Question 1

In a multilevel model in which an outcome was measured in children from different classrooms, a large intraclass correlation would imply that:&#10;A)The outcome measure varied a lot across children within a classroom.&#10;B)Children within a particular class behaved very differently.&#10;C)Children in different classes behaved very differently.&#10;D)The outcome variable varied very little across children from different classrooms.

Accepted Answer

DA large intraclass correlation implies that units within the same group (in this case, children within the same classroom) are more similar to each other than to units in other groups. This means that there is less variation within classrooms (compared to between classrooms), indicating that children in different classes behave more differently (C) and that the outcome variable varies little across children from different classrooms (D).

Question 2

A researcher had data collected at several schools measuring children's emotional intelligence, age, and academic performance. Which analysis should they perform to test whether academic performance is predicted by emotional intelligence when controlling for age, taking into account that students were from different schools?

A)Multiple regression
B)Multilevel model
C)Analysis of covariance
D)Discriminant function analysis

B

Accepted Answer

A multilevel model is the best choice as it allows for the analysis of individual-level predictors (emotional intelligence, age) on an outcome (academic performance) while accounting for the nested structure of the data (students within schools). This approach recognizes that students are more similar to other students at their own school than to students at different schools, and therefore accounts for the non-independence of the data.

Question 3

The matrix below describes what kind of covariance structure in a multilevel model?
$\left( \begin{array} { c c c c } 1 & \rho & \rho ^ { 2 } & \rho ^ { 3 } \\\rho & 1 & \rho & \rho ^ { 2 } \\\rho ^ { 2 } & \rho & 1 & \rho \\\rho ^ { 3 } & \rho ^ { 2 } & \rho & 1\end{array} \right)$

A)Diagonal
B)AR(1)
C)Variance components
D)Unstructured

Unstructured

Accepted Answer

Unstructured&#10;

Question 4

What is a second-order polynomial also known as?&#10;A)A linear trend&#10;B)A quadratic trend&#10;C)A cubic trend&#10;D)A quartic trend

Accepted Answer

A second-order polynomial is also known as a quadratic trend.

Question 5

What do we mean by centring?&#10;A)The process of transforming a variable into deviations around a fixed point&#10;B)Expressing an outcome variable as deviations from the mean of a predictor variable&#10;C)Calculating the central point of a distribution&#10;D)Multiplying a variable by the mean of a different variable

Accepted Answer

Centring in statistical analysis typically refers to the process of transforming a variable by subtracting a constant (often the mean of that variable) from each value, resulting in a new variable whose mean is zero. This is done to create deviations around a fixed point, usually to simplify the interpretation of regression coefficients in models involving interaction terms.

Question 6

A paediatrician measured children's asthma and stress levels each month for six months. What analysis would they use to find out whether stress significantly predicts asthma?&#10;A)A growth model&#10;B)Biserial correlation&#10;C)Ordinary least squares regression&#10;D)Analysis of covariance

Accepted Answer

The answer of A paediatrician measured children's asthma and stress...

Question 7

The matrix below describes what kind of covariance structure in a multilevel model?
$\left( \begin{array} { c c c c } 1 & \rho & \rho ^ { 2 } & \rho ^ { 3 } \\\rho & 1 & \rho & \rho ^ { 2 } \\\rho ^ { 2 } & \rho & 1 & \rho \\\rho ^ { 3 } & \rho ^ { 2 } & \rho & 1\end{array} \right)$

A)Diagonal
B)AR(1)
C)Variance components
D)Unstructured

Unstructured

Accepted Answer

The matrix is a diagonal matrix, which means that the covariances between the variables are zero. This is the covariance structure of a variance components model.

Question 8

The SPSS output below is from a multilevel model. What does UN(1,1) estimate?  &#10;A)The variance of residuals&#10;B)The covariance between intercepts and slopes&#10;C)The variance of slopes&#10;D)The variance of intercepts

Accepted Answer

UN(1,1) estimates the variance of intercepts in a multilevel model.

Question 9

In the context of multilevel models what do we mean by a fixed regression coefficient?&#10;A)A regression coefficient that is stable across different samples&#10;B)A regression coefficient that is assumed to be the same in the population and the sample&#10;C)A regression coefficient that is assumed not to vary across contexts&#10;D)A regression coefficient that is always a fixed value and does not need to be estimated

Accepted Answer

In multilevel models, a fixed regression coefficient refers to a parameter that is assumed not to vary across different contexts or levels of analysis. This is in contrast to a random coefficient, which is allowed to vary across groups or individuals. Fixed coefficients are typically estimated using maximum likelihood or Bayesian methods, and are used to test hypotheses about the relationships between predictors and outcomes.

Question 10

The matrix below describes what kind of covariance structure in a multilevel model?
$\left( \begin{array} { c c c c } \sigma _ { 1 } ^ { 2 } & \sigma _ { 21 } & \sigma _ { 31 } & \sigma _ { 41 } \\\sigma _ { 21 } & \sigma _ { 2 } ^ { 2 } & \sigma _ { 32 } & \sigma _ { 42 } \\\sigma _ { 31 } & \sigma _ { 32 } & \sigma _ { 3 } ^ { 2 } & \sigma _ { 43 } \\\sigma _ { 41 } & \sigma _ { 42 } & \sigma _ { 43 } & \sigma _ { 4 } ^ { 2 }\end{array} \right)$

A)Variance components
B)Diagonal
C)Unstructured
D)AR(1)

Accepted Answer

This matrix represents an unstructured covariance structure because each element can have a unique value, indicating that there is no specific pattern or restriction on the relationships between different levels or units.

Question 11

In a multilevel model in which reaction times on different trials (level 1) were collected from within different people (level 2), what does the intraclass correlation represent?&#10;A)The proportion of the total variability in reaction times that is attributable to the people&#10;B)The proportion of the total variability in reaction times that is attributable to the trials&#10;C)The difference in the total variability in reaction times explained by the trials compared to that explained by the people&#10;D)The relationship between the variance in reaction times explained by people and that explained by trials

Accepted Answer

The answer of In a multilevel model in which reaction...

Question 12

The graph below is from Wright and London (2009). Which of the following descriptions best applies to this graph:  &#10;A)Fixed slopes, fixed intercepts&#10;B)Fixed slopes, random intercepts&#10;C)Random slopes, random intercepts&#10;D)Random slopes, fixed intercepts

Accepted Answer

The answer of The graph below is from Wright and...

Question 13

It is common when fitting multilevel models to start with a simple model, and build it up by adding new terms and re-estimating the model. If you want to compare the fit of a multilevel model with a simpler variant of the same model, what estimation method must you use?

A)Ordinary least squares
B)Maximum likelihood
C)Restricted maximum likelihood
D)Generalized least squares

Accepted Answer

The answer of It is common when fitting multilevel models...

Question 14

The SPSS output below is from a multilevel model. What does UN(2,2) estimate?  &#10;A)The variance of slopes&#10;B)The variance of residuals&#10;C)The variance of intercepts&#10;D)The covariance between intercepts and slopes

Accepted Answer

The answer of The SPSS output below is from a...

Question 15

Multilevel linear models differ from regression in that they:&#10;A)Allow you to do mediation analysis.&#10;B)Allow you to include multiple predictor variables.&#10;C)Can have categorical variables as predictors.&#10;D)Take account of hierarchies in the data structure.

Accepted Answer

The answer of Multilevel linear models differ from regression in...

Question 16

In the output for a multilevel model, the coefficient estimate for each effect can tell us:&#10;A)Whether your predictors significantly predict the outcome.&#10;B)All of these.&#10;C)Whether the relationship between each predictor and the outcome is positive or negative.&#10;D)About any random effects in the model

Accepted Answer

The answer of In the output for a multilevel model,...

Question 17

The matrix below describes what kind of covariance structure in a multilevel model?
$\left( \begin{array} { c c c c } 1 & \rho & \rho ^ { 2 } & \rho ^ { 3 } \\\rho & 1 & \rho & \rho ^ { 2 } \\\rho ^ { 2 } & \rho & 1 & \rho \\\rho ^ { 3 } & \rho ^ { 2 } & \rho & 1\end{array} \right)$

A)Diagonal
B)AR(1)
C)Variance components
D)Unstructured

Unstructured

Accepted Answer

The answer of The matrix below describes what kind of...

Question 18

In the context of multilevel models what do we mean by a random regression coefficient?&#10;A)A regression coefficient that is assumed to be different in the population and the sample&#10;B)A regression coefficient that is assumed to vary across contexts&#10;C)A regression coefficient that varies across different samples&#10;D)A regression coefficient that is a random value and rather than an estimated value

Accepted Answer

The answer of In the context of multilevel models what...

Question 19

The SPSS output below is from a multilevel model. What does UN(2,1) estimate?  &#10;A)The variance of residuals&#10;B)The variance of intercepts&#10;C)The covariance between intercepts and slopes&#10;D)The variance of slopes

Accepted Answer

The answer of The SPSS output below is from a...

Question 20

Which of the following is a measure of the fit of a multilevel model?&#10;A)CAIC&#10;B)ACIC&#10;C)ACCI&#10;D)ICAC

Accepted Answer

The answer of Which of the following is a measure...

Deck 21: Multilevel Linear Models