Multi-Level Modelling Concepts

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Questions and Answers

What is the purpose of aggregating data in multilevel modeling?

To examine cross-level interactions

To interpret data at a lower level

To obtain macro-level information (correct)

To reduce the power of the analysis

What is an example of when you would need to change two levels into one?

Schools within districts

Districts within states

Teachers within schools

Pupils within classrooms (correct)

What is the term for mistakenly interpreting aggregated data at a lower level?

Shift of meaning

Ecological fallacy (correct)

Reduction of power

Aggregation bias

When is it okay to use aggregation in multilevel modeling?

When interested in macro-level information Signup and view all the answers

What is one of the issues with aggregation in multilevel modeling?

Shift of meaning Signup and view all the answers

How would you manage an aggregation in multilevel modeling?

Calculate the means of the test and then do a regression at the macro level Signup and view all the answers

What is disaggregation in multilevel modeling?

Separating data into different levels Signup and view all the answers

What is the definition of aggregation in multilevel modeling?

Combining data points at a lower level to a single data point at a higher level Signup and view all the answers

What is the issue with disaggregation in multilevel data?

Measure of macro-level variable considered as micro-level Signup and view all the answers

Why is it recommended to combine a multilevel approach with micro and macro level data?

To minimize the risk of erroneous conclusions Signup and view all the answers

What is the key assumption in a fixed effects ANOVA?

Groups refer to categories with distinct interpretations Signup and view all the answers

What does the equation β0j = γ00 + u0j represent in a random effects ANOVA?

A mixed effects model with both fixed and random components Signup and view all the answers

What is the purpose of the ICC (Intra-Class Correlation) in a random effects ANOVA?

To measure the resemblance between individuals within a group Signup and view all the answers

What is the equation for a random effects ANOVA?

Y<del>ij</del> = γ<del>00</del> + u<del>0j</del> + ε<del>ij</del> Signup and view all the answers

What is the difference between a fixed effects ANOVA and a random effects ANOVA?

The assumption about the groups Signup and view all the answers

What is the equation for the total variance in a random effects ANOVA?

τ^2 + σ^2 Signup and view all the answers

What proportion of variance in test score is due to the group structure?

14.7% Signup and view all the answers

What is the range of the ICC?

0 to 1 Signup and view all the answers

What is the purpose of calculating the ICC?

To justify doing MLM Signup and view all the answers

How would you calculate the total variance?

Add the residual and the intercept Signup and view all the answers

What is the role of the random intercept multilevel model?

To explain the variance due to the group structure Signup and view all the answers

What is an example of a random intercept model?

A group of school with SES (social status) as a predictor Signup and view all the answers

How does the computer generate MLM?

In two stages Signup and view all the answers

What is the first stage of MLM?

Estimating relationships among level 1 variables Signup and view all the answers

What is the primary goal of Z predicting Y?

To identify the relationship between Z and individual performance Signup and view all the answers

What is the role of X in Example 3?

X is a predictor of Y at the individual level Signup and view all the answers

What is the purpose of holding constant the score on X in Example 2?

To control for the effect of X on Y Signup and view all the answers

What is the main difference between Example 1 and Example 3?

The level of analysis (individual vs. school) Signup and view all the answers

What is the name of the method used in Example 2?

Multiple Linear Regression Signup and view all the answers

What is the outcome variable in Example 3?

Individual results (Y) Signup and view all the answers

What is the purpose of multiple level modelling?

To account for the nested structure of data Signup and view all the answers

What is the relationship between verbal IQ and year 12 results, according to Example 3?

Verbal IQ has a positive effect on year 12 results Signup and view all the answers

What is the role of YOO (Gamma 00) in a multilevel model?

It is the overall mean Signup and view all the answers

What does the intercept represent in the null model?

The individual school's deviation from the overall mean Signup and view all the answers

What is the percentage of variation in math achievement due to the variation in groups or schools?

13.8% Signup and view all the answers

What is the relationship between SES and math achievement according to the model?

As SES increases by one unit, predicted math achievement rises by 3.87 units Signup and view all the answers

What does the term ICC represent in the multilevel model?

Inter-Class Correlation Signup and view all the answers

How many parameters are estimated in the multilevel model?

4 Signup and view all the answers

Study Notes

Multilevel Modeling (MLM)

MLM is a statistical approach that can be used to predict Y (individual level) based on Z (group level) while holding constant X (individual level).
Example 1: Maro predicts micro-level - individual performance, using higher resourced classrooms (Z) to predict higher individual performance.
Example 2: Z predicts Y (holding constant score on X), using regression to predict Y.
Example 3: X and Y are dependent on Z, using verbal IQ (X) to predict individual results (Y) at any school (Z).

Aggregation

Aggregation in MLM refers to the procedure of taking all data points at the lowest level and aggregating them into a single data point at a higher level.
It is okay to use aggregation if you are only interested in macro-level information.
Issues with aggregation:
- Shift of meaning: Variables aggregated to the macro level tell us about the macro level, not directly about the micro level.
- Neglect of original data structure: Reduction of power, prevents examination of cross-level interactions.
- Ecological fallacy: Mistaken attempts to interpret aggregated data at a lower level (e.g., micro level).

Disaggregation

Disaggregation in MLM involves breaking down aggregate data into its individual components.
Issues with disaggregation:
- Measure of macro-level variable considered as micro-level.
- Miraculous multiplication of the number of units.
- Risks of type 1 errors.
- Does not take into account that observations within a macro-unit could be correlated.

Random Effects ANOVA

Random effects ANOVA is a type of analysis that assumes groups are samples from a population of possible macro units.
The null hypothesis for a random effects ANOVA does not change.
Equation for a random effects ANOVA: Yij = γ00 + u0j + εij.
Equation for the total variance in a random effects ANOVA: Total variance = variance of intercept + variance due to residual.

Intraclass Correlation Coefficient (ICC)

ICC is a measure of the proportion of variance in the outcome variable that is due to the group structure.
ICC is also the correlation between two randomly drawn individuals in one randomly drawn group.
ICC falls between 0 and 1.
A high ICC indicates that the group structure is an important factor in explaining the variance in the outcome variable.

Random Intercept Model

The random intercept model attempts to explain the variation in the outcome variable due to the group structure.
The random intercept model is a null model that estimates the variance in the intercepts between groups.
The random intercept model with one predictor estimates the relationship between the predictor and the outcome variable while taking into account the variance in the intercepts between groups.

Multilevel Modeling (MLM) Example

A simple example of a random intercept model would be to investigate whether SES (social status) is associated with performance on a math test.
The model would estimate the overall mean of the math test score, the variation in the intercepts between schools, and the relationship between SES and math test score while controlling for the interclass correlation.

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Description

This quiz covers key concepts related to multi-level modelling, including predicting variables and using machine learning algorithms like MLM. Test your understanding of these advanced statistical techniques!