Part 1: Proportional Odds Models
It can be helpful to credit card companies to look at the characteristics of individuals to determine if a potential customer will use their card. Data was collected in a large survey on the psychology of debt and can be found in the debt data set in the faraway package.
1. (1 point) Load the debt data from the Jara way package and read the help file. How many columns are in the data frame debt?
2. (2 points) Because of missing data, some of the functions in this lab will not run properly. Use the following code to “clean” the data. How many columns are in the data frame debt after running this code?
debt <- data. frame(cbind(debt$ incomegp, debt$ agegp, debt $bankacc, debt $ ccarduse))
colnames(debt) <- cÇ’incomegp”, “agegp”, “bankacc”, “ccarduse”)
debt <- na.omit(debt)
3. (3 points) Fit a proportional odds (PO) model predicting ccarduse from agegp, incoinegp and bankace.
a. What is the code to do this?
b. What is the interpretation for the slope of bankacc?
4. (5 points) Consider a subject who does not have a bank account, is in age group 1 and is in income group 1.
a. Use the proportional odds model that you fit in question 1 to compute P (ccarduse < 2) “by hand”.
b. What is the value inside the exponential function for this calculation?
5. (7 points) Suppose we believe that age group has a different effect on credit card use at different age levels. Fit a Generalized Ordinal (GENORD) model to the debt data. Test the proportional odds assumption by comparing the deviances of the PO model and the GENORD model. Make sure to include all steps of the hypothesis testing process.
6. (7 points) Assess the model fit for the PO model using the generalized HL test. Make sure to include all steps of the hypothesis testing process.
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