Applied Statistics For The Social And Health Sciences 1st Edition Rachel A. Gordon - Solutions

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Complex Sampling Designsa) SAS/Stata Tasks.i) Use the survey commands in SAS and Stata to re-estimate the logit model that you estimated in Question 16.1 ii) Use the survey commands in SAS and Stata to re-estimate the multinomial logit that you estimated in Question 17.1, with the fourth category
Ordered Logit Modela) SAS/Stata Tasks.i) Use proc logistic in SAS and ologit in Stata to regress bmiC on the the female dummy and the age and exfreqwR variables.ii) In Stata, use the brant command to test proportional odds assumption.(The test of proportional odds is already in the default SAS
and less than 25 (healthy weight), (3) body mass index at or above 25 and less than 30 (overweight), and (4) body mass index at or above 30 (obese).iii) Use proc logistic with the /link=glogit option in SAS and mlogit in Stata to regress bmiC on the female dummy and the age and exfreqwR variables.
(underweight), (2) body mass index at or above
Multinomial Logit Modela) SAS/Stata Tasks.i) Create a dummy variable to indicate females (as you did in Chapter 16 ).ii) Create a categorical variable named bmiC with the following categories:(1) body mass index below
Suppose that you estimated a multinomial logit model with a categorical variable indicating mothers’ employment status as the outcome (1=not employed, 2=employed part-time, 3=employed full-time) and father’s annual earnings as the predictor (rescaled to $10,000 units, Range: 1 to 20). Suppose
Suppose that you estimate a multinomial logit model predicting one of three types of child care used by families (center, family day care, or relative care) based on the mother’s years of schooling, using relative care as the reference outcome category.Imagine that the coeffi cient for mother’s
Discuss how you would evaluate whether the assumptions of the multinomial and ordered logit models are met.
Discuss some strengths and limitations of the multinomial and ordered logit models.
Show why a factor change interpretation can be used in the multinomial logit and ordered logit models.
Write the formulas for predicting probabilities for the multinomial logit and ordered logit models and discuss how they relate to the formula for predicting probabilities based on the binary logit model.
Write the link for the multinomial logit and the ordered logit models and discuss how they relate to the link for the binary logit model.
Interpreting the Coeffi cients of a Logit Modela) SAS/Stata Tasks.i) Ask Stata to show the odds ratios for Regression #2. (The odds ratios are already in the SAS default output).ii) Based on Regression #2, use the prchange, fromto command to calculate discrete and marginal change in Stata for each
Evaluating the Fit of a Logit Modela) SAS/Stata Tasks.i) Create a dummy variable to indicate females (as you did in Chapter 7 ).ii) Create a dummy variable to indicate whether the respondent is overweight(coded 1 if bmiR is at or above 25 and 0 if bmiR is below 25).iii) Use proc logistic in SAS and
Consider that a colleague of yours has estimated a logit model predicting whether couples’ divorce (dummy coded 0=stay married, 1=divorce) and obtains for the predictor variable POVERTY (dummy coded 0=family income above poverty line and 1=family income below poverty line) a coeffi cient of
Suppose that you estimated a regression model using ordinary least squares with a dummy indicator of adults’ marital status as the outcome (0=not married, 1=married) and a continuous measure of years of schooling (range: 9 to 22) as the predictor. Suppose that you obtained the following
Suppose that you interview 15 10th grade boys and that 5 of these boys report to you that they belong to a gang. Which of the following probabilities of an adolescent boy being in a gang do these results suggest is more likely in the population from which this sample was drawn: .33 or .50?
Calculate the odds and the log-odds for the following probabilities: 0.20, 0.50, and 0.80. Comment on how the results relate to the theoretical minimum and maximum of probabilities, odds, and log-odds.
Show algebraically that the difference in BICs would work out to the same value for all three formulas shown in the chapter (Equation 16.9, Equation 16.10, and Equation 16.11) in the simplest case when you compare a full model with one predictor to a reduced intercept-only model.
For what types of variables are marginal effects appropriate?
When will the marginal effect be similar in value to the discrete change?
Discuss how values of odds ratios relate to values of coeffi cients, focusing on coeffi cient values that are negative, zero, and positive.
Discuss the advantages and disadvantages of the three main strategies for predicting values discussed in the chapter (predict then average, average then predict, and ideal types).
Why are there so many different R-squared values for maximum likelihood estimation?
Write the formula for converting predicted probits into predicted probabilities.
Write the formula for converting predicted logits into predicted probabilities.
Write the formula for the binomial distribution and discuss what each major piece of the formula accomplishes.
How do the logit and probit link achieve our goal of converting values that can only fall between 0 and 1 to values that range from negative infi nity to positive infi nity?
What is the formula for the probit link? How do we refer to its values?
What is the formula for the logit link? How do we refer to its values?
What is a linear probability model? What are its advantages and disadvantages?
The Generalized Linear Model with a Continuous Outcomea) SAS/Stata Tasks.i) Use the SAS genmod and Stata glm commands to estimate a generalized linear model that regresses bmiR on age assuming an identity link and normally distributed errors. Call this Regression #1.ii) Use the SAS genmod and Stata
What distributional assumption and link are used to obtain coeffi cient estimates identical to OLS regression using the generalized linear model approach?
What is a link function?
What are some techniques we learned for OLS regression that can also be used in the generalized linear model?
What are the three main ways in which the generalized linear model differs from OLS regression?
When and how are the z -statistic and Wald χ2 statistic related to each other?
What are the similarities and differences between the Likelihood Ratio χ2 and the Wald χ2 ?
What is the difference between an iterative search and a closed form solution?
What is the basic objective of maximum likelihood estimation?
What is a likelihood function?
What is a likelihood and a log-likelihood?
What is a density function?
Write the general equation for the VIF.(a) Interpret the VIF for the NUMKID variable in the results shown below.(b) Why is the VIF for MARRY identical to the VIF for NUMKID in this model?
What is the formula for calculating the VIF and how does it relate to the formula for the standard error of the slope in multiple regression? In a regression model with two predictors, how does the VIF change as the correlation between the two predictors becomes smaller (approaches and then equals
What are three telltale signs of multicollinearity?
What is the major difference in the formulas for heteroskedasticity-consistent standard errors and OLS standard errors? What are the differences in the assumptions for these standard errors?
What is the difference between an outlier and an infl uential observation? How might you proceed if you identifi ed some outliers and infl uential observations in your dataset?
Total, Direct and Indirect Effectsa) SAS/Stata Tasks.i) After using the data with non-missing values, verify that WKDAYR and the twelve functional limitations variables have only valid values (0 to 366 for WKDAYR and 0 “not at all diffi cult to 3 “very diffi cult” for the twelve functional
Consider the three regression model results presented below.(a) Calculate the missing coeffi cient for the bivariate regression of SATMATH on FEMALE (cell labeled A below) based on the other coeffi cients listed in the table.(b) As you answer the question, be sure to fi ll out the diagram by
Suppose that a researcher anticipates that the association between stress and distress may be suppressed because persons who are exposed to stressors may elicit social support from their social networks and social support reduces distress.(a) Calculate the indirect effect of stress on distress
Refer to Dooley and Prause’s Table 3 presented in Literature Excerpt 9.1.(a) Compare the coeffi cients for Age in Model 2 and Model 3. What do the results suggest is the possible direction of correlations among Age, Weeks of Gestation , and Birth Weight ?(b) Compare the coeffi cients for Weight
Refer to Brumbaugh and colleagues Table 3 presented in Literature Excerpt 13.1.Compare the coeffi cients for the Female and Age variables in Model 2 versus Model 3 (when marital, cohabitation, and parenthood histories are added to the model). Discuss whether you would interpret the changes in
How can you draw examples of path diagrams in which omitted variable bias overstates the direct effect of X2 on Y away from zero in a positive direction, in which omitted variable bias overstates the direct effect of X2 on Y away from zero in a negative direction, and in which omitted variable bias
How can you calculate the total effect based on the direct and indirect effects?
How can you calculate the direct and indirect effects in a path diagram in which the effect of X2 on Y is partially mediated by X 3 ?
Consider the following regression equation:EARNˆ INGS = 1,000 + 1,600 * AGE − 20 * SQAGE where SQAGE is the square of AGE, AGE is measured in years, and EARNINGS is annual earnings.(a) If you plotted predicted values from this prediction equation, would you expect to see a U- or inverted
Suppose that your collaborator regressed the log of income on a dummy indicator of being African American versus white and found that the coeffi cient for the African American dummy variable was −0.511.(a) Help your collaborator interpret this coeffi cient with a factor and percentage change
Imagine that your collaborator regressed the log of respondents’ earnings on their years of schooling, and obtained the following results:LNÊARN = 5.31 + 0.22 * YRSCHL(a) Help your collaborator interpret the coeffi cient for YRSCHL with a factor and percentage change approach (i.e., calculate
How can you calculate the various types of change (absolute, factor, relative, and percentage) for two values?
How would you write a general prediction equation for a quadratic functional form?(a) Suppose 5 was a valid value on the predictor. How would you make a prediction for this value of the predictor?(b) What do the signifi cance and sign of the coeffi cient estimate for the quadratic term tell us?(c)
What are the approximate interpretations for a model with a logged predictor when the outcome is also logged (log-log model) and when the outcome is not logged (lin-log model)?
What are the approximate and exact interpretations of the coeffi cient estimate for a logged outcome variable when the predictor is in its natural units (log-lin model)?
How would you create a logged predictor variable when the predictor includes zero (but no negative values)?(a) How would you write the prediction equation when a linear outcome variable is regressed on this variable?(b) Suppose 5 was a valid value on the predictor. How would you make a prediction
How would you choose among three models that predicted an outcome variable with: (a) a linear predictor variable, (b) a logged predictor variable, and (c) a quadratic predictor variable?
Based on the two regression models shown below, do the following:(a) Statistically compare Model 1 and Model 2 using the Chow test (use a cutoff of F = 2.22 for a signifi cant test at alpha = 0.05). Be sure to list the null and alternative hypotheses for the test.(b) Write the prediction equation
Refer to Model 2 in Literature Excerpt 11.2a. Note that the author’s measure% women with bachelor’s degree is: “a measure of the percentage of women ages 25 or older who have earned a bachelor’s degree (including those who have also earned a graduate or professional degree” (p. 467).(a)
Suppose that you hypothesize that earnings is explained by a person’s education level (EDUC, years of schooling) and experience (EXPER, years in the occupation)but that this regression model differs for men and women (FEMALE, 0 = men, 1 =women).(a) Write the general equation for a fully
Imagine that you hypothesize that the racial gap in earnings is smaller for women than for men (that is, the difference in average earnings between African Americans and whites is smaller for women than for men). You estimate the following prediction equation:EARNINGS = 35,000 − 15,000 * FEMALE
Consider the research question: “Greater job stress is associated with harsher parenting, but this association weakens with each additional increment of social support received from family and friends.” How would you set up a regression model to examine this research question?
For interval*interval interaction models:(a) How do you interpret the coeffi cients in a model with an interaction between two interval variables (the intercept, the coeffi cient for each of the predictor variables and the coeffi cient on the product term)?(b) How would you write conditional
For dummy*interval interaction models:(a) In a basic model, with one interval predictor (X), one dummy predictor (D), and the product term of the dummy times the interval predictor (D*X), how would you interpret the intercept and three variables’ coeffi cients?(b) How would you write the
For dummy*dummy interaction models:(a) What is the difference between the conditional means and the conditional effects?(b) How do you write each conditional effect based on the general regression equation and/or the prediction equation?(c) How do you interpret each coeffi cient in the model (the
Complex Sampling Designa) SAS/Stata Tasks.i) Regress bmiR on the female dummy variable, accounting for the NHIS complex sampling design (we will refer to this as Regression #6 in the Write-Up Tasks).ii) Regress bmiR on fi ve of the six dummy variables, using persons of nonHispanic white
Multi-Category Original Variablea) SAS/Stata Tasks.i) Create six dummy variables to indicate persons of: 1) Hispanic ancestry and any race, 2) non-Hispanic ancestry and white only race, 3) non-Hispanic ancestry and African American only race, 4) non-Hispanic ancestry and American Indian or Alaskan
Two-Category Original Variablea) SAS/Stata Tasks:i) Create a dummy variable to indicate women. (Be careful to account for missing value codes).ii) Regress bmiR on this dummy variable (we will refer to this as Regression#1 in the Write-Up Tasks).iii) Create another dummy variable to indicate men.
Below are SAS results from a hypothetical data set using the following variables:WAGE Outcome variable ranging from $2/hour to $15/hour EDUC Education level ranging from 8 to 13 UNION Dummy variable (1 = in a union job; 0 = not in a union job)JOBCLUB Dummy variable (1 = got job from job club; 0 =
Refer to Model 2 of Literature Excerpt 10.3.(a) Write the null and alternative hypotheses for each of the “Educational attainment of household head” dummy variables. Make a conclusion based on the presented results.
The authors present the items for the outcome variable, Sense of Control, in the Appendix (p. 117). Sense of Control is the average of eight items in which the respondent claims or denies control over good and bad outcomes. The average ranges from −2 to 2. The mean (standard deviation) of the
Refer to Literature Excerpt
Suppose that you obtain a new software package and want to verify that you are correctly using its regression command. You know that in your data set the average number of days that low birthweight newborns stay in the hospital(NUMDAYS) is 15 for white babies and 30 for Latino babies. Write the
Suppose you have sample data in which average household income was $50,000 per year for non-Hispanic white adults, $34,000 per year for non-Hispanic Black adults, and $40,000 for Hispanic adults. Write the prediction equations (including the intercept and slope) that you would see if you estimated
Suppose you estimated the following regression equation:EARNˆ INGS = 32,000 − 12,000 * FEMALE where EARNINGS is a respondent’s annual earnings and FEMALE is a dummy variable coded 1 for women and 0 for men.(a) How can you interpret the intercept and dummy coeffi cient from this model?(b) What
What are the three approaches to testing the differences in means among the included groups?
In the case of an original variable with two categories and an original variable with three categories, how would the intercept and dummy variable coeffi cient(s)change if you changed the reference category?
Why is one dummy variable excluded when you estimate a regression model?How do you choose this reference category?
Conceptually, how do you defi ne a set of dummy variables based on an original nominal or ordinal variable?
How are TSS = total sum of squares, MSS = model sum of squares, and SSE =sum of squared errors mathematically related?
Imagine that you conducted an exploratory regression analysis with 10 predictor variables and you wanted to control the Bonferroni alpha level across the tests of the 10 slopes at 0.05. What would be the alpha level you should use for each individual slope t-test?
Suppose that you estimate a multiple regression model using the following variables:DEPRESS Depression scale (ranging from 0 to 105)REDUC Respondent’s education level (ranging from 0 to 20)REARNINC Respondent’s annual earned income (ranging from $1 to $800,000)HRWORK Respondent’s hours spent
Refer to Literature Excerpt 9.1.(a) Write the null and alternative hypotheses for the F-test presented in Model 1.Make a conclusion based on the presented results.(b) Write the null and alternative hypotheses for the t-ratio for Age. Make a conclusion based on the presented results.(c) Interpret
If you have bivariate regression results in which the t -value for the slope is 4, what would be the overall (model) F-statistic for this simple regression model?
Suppose that you know that the Pearson correlation between two variables is 0.70.What percentage of variation do these two variables share?
Suppose that the unadjusted R-squared value from a regression of wages (WAGE)on years of work experience (EXPER) is 0.25.(a) Interpret this R-squared value.(b) What is the Pearson correlation ( r ) between WAGE and EXPER?
Consider the following regression models, predicting national female labor force participation rates based on the proportion of women with a secondary education, the ratio of children to women, and the percentage of the population that is female.femlfp = β0 femlfp = β0 + β1 femeduc femlfp = β0
In Example 9.2, what would the estimates of the intercept and slope be if we used the two rescaled variables, g2earn 10000 and g1yrschl4 as the predictors?
Verify the values in the conditional equations shown in Figure 9.1 . What would be the expected change in Y if we simultaneously increased X1 by 2 and X2 by 3?
How do we interpret R-squared in the case of simple and multiple regression?How does R-squared relate to the Pearson correlation in simple regression?
What relationship do you expect to see between the numerator degrees of freedom in the General Linear F-test and the null hypothesis associated with that test? Under what circumstances do you expect the F-test to be equivalent to a t -test (and the t-value to equal the square root of the F-value)?
Write the null hypothesis for the General Linear F-test that is found in standard SAS and Stata regression output. Write the alternative hypothesis and the full and reduced models associated with this test in the case of bivariate regression and multiple regression with two predictors (use Y as the

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Applied Statistics For The Social And Health Sciences 1st Edition Rachel A. Gordon - Solutions

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