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Quantitative practice questions
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- 1What is 'nested data'? Give examples!Nested data means that all terms of a smaller model occur within a larger model.
E.g. students in classes; people in countries - 2What are the consequences of nested data if we want to do regression analysis?If one ignores the multilevel structure of the data, one is likely to underestimate standard errors, which leads to either (1) rejecting the H0 too quickly or (2) making a type 1 error
- 3What important assumption of OLS regression is likely to be violated in your data example?OLS doesn't take into consideration group effects.
In OLS there's no reason to doubt the assumption of independent errors. - 4How does multilevel regression take care of the problems arising from nested data?The assumption of uncorrelated errors may no longer be reasonable, values of Y are correlated within groups.
Multilevel regression runs a separate regression analysis for each group, thereby controlling for the variance. - 5What does one mean by 'variance decomposition' how does it relate to nested data and multilevel regression analysis?Variance decomposition takes into account both the variance between country means & variance between persons within countries.
We use the estimated variances to calculate the ICC - 6How should we interpret the ICC?ICC = how much does being in a certain group influences individual cases; correlation of Y-values within higher level units
- 7How does one calculate the ICC?ρ= (σ_u0^2)/(σ_u0^2+σ_r^2 )
ICC = variance between country means divided by variance between country means plus variance between persons within countries - 8What is the name of the regression model one uses to estimate the ICC and why is is called that?One must estimate the multilevel null model. It's called so, because it has no explanatory variables.
- 9What does γ00, σ_u0^2 and σ_r^2 mean?γ00 = grand mean; mean intercept in population of groups
σ_u0^2 = variance of intercepts in population of groups
σ_r^2 = variance of deviation from the regression line within each group - 10What is a 'nested model'?If one can get a model by putting constraints on the parameters of another model, then the models are nested.
- 11How does one test if the ICC is significant?With the deviance/likelihood ratio test:
(1) (-2LL Restricted Model) - (-2LL Full Model) = x
(2) =chidist (x, df) => p-value
degrees of freedom - add one for each constraint
(3) p-value / 2
(4) if p < α this proves that there is statistical significance at the higher level - 12What are level 1 (X) and level 2 (W) predictors? Give examples!Level 1 predictors are lower level variables. E.g.: income, age, political preference, level of education, trust in political parties, happiness, marital status
Level 2 predictors are higher level variables
E.g.: inequality, GDP, unemployment rate, freedom of press, population size - 13How should we interpret a RI/FS model for X and W?The effect is always the same no matter where the starting point the intercept. The level 2 predictor doesn't influence how much the level 1 predictor affects the DV.
In other words, no matter the starting value of Y, an increase in the value of X will always have a fixed effect on Y. - 14How does one interpret a RI/RS model for X?The starting point of the intercept signifies how much X influences Y.
- 15What is meant with covariance of slope and intercept of X and when is this relevant?Covariance is relevant in a RI/RS model.
Covariance is a unstandardized coefficient, and an interaction variable.
Covariance (if significantly positive or negative) may offer (partial) explanation on what causes the slopes to differ, and under what circumstances. - 16How should one test the statistical significance of fixed effects?One can use the t-test provided by SPSS to test the statistical significance of fixed effects.
H0: γ10 (level 1 predictor) = 0
H0: γ01 (level 2 predictor) = 0 - 17How should one test the statistical significance of random effects, and how should one interpret such a test?Testing random effects means testing (co-)variance.
SPSS provides Wald Z-tests, but these are not reliable for testing variance.
Better use likelihood ratio/deviance test
One tests to see whether X is a fixed or random effect. - 18What is a cross level interaction? Give examples of cross level interaction hypothesis/effects! How do cross level interactions relate to the random effect of level 1 predictors?H1: The lower income is, the more people will like left-wing parties
H2: The previously mentioned effect is stronger the more unequal the distribution of wealth in a country is.
H2 is a cross-level interaction hypothesis, because we expect the slope of the effect of the people's income on their liking of left-wing parties to be affected by the level of inequality in a country. - 19What is 'BLUE'?Best Linear Unbiased Estimate
Predicted values for each case based on the only fixed part of the model - 20What is 'BLUP'?Best Linear Unbiased Prediction
Predicted value for each case based on the fixed and random parts of the model
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