 and the variance of U1j(i.e., τ1 2) is estimated to be 0.1.a. Interpret these
11.4 For the data set described in Problem 11.1, suppose that you obtain the following results for the random slope model, where πij is the predicted probability of proficiency and ATTc is
11.3 For the model described in Problem 11.2, suppose that the variance of U0j(i.e., τ0 2) is estimated to be 0.3.a. Interpret this value in the context of this model and variables.b. How does this
11.2 For the data set described in Problem 11.1, suppose that you obtain the following results for the random intercept model, where πij is the predicted probability of proficiency and ATTc is
11.1 Suppose that you are analyzing a data set consisting of a random sample of students who were selected from a random sample of schools, and you would like to predict whether a given student will
10.10 Pick your own research question that can be addressed using variables from the 2006 GSS data set and a logistic regression model with at least two predictors and a response variable containing
10.9 Explain what the proportional odds assumption means in the context of the study described in Problem 10.7.
10.8 Use the information from Problem 10.7 to answer the following (show your work):a. What is the predicted cumulative probability for a boy to reach the fourth proficiency level (level 3) or less?
10.7 O’Connell (2006) used data from the Early Childhood Longitudinal Study to examine how gender affects literacy proficiency for first-grade children. The outcome variable of literacy proficiency
10.6 Explain what the proportional odds assumption requires in general. Use the variables from the model in Problem 10.5 to illustrate your answer specifically and explain whether the assumption is
10.5 Use the logist1 data from www.psych.yorku.ca/lab/psy6140/ex/logistic.htm to fit the proportional odds model predicting the level of improvement from sex and treatment.Assume that the level of
10.4 Use the logist1 data from www.psych.yorku.ca/lab/psy6140/ex/logistic.htm to fit a logistic regression model predicting the level of improvement from the patient’s sex and treatment(without
10.3 Use the diabetes data set (see also Problem 8.11, http://friendly.apps01.yorku.ca/psy6140/examples/logistic/logidiab.sas, from Michael Friendly’s web site) to fit a logistic regression model
10.2 Refer to the information in Problem 10.1 to answer the following questions (show your work):a. What is the logistic regression model to predict the preference of vanilla over strawberry ice
10.1 Suppose that we would like to investigate whether gender has a significant effect on one’s choice of ice cream flavor. The data file (obtained from
9.10 Pick your own research question that can be addressed using variables from the 2006 GSS data set and a logistic regression model with at least two predictors.a. State your research question and
9.8 Choose a research question that can be addressed with the data from Problem 7.4 using a logistic regression analysis. Explain which of the variables would be used as the outcome and which
9.7 Using the data from Problem 7.2, create a binary response variable to represent agreement with spanking (e.g., combine the first two agreement categories and combine the last two agreement
9.6 Use the data from Problem 7.1 to predict the probability that a respondent will favor the death penalty from the respondent’s fundamentalism level and sex as well as their interaction. Fully
9.5 Table 9.7 provides data (obtained from Michael Friendly’s web site at York University)pertaining to the relationship between a treatment for diabetes (treated or placebo), sex(male or female),
9.4 Use the 2006 GSS data set to predict whether a respondent favors the death penalty for murder (CAPPUN) from the respondent’s sex (SEX) and race (RACE) as well as their interaction.a. Use the
9.3 Fit the log-linear model that is equivalent to the logistic regression model from Problem 9.2a. Indicate the parameter estimates that are equivalent across both models and show that their
9.2 Using the data in Table 7.2 from the 1992 United States presidential election, logistic regression was used to model voting for Clinton (i.e., yes rather than no) from the voter’s political
9.1 Suppose that a logistic regression model contains one categorical predictor with three categories: A, B, and C. Using dummy coding for the predictor with category A as the reference category, the
8.11 The diabetes data set, provided by Michael Friendly at http://friendly.apps01.yorku.ca/psy6140/examples/logistic/logidiab.sas, contains 145 observations on four measures of glucose or insulin
8.10 Pick your own research question that can be addressed using variables from the 2006 GSS data set and a logistic regression analysis. You should include at least two predictors.a. State your
8.9 Use the 2006 GSS data set (e.g., at http://sda.berkeley.edu/archive.htm) to predict whether a respondent favors sex education in the public schools (SEXEDUC) from the respondent’s age (AGE),
8.8 Use the ADD data set to select a binary outcome measure and at least two continuous predictors of this outcome.a. Fit the logistic regression model and report its fit.b. Conduct the appropriate
8.7 Compare the models fit in Problems 8.5 and 8.6:a. Conduct the likelihood ratio (G2) test to compare the two models. Is there a significant difference between these two models in terms of fit?
8.6 Use the ADD data set and fit a logistic regression model to predict whether a student dropped out before completing high school from average ADD score (ADDSC) only.a. Fully interpret the value,
8.5 Use the ADD data set and fit a logistic regression model to predict whether a student dropped out before completing high school (DROPOUT) from average ADD score(ADDSC) and ninth-grade GPA.a. Does
8.4 Consider a logistic regression model with two predictors and the following parameters:the intercept is α = 1.5, and the slopes are β1= 0.4 and β2= −0.1.a. Compute the predicted odds when X1=
8.3 Consider a logistic regression model with two predictors and the following parameters:the intercept is α = 2, and the slopes are β1= 0.5 and β2= −0.3.a. Compute the predicted odds when X1= 2
8.2 Consider a logistic regression model with two predictors and the following parameters:the intercept is α = 1.5, and the slopes are β1= 0.4 and β2= −0.1.a. Compute the predicted logit of the
8.1 Consider a logistic regression model with two predictors and the following parameters:the intercept is α = 2, and the slopes are β1= 0.5 and β2= −0.3.a. Compute the predicted logit of the
7.8 What are the advantages and disadvantages of fitting a log-linear model rather than using the procedures described in Chapter 5? When would a researcher be more likely to fit a log-linear model
7.7 In Chapter 5 (Section 5.6), we discussed the Berkeley graduate admissions data, where the variables of interest involved the applicant’s sex and admission to graduate school across six
7.6 In Chapter 5 (Section 5.6), we discussed the Berkeley graduate admissions data, where the variables of interest involved the applicant’s sex and admission to graduate school across six
7.5 Table 7.24 depicts data obtained from the 1994 administration of the GSS. Describe how you found the most parsimonious log-linear model for this data, fit this model, and use the model parameters
7.4 Table 7.23 depicts data that was obtained from the 1994 GSS on respondents’ sex, whether they are separating from a spouse/partner, ability to afford needed medical care, and condition of
7.3 Table 7.22 depicts data that was obtained from the 1994 administration of the GSS on whether the respondent was born in the United States, the respondent’s sex, and the respondent’s ability
7.2 Table 7.21 depicts data that was obtained from the 1994 administration of the GSS on respondents’ sex, race, and level of agreement with spanking to discipline a child. Suppose that the main
7.1 Table 7.20 depicts data that was obtained from the 1994 administration of the General Social Survey (GSS) on respondents’ sex, level of fundamentalism, and whether they favor or oppose the
6.11 Suppose that the results shown in Figure 6.8 were obtained for the study described in Problem 6.8, using only x4= years of schooling as a predictor:a. What are the estimated values of the
6.10 Refer again to the overall model described in Problem 6.8. Explain your reasoning for each of the following:a. What is the random component of the GLM used in this study?b. What is the
6.9 Refer again to the study described in Problem 6.8. Suppose that the model containing only the “demographic” variables, x3= annual income and x4= years of schooling, results in
6.8, what is the value of the likelihood ratio statistic for the overall fit of the model(containing all four predictors)?b. Is the likelihood ratio statistic for the overall fit obtained in part (a)
6.8 Suppose that a study was conducted to predict whether an individual regularly smoked, or the expected probability of smoking, based on four continuous predictors such as x1= smoking exposure, x2=
6.7 Use the data in Table 6.2, where X represents a continuous predictor and Y represents a probability.a. Create a scatter plot of the data (with values of X on the horizontal axis and values of Y
6.6 Come up with an example of a study in which the outcome variable is likely to follow the binomial distribution. Explain what the random component, systematic component, and link function would be
6.5 Come up with an example of a study in which the outcome variable is likely to follow the Poisson distribution. Explain what the random component, systematic component, and link function would be
6.4 Suppose that a researcher would like to predict the probability that a voter will vote for a particular candidate based on several characteristics of the voter such as family income, educational
6.3 Suppose that a researcher would like to predict the number of students who are absent from a given classroom per day based on several predictors such as family income, race, and gender. Explain
6.2 What advantages do GLMs (generalized linear models) have over general linear models(such as regression and ANOVA models)?
6.1 What is the general purpose of a link function, and why is a link function other than the identity needed in some cases but not in others?
5.15 In a three-way contingency table, if there is no homogeneous association, is it possible for any pair of the variables to be conditionally independent? Explain your answer.
5.14 In a three-way contingency table, suppose that X and Y are conditionally independent (conditional on Z). Will the data then necessarily show homogeneous association?Explain your answer.
5.13 Think of three categorical variables that theoretically should display conditional independence and explain why you believe that to be the case.
5.12 Think of three categorical variables that theoretically should display homogeneous association and explain why you believe that to be the case.
5.11 Using a substantive example, explain the difference between homogeneous association and conditional independence.
5.10 Using a substantive example, explain the difference between marginal and conditional associations.
5.9 Use the data in Table 5.17, obtained from the 2003 PISA study, and combine the categories of every lesson and most lessons, as well the categories of some lessons and never or hardly never.
5.8 Use the data in Table 5.16, obtained from the 2003 PISA study. Is there homogeneous association or a three-way association among these variables? Justify your answer with the appropriate
5.7 Use the data in Table 5.15, obtained from the 2003 Programme for International Student Assessment (PISA) study. Come up with three specific research questions that can be answered using this data
5.6 Answer the following questions using the data in Table 5.14, obtained from the 1993 administration of the GSS:a. What is the marginal association between gender and attitude toward life?
5.5 Table 5.13 contains data obtained from the 2006 administration of the GSS. Analyze these data and summarize the results. Include a discussion of any associations that exist.Specifically, discuss
5.4 Answer the following questions using the data in Table 5.12, obtained from the 2006 administration of the GSS:a. What is the marginal association between gender and belief in the afterlife?
5.3 Analyze the data in Table 5.11 and summarize the associations among the three variables.Specifically, discuss whether there appears to be homogeneous association or a threeway association, and
5.2 Using Table 5.11, examine the conditional associations between type of employment(someone else or self) and work time (part or full), conditional on gender.a. Report the conditional odds ratios,
5.1 Table 5.11 contains data obtained from the 2006 administration of the General Social Survey (GSS).a. Provide the marginal table for the association between type of employment (someone else or
4.12 Find a contingency table from a recent news story or study to use for this problem. Cite the source of the data and use it to:a. Provide a research question that can be answered with the data.b.
4.11 If the two officers in Problem 4.10 agreed perfectly, what might the observed contingency table have been? Provide an example of such a table and compute the value of Cohen’s kappa that would
4.10 A study was conducted to determine the level of agreement between two personnel officers in their ratings of prospective job candidates. The officers rated each of 20 job candidates as
4.9 A medical study examined the probability of making a full recovery for patients who receive a particular treatment and found that the probability was 0.866 for those over 70 years of age and
4.10 Select two categories for each variable in Table 4.13 and compute the odds ratio for the resulting sub-table. Interpret this value.
4.9 Use Table 4.13 to compare the odds of finding life exciting rather than routine for those who are married and those who were never married. Report the appropriate odds ratio and interpret its
4.8 In a random sample of 996 Americans, individuals were classified according to their marital status and whether they considered life dull, routine, or exciting.The results (based on a subset of
4.7 Obtain the residuals and contributions to chi-squared for each of the cells in Problem 4.6.a. Which cells show the largest and smallest deviations from the results expected under independence?b.
4.6 Use computer software and the data in Table 4.12 to test whether there is a statistically significant association between taking Vitamin C and the incidence of colds.a. Report the results of the
4.5 Think of two categorical variables that theoretically should be independent and explain why you believe they should be independent.
4.4 Use computer software and the data in Problems 4.1 (Table 4.11) toa. Obtain the odds ratio (as in Problem 4.1).b. Obtain the 95% confidence interval for the odds ratio (as in Problem 4.2).c.
4.3 Is there a statistically significant association between proficiency and NES status based on the data in Problem 4.1? State the null hypothesis and report the conclusions.
4.2 Find the 95% confidence interval for the odds ratio in Problem 4.1 and interpret the result.
4.1 Suppose that fourth-grade students from a national random sample were classified as either proficient or not proficient in mathematics as well as whether each was a native English speaker (NES).
3.14 With dichotomous variables, tests can be conducted using either single proportion methods or the goodness-of-fit methods (with c = 2). Repeat Problem 3.1 using the Pearson chi-squared
3.13 Repeat Problem 3.11 using the likelihood ratio test statistic.
3.12 Repeat Problem 3.10 (parts a andb) using the likelihood ratio test statistic.
3.11 In a study on whether several issues are equally important to voters, a random sample of 200 registered voters were asked to select which of four issues they consider most important. The results
3.10 After introducing a new teaching curriculum, a principal would like to determine whether the grade distribution in her school is significantly different than it has been in previous years.
3.9 Use the information in Problem 3.8 to construct and interpret:a. The results of a 95% confidence interval for the proportion of votes for Candidate X.b. The results of a 99% confidence interval
3.8 In an election consisting of two candidates, a researcher would like to determine whether it is fair to say that one of the candidates will receive the majority of votes(where majority is defined
3.7 Repeat Problem 3.1 using the likelihood ratio test. State the null and alternative hypotheses (note that this method requires a two-tailed test). Report the p-value and state the conclusions.
3.6 Use the results of Problems 3.2 and 3.4 to explain why the exact test (based on the binomial distribution) is considered to be more conservative than the score test (based on the normal
3.5 Use the results of Problems 3.1 and 3.3 to explain why the exact test (based on the binomial distribution) is considered to be more conservative than the score test (based on the normal
3.4 Repeat Problem 3.2 using the score test.

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