Questions & explanations
1. Why might an unbalanced network cause stress?
People in unbalanced triangles feel pressure to change relationships. For example, if two friends dislike each other (two positives, one negative? Actually, that's positive-positive-negative which is balanced? Wait, two positives and one negative is balanced according to balance theory? No, balance theory: positive-positive-positive (all positive) is balanced; positive-positive-negative (two positives, one negative) is unbalanced? Actually, classic balance: a triangle with exactly one negative tie is unbalanced. Correction: Balanced triangles have 0 or 2 negative ties. So positive-positive-negative has one negative, unbalanced. So if two friends both dislike a third person, that's balanced (positive-positive-negative? Actually, that's two positive ties (friends) and one negative tie (both dislike the third) – that's one negative, unbalanced? Wait, careful: In a triangle of A, B, C: if A and B are friends (positive), A and C are enemies (negative), B and C are enemies (negative). That's two negatives, balanced. If only one negative, unbalanced. So example: A and B are friends, A and C
2. What is a generalized linear model?
A generalized linear model (GLM) extends ordinary linear regression to handle outcome variables that are not normally distributed. Ordinary regression assumes the outcome is continuous and errors are normal. GLM allows outcomes like binary (yes/no), counts, or categories. It has three parts: a random component specifying the distribution of the outcome (e.g., Binomial for binary), a linear predictor (a sum of predictors times coefficients), and a link function that connects the linear predictor to the mean of the outcome. Common link functions are logit for logistic regression and log for Poisson regression. GLM makes regression more flexible for different types of data.
3. What is the difference between structural equivalence and regular equivalence?
Structural equivalence requires two nodes to have exactly the same neighbors. Regular equivalence is looser: two nodes are regularly equivalent if they connect to nodes that are themselves equivalent. For example, two professors in different departments are regularly equivalent if each has students and colleagues that look similar, even if the specific people differ. Blockmodeling often uses regular equivalence because it captures roles better. In a school, a math teacher and a history teacher may be regularly equivalent because both teach students, even though their students are different. Regular equivalence produces blocks of nodes with similar roles.
4. What special care does debriefing need when the study involved deception?
When deception was used, the debriefing must explain clearly why the researcher could not tell the truth at the start. The researcher should make sure the participant does not feel angry or tricked. The researcher must also ask if the participant still wants their data used now that they know the real purpose. If the participant says no, the researcher must remove their data. The debriefing should also fix any wrong ideas the participant might have from the deception. For example, if the study made participants think they hurt someone, the researcher explains it was not real. The goal is to leave the participant with a positive feeling about the study.
5. What is a mixed model?
A mixed model, also called a multilevel or hierarchical model, includes both fixed effects and random effects. Fixed effects are the usual coefficients for predictors that are constant across groups. Random effects allow the intercepts and/or slopes to vary across groups, like different schools or subjects. This is useful when data are clustered, meaning observations within the same group are more similar than observations from different groups. For example, students in the same class share a teacher, so their test scores are correlated. Mixed models account for this correlation and give correct standard errors and generalizable conclusions.
6. How is big data changing content analysis?
Big data means very large amounts of text, like millions of social media posts. Computers can now process this quickly, finding patterns that humans would miss. Content analysis with big data can track topics in real time, like how people discuss an event. For example, researchers can analyze millions of tweets about a protest to see what words are used most. This gives a broader picture than small samples. However, big data also brings challenges, like ensuring the data is representative. The methods are evolving to handle this scale, using machine learning to code automatically. The future will combine human judgment with computer speed.
7. What is the bootstrap method in statistics?
The bootstrap is a resampling technique used to estimate the variability of a statistic without relying on strict assumptions about the data distribution. You take many samples (with replacement) from your original data, each of the same size as the original. For each bootstrap sample, you compute the statistic of interest (e.g., mean, median, regression coefficient). Then you look at the distribution of these bootstrap statistics. This gives you an estimate of the standard error and confidence intervals. The bootstrap is especially useful when theoretical formulas are complex or unavailable. It works for many kinds of data and statistics.
8. How can you use bootstrapping to estimate the standard error of a statistic?
To estimate the standard error, first generate a large number (e.g., 1000) of bootstrap samples from your original data by sampling with replacement. For each sample, compute the statistic (e.g., sample mean). Then calculate the standard deviation of these 1000 bootstrap statistics. That standard deviation is the bootstrap estimate of the standard error of your original statistic. For example, if you have a sample mean of 50 and the bootstrap standard deviation is 2, the standard error of the mean is about 2. This method does not require normality or known formulas and works for complex statistics like medians or correlation coefficients.
9. Explain the difference between a necessary condition and a sufficient condition using set theory.
A necessary condition means that to have the outcome, the condition must be there. In set terms, the outcome set is a subset of the condition set. For example, if all democracies are rich, then being rich is necessary for democracy (democracy subset of rich). A sufficient condition means that if the condition is present, the outcome always follows. Here, the condition set is a subset of the outcome set. For example, if all rich countries are democracies, then being rich is sufficient for democracy (rich subset of democracy). They are different: necessary is required but may not be enough; sufficient is enough but may not be required.
10. Why are mixed models useful when you have repeated measurements on the same subjects?
Repeated measurements on the same subjects are correlated because measurements from the same person are more alike than measurements from different people. Mixed models handle this by including a random intercept for each subject, which captures the subject's baseline level. They also allow for random slopes to model how a subject's trend over time might differ. This avoids the problem of underestimating standard errors that would occur if you treated all measurements as independent. Mixed models provide valid inference for fixed effects and can also model the correlation structure explicitly, such as AR(1) for equally spaced times.
11. In QCA, what does a truth table show, and how is it used to find patterns?
A truth table lists all possible combinations of conditions (e.g., rich/poor, democratic/not) and shows for each combination whether the outcome (e.g., revolution) occurred. Each row represents a logical combination, and you count how many cases fall into each row. Then you apply Boolean minimization: you combine rows that differ in only one condition but have the same outcome to simplify the expression. For example, if both 'rich AND democratic' and 'rich AND non-democratic' lead to revolution, then 'rich' alone might be sufficient (democracy doesn't matter). This yields a concise formula of necessary/sufficient conditions.
12. How do you fit an SBM to an observed network?
Fitting an SBM means finding the best block assignment and edge probabilities to explain the observed network. This is often done using maximum likelihood or Bayesian inference. The goal is to maximize the probability of observing the network given the model. For example, you try different numbers of blocks and assignments, then pick the one with highest likelihood. Techniques like variational inference or Markov Chain Monte Carlo are used. Many software packages (e.g., graph-tool in Python) can fit SBMs automatically. The result gives block memberships for each node and a matrix of connection probabilities between blocks.