Homework 4: Longitudinal Networks or a Research Conversation
ICPSR Network Analysis: Advanced Topics
The Assignment
Choose one of the two options below. You do not need to complete both.
Option A asks you to interpret results from a longitudinal network model. Option B lets you bring a piece of research connected to the course and talk it through with me. The point of either option is to connect the methods from class to an actual research question.
There is no model fitting or new coding required for Option A. A concise response that answers the questions directly is enough. For Option B, the conversation takes the place of the written interpretation.
Option A: Interpret a Longitudinal Network Model
The results below come from a stochastic actor-oriented model of friendship and drinking among 50 Scottish adolescents observed at three points in time. The model represents the changes between observations as a sequence of possible friendship and behavior changes.
The friendship equation asks which possible friendship changes receive more weight in the fitted change process. The behavior equation asks whether reported drinking tends to move toward the average reported drinking of a student’s friends.
| Part of the model | Result | Estimate | Standard error |
|---|---|---|---|
| Friendship equation | Outdegree | -2.77 | 0.14 |
| Friendship equation | Reciprocity | 2.38 | 0.22 |
| Friendship equation | Transitive triplets | 0.66 | 0.13 |
| Friendship equation | Drinking similarity | 1.44 | 0.61 |
| Drinking equation | Friends’ average drinking | 1.36 | 0.95 |
The overall convergence statistic was 0.163, below the usual 0.25 threshold. That means the estimation algorithm converged well enough for us to interpret the fitted results. It does not tell us that the model is correctly specified or that the estimates are causal.
Write approximately 400 to 600 words that answers the following questions:
- What is the research question? In one or two sentences, explain what the model is trying to learn about friendship and drinking over time.
- What do reciprocity and transitivity tell us? Choose either reciprocity or transitive triplets. Explain the result by describing a possible friendship action. Do not define the term only with statistical language.
- What do we learn about selection and influence? Drinking similarity belongs to the friendship equation and represents a selection pattern. Friends’ average drinking belongs to the behavior equation and represents an influence pattern. Explain what each estimate suggests and use the standard errors to discuss which conclusion is more precise.
- What can we conclude? End with two or three sentences stating what the model helps us understand and what it does not establish. In particular, do not treat the influence estimate as proof that friends cause one another to drink more.
A positive coefficient means that the corresponding possible change receives more weight in the fitted change process, holding the other included terms fixed. The coefficient is not itself a friendship probability or a percentage-point change. As a rough uncertainty check, an estimate that is about twice its standard error is more clearly separated from zero than an estimate that is close to its standard error.
What to Submit for Option A
Submit one short document in any readable format, such as PDF, Word, or HTML. No code is required. Please write in complete sentences and connect the results to the students, their friendship nominations, and their reported drinking.
Option B: Bring Research to Discuss
Share a piece of research connected to something we have covered in the course and schedule a short conversation with me about it. This can be:
- Your own paper, proposal, dissertation chapter, research design, model output, or data idea
- A published paper or working paper that you want to understand more carefully
- A research question for which you are considering network data or a network model
Before we meet, send me the research item or a link to it along with a short paragraph that answers:
- What is the main research question?
- Where does the network enter the argument or analysis?
- What would you most like to work through together?
The material does not need to be polished. If you cannot share the document or data, send a brief description instead. We can use the conversation to discuss the research question, measurement, model choice, interpretation, or the next useful step.
What to Submit for Option B
Send the research item and your short paragraph, then arrange a time to talk with me. The conversation completes this option. You do not need to write an additional response afterward.
A Final Reminder
Choose the option that is most useful for you. Option A gives you practice translating a longitudinal model into a careful substantive conclusion. Option B gives us room to connect the course directly to research you want to understand or develop.