The NMES1988 dataset in the AER package contains information on the demand for medical care in the US in 1987 and 1988. Specifically, it has the following columns: visits: Number of physician office visits. nvisits: Number of non-physician office visits. ovisits: Number of physician hospital outpatient visits. novisits: Number of non-physician hospital outpatient visits. emergency: Emergency room visits. hospital: Number of hospital stays. health: Factor indicating self-perceived health status, levels are “poor”, “average” (reference category),“excellent”. chronic: Number of chronic conditions. adl: Factor indicating whether the individual has a condition that limits activities of daily living(“limited”) or not (“normal”). region: Factor indicating region, levels are northeast, midwest, west, other (reference category). age: Age in years (divided by 10). afam: Factor. Is the individual African-American? gender: Factor indicating gender. married: Factor. is the individual married? school: Number of years of education. income: Family income in USD 10,000. employed: Factor. Is the individual employed? insurance: Factor. Is the individual covered by private insurance? medicaid: Factor. Is the individual covered by Medicaid?STAT 4520/7520 – Homework 2

Spring 2021

Due: February 22, 2021

1) LOS data

The NMES1988 dataset in the AER package contains information on the demand for medical care in the

US in 1987 and 1988. Specifically, it has the following columns:

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visits: Number of physician office visits.

nvisits: Number of non-physician office visits.

ovisits: Number of physician hospital outpatient visits.

novisits: Number of non-physician hospital outpatient visits.

emergency: Emergency room visits.

hospital: Number of hospital stays.

health: Factor indicating self-perceived health status, levels are “poor”, “average” (reference category),

“excellent”.

chronic: Number of chronic conditions.

adl: Factor indicating whether the individual has a condition that limits activities of daily living

(“limited”) or not (“normal”).

region: Factor indicating region, levels are northeast, midwest, west, other (reference category).

age: Age in years (divided by 10).

afam: Factor. Is the individual African-American?

gender: Factor indicating gender.

married: Factor. is the individual married?

school: Number of years of education.

income: Family income in USD 10,000.

employed: Factor. Is the individual employed?

insurance: Factor. Is the individual covered by private insurance?

medicaid: Factor. Is the individual covered by Medicaid?

The dataset can be loaded with the command

data(NMES1988,package=”AER”)

We are interested in determining if the number of times patients seek medical care depends on the various

patient demographics. For now, we will focus on the number of normal physician office visits, and remove all

other types of visits.

library(dplyr)

NMES1988 %

dplyr::select(-c(nvisits,ovisits,novisits,emergency,hospital))

a. Create a histogram of the number of physician office visits. Adjust the number of bins with the breaks

argument to obtain a plot which describes the variable well. Briefly describe your findings.

b. Make some exploratory plots to show the relationship between the response, visits, and insurance, with

and without applying the log function to visits. What do you find? Which plot makes it easier to see

the potential relationship?

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c. Build a Poisson regression model with visits as the response all other variables as possible predictor

variables. Examine the summary output and comment on the significance of variables as well as the

quality of model fit via the deviance.

d. Interpret the value of the coefficient for the employed variable.

e. Compute the mean and variance of the visits variable within each value of the school variable. Comment

on the relationship you observe and the viability of a Poisson model for this data.

f. Fit a negative binomial model with visits as the response all other variables as possible predictor

variables. Examine the summary output and comment on the significance of variables as well as the

quality of model fit via the deviance. Is it better than the Poisson model? Overall, do the directions of

significant relationships make sense?

g. Plot the residuals against the fitted values. Why are there lines of observations on the plot?

2)

The ccancer dataset in the GLMsData package contains the estimated number of deaths from cancer in

three regions of Canada by cancer site and gender.

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Count: the estimated number of deaths by the given cancer; a numeric vector

Gender: gender; a factor with levels either codeF (female) or codeM (male)

Region: the region; a factor with levels Ontario, Newfoundland or Quebec

Site: the cancer site; a factor with levels Lung, Colorectal, Breast, Prostate or Pancreas

Population: the estimated population of the region in 2000/20001; a numeric vector

a. Investigate the data and note the 0 values. Are these counts obtained at random, or are they structural

(impossible to be nonzero)? Remove these observations.

b. Create a variable storing the rate of number of deaths by the given cancer per 10,000 inhabitants. Plot

this against each of the three potential predictors and comment on the relationships.

c. Fit a Poisson rate model for number of deaths using the same variables as predictors. Does this model

fit the data well?

d. Interpret the coefficients of the Region variable.

3)

The kstones dataset in the GLMsData package contains a table summarizing treatment of kidney stones. It

has the variables:

• Counts: the number of subjects in the given classification; a numeric vector

• Size: whether the subject has kidney stones with mean diameter less than 2cm (coded as Small) or

greater than or equal to 2cm (coded as Large); a factor with levels Large and Small

• Method: the treatment method; a factor with levels A (open surgery) or B (percutaneous nephrolithotomy)

• Outcome: the outcome of the stated treatment; a factor with levels Failure and Success

a. Print a three way table of the data using the xtabs function. Describe any patterns you see with

respect to how the variables or relationships between variables effect the counts.

b. Fit a partial independence model where Size and Method interact. Does the model fit well?

c. Fit a conditional independence model where Outcome and Method are independent, given the Size of

the kidney stones. Compare this model to the partial independence model.

d. Fit a uniform association model. Compare this to the conditional independence model. Which model

should be used? Why?

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e. (7520 only) Interpret the dependence structure in the conditional independence model. In other words,

what does this mean about the relationships between variables and how they determine the counts?

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