STA 279 Lab 5: Mixed Effects Models

Complete all Questions and submit final PDF under Assignments in Sakai.

The Data

Today we will be working with data on teen drinking behavior. This data was collected by surveying 82 adolescents. The survey was conducted 3 times for each subject, at ages 14, 15, and 16. The data may be found on Sakai, and contain information on the following variables:

• id: numerical identifier for subject.
• age: 14, 15, or 16
• coa: 1 if the teen is a child of an alcoholic parent; 0 otherwise.
• male: 1 if physically male; 0 if physically female.
• peer: a measure of peer alcohol use, taken when each subject was 14. This is the square root of the sum of two 6-point items about the proportion of friends who drink occasionally or regularly.
• alcuse: a numeric measure of alcohol use. Four items were used to obtain this measure: (a) drank beer or wine, (b) drank hard liquor, (c) 5 or more drinks in a row, and (d) got drunk-were each scored on an 8-point scale, from 0="not at all" to 7="every day". Then alcuse is the square root of the sum of these four items.

We are interested in two primary research questions today. (1) Do trajectories of alcohol use differ by parental alcoholism? (2) Do trajectories of alcohol use differ by peer alcohol use?

Research Question 1

We're going to begin with Research Question 1: Do trajectories of alcohol use differ by parental alcoholism?

3. Make a plot to explore the relationship between alcohol use in the teens and the drinking behavior of the parent. Make sure you label your axes! Based on what you see in the plot, if you were to fit a model to answer Research Question 1, would you expect the slope for alcoholic parent (coa) to be positive or negative? Explain.

3. Based on the data set and our question of interest, write down the form of a mixed effects model with a random intercept we could use to answer our question of interest. What is the group effect? We will call this model Model1.

3. Fit Model 1 in R. Show the output in R, and write down the fitted model.

3. Interpret the standard deviation term(s).

3. Use AIC to compare Model 1 to a model with no random effect. Using this comparison and the intraclass correlation, explain whether the random effect is useful for explaining variation in teen alcohol use.

3. Build a 95% confidence interval for your model. Based on your model and your interval, how would you respond to Research Question 1?

Research Question 2

Now we move on to Research Question 2: Do trajectories of alcohol use differ by peer alcohol use?

Previous research has told us that the effect of peer alcohol use on teenage drinking behavior can change quite a bit from teen to teen. This means that teenagers can be exposed to the same level of peer alcohol behavior, and yet this can have a different effect on their own drinking behavior.

3. How might we build a model (call it M2) to incorporate this information? Write down the form of the model, and explain your choice. Hint: Write down the fixed effects first, and then think about random effects you might need.

3. Fit M2 and write down the fitted model.

3. According to M2, what percent of the variation in the response variable can be attributed to individual-specific differences in the effect of peer drinking behavior on alcohol use?

3. For the first student in the data set, write out the fitted line. What are the estimate values of any random effects? What does this tell us about the student?

3. Build a 95% confidence interval for your model. Based on your model and your interval, how would you respond to Research Question 2?

Research Question 3

We are presented with a third research question. We want to build on our model from Research Question 2, but now we want to see if the sex of the teen is related to alcohol use.

3. Fit a model to answer Research Question 3. Write down the fitted model for (1) males and (2) for females.

Turning in your assignment

When your Markdown document is complete, do a final knit and make sure everything compiles. You will then submit your document on Sakai. You must submit a PDF document to Sakai. No other formats will be accepted. Make sure you look through the final PDF to make sure everything has knit correctly.

The css file used to format this lab was retrieved from the GitHub of Mine Çetinkaya-Rundel, version 2016 Jan 13.

The data set used in this lab is part of the data provided as accompanying data sets for the online textbook Broadening Your Statistical Horizons. The data were accessed through the book GitHub repository. The lab is based on the guided exercise in Section 9.9.2 of the same text.