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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

For the school example and GEE marginal approach we mentioned that the most appropriate correlation structure is exchangeable. Give reasons why the AR(1) or the unstructured options for correlation
For the mice data, instead of modeling weight linearly over time, model weight as a quadratic function of time by including a term for days as well as for days2. Which model (random intercept, random
There might be siblings represented in the school data set. The factor parental education could potentially be considered another level in the hierarchical model. Give reasons for when and why this
For the school data set (again, using math score as the outcome variable) start with fitting a model with the following fixed effects: SES centered around its respective school mean, school mean SES,
For the school data set (again, using math score as the outcome variable) fit the following models:a) A random intercept model with random intercepts for schools and both the raw SES scores and the
For the school data set (again, using math score as the outcome variable) fit a random intercept model with random intercepts for schools and SES centered around its respective school mean as a fixed
For the school data set using math score as the outcome variable, fit the following models:a) A fixed effects model with schools and SES as fixed effects.b) The same as (a), but with each SES
For the school data set generate box plots of SES by schools (similar to Figure 18.2). Interpret the graph with respect to potential differences in mean SES and differences in variability of SES
Three students have the following scores on their math, english and social science classes.Student 1: 87.3, 91.2 and 86.0, Student 2: 75.4, 81.3 and 79.6, Student 3: 98.8, 95.0 and 94.7.a) Using a
(Problem 17.9 continued) Compare the results you get from Problem 17.9 and Problem 12.30.
This problem uses the Northridge earthquake data set. Look for significant associations in homeowner status (V449), home evacuation status (V173), and status of home damage (V127)using a log-linear
Look for significant associations among the variables gender, currently living with(LIVWITH), the financial situation (FINSIT), and having enough money for food (MONFOOD)in the Parental HIV data
In Problem 17.5, eliminate the four-way interaction, then compare the two models: the one with and the one without Smokfu. Interpret the results.
Rerun the analyses given in Problem 17.4 adding a delta of 0.01, 0.1, and 0.5 to see if it changes any of the results.
Run a four-way log-linear analysis using the variables Stagen, Hist, Smokfu and Death in the lung cancer data set. Report on the significant associations that you find.
Perform a log-linear analysis using data from the lung cancer data set described in Section 13.3 and Appendix A. Check if there are any significant associations among Staget, Stagen and Hist. Which
Split the variable EDUCAT in the depression data set into two groups, those who completed high school and those who did not. Also split INCOME at 18 or less and greater than 18 (this is thousands of
Run a log-linear analysis using the variables DRINK, CESD (split at ten or less), and TREAT from the depression data set to see if there is any significant association among these variables.
Using the variables AGE and CESD from the depression data, make two new categorical variables called CAGE and CCESD. For CAGE, group together all respondents that are 35 years old or less, 36 up to
For the Parental HIV data consider the subgroup of adolescents who have used marijuana. Perform a hierarchical cluster analysis separately for females on the following variables from the Parental HIV
Repeat Problem 16.1, using the variables age, income, and education instead of the last seven variables.
Create a data set from the family lung function data described in Appendix A as follows. It will have three times the number of observations that the original data set has—the first third of the
Repeat Problem 16.6, using the K-means method for K = 4. Compare the results with the four clusters produced in Problem 16.6.
Repeat Problem 16.6, using AREA as an additional clustering variable. Comment on your results.
Describe how you would expect guards, forwards, and centers in basketball to cluster on the basis of size or other variables. Which variables should be measured?16.6 For the family lung function data
Perform a cluster analysis on the chemical company data in Table 9.1, using the K-means method for K = 2;3; 4.16.4 For the accompanying small, hypothetical data set, plot the data by using methods
For the situation described in Problem 8.7, modify the data for X1, X2,. . . , X9 as follows. For the first 25 cases, add 10 to X1, X2, X3. For the next 25 cases, add 10 to X4, X5, X6. For the
For the depression data set, use the last seven variables to perform a cluster analysis producing two groups. Compare the distribution of CESD and cases in the groups. Compare also the distribution
This problem uses the Northridge earthquake data set. Perform a factor analysis on the following items in the Brief Symptom Inventory (BSI): V346, V357, V364, V383, V390, V394, V351, V358, V385,
Repeat Problem 15.8 using an oblique rotation. Do the substantive conclusions change?
Perform a factor analysis on all of the items of the Parental Bonding scale for the Parental HIV data (see Appendix A and the codebook). Retain two factors. Rotate the factors using an orthogonal
For the depression data set, perform four factor analyses on the last seven variables DRINK–CHRONILL (Table 3.4 or 3.5). Use two different initial extraction methods and both orthogonal and oblique
Separate the depression data set into two subgroups, men and women. Using four factors, repeat the factor analysis in Table 15.7. Compare the results of your two factor analyses to each other and to
For the data generated in Problem 8.7, perform four factor analyses, using two different initial extraction methods and both orthogonal and oblique rotations. Interpret the results.
Perform a factor analysis on the data in Table 9.1 and explain any insights this factor analysis gives you.
Another method of factor extraction, maximum likelihood, was mentioned in Section 15.6 but not discussed in detail. Use one of the packages which offers this option to analyze the data along with an
Repeat the analysis of Problem 15.1 and Table 15.7, but use an iterated principal factor solution instead of the principal components method. Compare the results.
The CESD scale items (C1–C20) from the depression data set in Chapter 3 were used to obtain the factor loadings listed in Table 15.7. The initial factor solution was obtained from the principal
Perform a principal components analysis on all the items of the Parental Bonding scale for the Parental HIV data (see Appendix A and the codebook). How many principal components would you expect to
Perform a principal components analysis on AGE and INCOME using the depression data set.Include all the additional data points listed in Problem 7.9(b). Plot the original variables and the principal
Using the family lung function data, perform a principal components analysis on mother’s height, weight, age, FEV1, and FVC. Use the covariance matrix, then repeat using the correlation matrix.
(Continuation of Problem 14.7.) Perform a regression of FEV1 for the oldest child on the principal components found in Problem 14.7. Compare the results to those from Problem 8.15.
Using the family lung function data, perform a principal components analysis on age, height, and weight for the oldest child.
Using the family lung function data described in Appendix A define a new variable RATIO= FEV1/FVC for the fathers. What is the correlation between RATIO and FEV1? Between RATIO and FVC? Perform a
Perform a principal components analysis on the data in Table 9.1 (not including the variable P/E). Interpret the components. Then perform a regression analysis with P/E as the dependent variable,
(Continuation of Problem 14.3.) Perform the regression of Y on the principal components.Compare the results with the multiple regression of Y on X1 to X9.
For the data generated in Problem 8.7, perform a principal components analysis on X1;X2; : : : ;X9. Compare the results with what is known about the population.
(Continuation of Problem 14.1.) Perform a regression analysis of CASES on the last seven variables as well as on the principal components. What does the regression represent? Interpret the results.
For the depression data set described in Appendix A, perform a principal components analysis on the last seven variables DRINK–CHRONILL (Table 3.5). Interpret the results.
Perform a proportional hazards regression using the variables Staget, Treat, and Perfbl and stratify the model by Poinf. Compare the estimated hazard ratios to the ones obtained in Problem 13.9.
Evaluate graphically and statistically the proportional hazards assumption for the variables Perfbl, Poinf, and Treat in the model presented in Table 13.4 using the methods described in Section 13.8.
Define a variable Smokchng that measures change in smoking status between baseline and follow-up, so that Smokchng equals 1 if a person changes from being a smoker to being an ex-smoker and equals 0
Repeat Problem 13.6 assuming a proportional hazards model.
Assuming a log-linear model, do the effects of smoking status upon survival change depending on the tumor size at diagnosis?
Repeat Problem 13.4 assuming a proportional hazards model.
Assuming a log-linear model for survival, does smoking status (i.e., the variables Smokbl and Smokfu) significantly affect survival?
Do the patterns of censoring appear to be the same for smokers at baseline, ex-smokers at baseline, and nonsmokers at baseline? What about for those who are smokers, ex-smokers, and nonsmokers at
Repeat Problem 13.1, using a Cox proportional hazards model instead of a log-linear. Compare the results.
(a) Find the effect of Stagen and Hist upon survival by fitting a log-linear model. Check any assumptions and evaluate the fit using the graphical methods described in this chapter.(b) What happens
(Problem 12.30 continued) Using an appropriate method in your software package, obtain confidence intervals for the odds ratios you computed in partsa, b and c of Problem 12.30.
(Problem 12.29 continued) Fit a logistic regression model (again using as the outcome “evacuate home” (V173)) which includes as the only covariates home owner status (rent/own, V449)and status of
This problem and the following ones also use the Northridge earthquake data set. Perform an appropriate regression analysis using variable selection techniques for the following outcome:evacuate home
(Problem 12.22 continued) Perform diagnostic procedures to identify influential observations.Remove the four (4) most influential observations using the delta chi-square method. Rerun the analysis
(Problem 12.22 continued) Is there an interaction effect between age and home ownership, controlling for gender and ethnicity?
(Problem 12.22 continued) Is there an interaction effect between gender and home ownership?That is, are the estimated effects of home ownership upon reporting emotional injuries different for men and
(Problem 12.22 continued) Are the effects of ethnicity upon reporting emotional injuries statistically significant, controlling for home ownership status, age, and gender? Use a likelihood ratio test
(Problem 12.22 continued) Based on your results, what is the estimated probability of reporting emotional injuries for a 30-year-old white female renter? For a 50-year-old Latino home owner?
(Problem 12.22 continued) Fit a logistic regression model using emotional injury (yes/no, W238) as an outcome and using home ownership status (rent/own, V449), age (RAGE), gender(RSEX), and ethnicity
This problem and the following ones use the Northridge earthquake data set. We wish to answer the questions: Were homeowners more likely than renters to report emotional injuries as a result of the
For the model in 12.20 use the referent time as given by the variable HMONTH to define the offset. Run the same model as in 12.20. Present rate ratios, including confidence intervals, and interpret
For the Parental HIV data perform a Poisson regression on the number of days the adolescents were absent from school without a reason. For this analysis assume that the referent time period was one
For the model in 12.18 find an appropriate cutoff point to discriminate between adolescents who were absent without a reason and those who were not. Assess how well the model predicts the outcome
Perform a binary logistic regression analysis using the Parental HIV data to model the probability of having been absent from school without a reason (variable HOOKEY). Find the variables that best
Perform a nominal and ordinal logistic regression analysis using the health scale as the outcome variable and age and income as independent variables. Present and interpret the results for an
For the family lung function data perform a nominal logistic regression where the outcome variable is place of residence and the predictors are those defined in Problem 12.11. Test the hypothesis
For the depression data perform an ordinal logistic regression analysis using the same outcome categories as in Section 12.9 which reverses the order and hence compares more severe depression to less
Generate a graph for income similar to Figure 12.2 to assess whether modeling income linearly seems appropriate.
Perform a logistic regression analysis for the depression data which includes income and sex and models age as ana) quadratic orb) cubic function. Use likelihood ratio test statistics to determine
Assume a logistic regression model includes a continuous variable like age and a categorical variable like gender and an interaction term for these. Is the P value for any of the main effects helpful
For the family lung function data set, define a new variable VALLEY (residence in San Gabriel or San Fernando Valley) to be one if the family lives in Burbank or Glendora and zero otherwise.Using
Using the definition of low FEV1 given in Problem 12.9, perform a logistic regression of low FEV1 on area for the fathers. Include all four areas and use a dummy variable for each area.What is the
Define low FEV1 to be an FEV1 measurement below the median FEV1 of the fathers in the family lung function data set given in Appendix A. What are the odds that a father in this data set has low FEV1?
Repeat Problem 12.7, but for chronic rather than acute illness.
Using the depression data set, appropriate variable selection techniques, and logistic regression, describe the probability of an acute illness as a function of age, education, income, depression,
(a) Using the depression data set, fill in the following table:What are the odds that a woman is a regular drinker? That a man is a regular drinker? What is the odds ratio?(b) Repeat the tabulation
Perform a logistic regression analysis on the data described in Problem 11.2.
Perform a logistic regression analysis with the same variables and data used in the example in Problem 11.13.
The accompanying table presents the number of individuals by smoking and disease status.What are the odds that a smoker will get disease A? That a nonsmoker will get disease A?What is the odds ratio?
Using the formula odds = P=(1????P), fill in the accompanying table. Odds P 0.25 0.20 0.5 1.0 0.5 1.5 2.0 2.5 3.0 0.75 5.0
If the probability of an individual getting a hit in baseball is 0.20, then the odds of getting a hit are 0.25. Check to determine that the previous statement is true. Would you prefer to be told
Calculate the Parental Bonding Overprotection and Parental Bonding Care score for the Parental HIV data (see Appendix A and the codebook). Perform a discriminant function analysis to classify
Refer to the table of ideal weights given in Problem 10.8 and calculate the midpoint of each weight range for men and women. Pretending these represent a real sample, perform a discriminant function
Is it possible to distinguish between men and women in the depression data set on the basis of income and level of depression? What is the classification function? What are your prior probabilities?
Divide the oldest children in the family lung function data set into two groups based on weight:less than or equal to 101 versus greater than 101. Perform a stepwise discriminant function analysis
(a) In the family lung function data in Appendix A divide the fathers into two groups: group I with FEV1 less than or equal to 4.09, and group II with FEV1 greater than 4.09. Assuming equal prior
At the time the study was conducted, the population of Lancaster was 48,027 while Glendora had 38,654 residents. Using prior probabilities based on these population figures and those given in Problem
From the family lung function data in Appendix A create a data set containing only those families from Burbank and Long Beach (AREA = 1 or 3). The observations now belong to one of two AREA-defined
(Continuation of Problem 11.7.) Do a variable selection analysis, using variables X4 to X9 only. Comment.
(Continuation of Problem 11.7.) Do a variable selection analysis for all nine variables. Comment.
(Continuation of Problem 11.7.) Perform a similar analysis, using only X1, X2, and X3. Test the hypothesis that these three variables do as well as all nine classifying the observations.Comment.

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