Podcast
Questions and Answers
What is the primary purpose of MLM?
What is the primary purpose of MLM?
To predict individual outcomes from other individual variables as well as group level variables, taking into account the grouping structure
Distinguish between a micro-level variable and a macro-level variable with an example.
Distinguish between a micro-level variable and a macro-level variable with an example.
A micro-level variable is an individual characteristic, such as a student's test score, whereas a macro-level variable is a group characteristic, such as a school's average test score.
Why do statistical procedures often require independent observations?
Why do statistical procedures often require independent observations?
To ensure the validity of statistical tests and to prevent biased results.
When is it necessary to account for group dependence in a model?
When is it necessary to account for group dependence in a model?
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Can MLM predict constructs at multiple levels, such as individuals nested in groups?
Can MLM predict constructs at multiple levels, such as individuals nested in groups?
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Provide an example of why we are interested in the dependency created by a group structure.
Provide an example of why we are interested in the dependency created by a group structure.
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What is multi-stage sampling, and how does it relate to MLM?
What is multi-stage sampling, and how does it relate to MLM?
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What does the diagram suggest about the relationship between micro-level and macro-level variables?
What does the diagram suggest about the relationship between micro-level and macro-level variables?
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What type of modeling is used to predict individual performance in a multi-level modeling approach?
What type of modeling is used to predict individual performance in a multi-level modeling approach?
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In Example 1, what does Maro predict?
In Example 1, what does Maro predict?
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What is the focus of Example 2?
What is the focus of Example 2?
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In Example 3, what is the dependent variable?
In Example 3, what is the dependent variable?
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What is the role of school (Z) in Example 3?
What is the role of school (Z) in Example 3?
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What is the relationship between verbal IQ and year 12 results?
What is the relationship between verbal IQ and year 12 results?
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What is the advantage of using multi-level modeling?
What is the advantage of using multi-level modeling?
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What is the goal of predicting Y from Z?
What is the goal of predicting Y from Z?
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What is an example of when you would need to change two levels into one in multilevel modeling?
What is an example of when you would need to change two levels into one in multilevel modeling?
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How would you manage an aggregation in multilevel modeling?
How would you manage an aggregation in multilevel modeling?
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What is the definition of aggregation in multilevel modeling?
What is the definition of aggregation in multilevel modeling?
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When is it okay to use aggregation in multilevel modeling?
When is it okay to use aggregation in multilevel modeling?
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What is one of the issues with aggregation in multilevel modeling?
What is one of the issues with aggregation in multilevel modeling?
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What is the definition of disaggregation in multilevel modeling?
What is the definition of disaggregation in multilevel modeling?
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Why would you use disaggregation in multilevel modeling?
Why would you use disaggregation in multilevel modeling?
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What is an example of a research question that would require multilevel modeling?
What is an example of a research question that would require multilevel modeling?
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What is the correlation between randomly drawn individuals in one randomly drawn group, according to the ICC?
What is the correlation between randomly drawn individuals in one randomly drawn group, according to the ICC?
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What is the cut-off value for ICC to justify doing MLM?
What is the cut-off value for ICC to justify doing MLM?
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How do you interpret the ICC value of 0.147 in the context of a multilevel model?
How do you interpret the ICC value of 0.147 in the context of a multilevel model?
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What is the range of the ICC value?
What is the range of the ICC value?
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How do you calculate the total variance in a multilevel model?
How do you calculate the total variance in a multilevel model?
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What does the random intercept multilevel model attempt to explain?
What does the random intercept multilevel model attempt to explain?
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What is an example of a random intercept model?
What is an example of a random intercept model?
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Does the computer generate MLM in two stages?
Does the computer generate MLM in two stages?
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What is the consequence of applying the class size effect to the pupil data in terms of test scores?
What is the consequence of applying the class size effect to the pupil data in terms of test scores?
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What are some issues associated with disaggregation?
What are some issues associated with disaggregation?
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What is the purpose of combining a multilevel approach when analyzing both micro and macro level data?
What is the purpose of combining a multilevel approach when analyzing both micro and macro level data?
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What is the key difference between fixed effects and random effects ANOVA?
What is the key difference between fixed effects and random effects ANOVA?
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What is the role of β0j in a random effects ANOVA model?
What is the role of β0j in a random effects ANOVA model?
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What is the null hypothesis in a random effects ANOVA?
What is the null hypothesis in a random effects ANOVA?
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What is the equation for the total variance in a random effects ANOVA?
What is the equation for the total variance in a random effects ANOVA?
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What is the interpretation of the ICC (Intraclass Correlation Coefficient) in a random effects ANOVA?
What is the interpretation of the ICC (Intraclass Correlation Coefficient) in a random effects ANOVA?
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Study Notes
What is MLM?
- MLM (Multi-Level Modeling) predicts individual outcomes from individual variables and group-level variables, taking into account the grouping structure.
- It involves two levels: lower level (micro) and upper level (macro).
Purpose of MLM
- To understand group-level effects.
- To predict constructs at more than one level (e.g., individuals nested in groups).
Group Dependence
- Grouping structure sets up dependence among observations.
- Sometimes independent observations are needed for statistical procedures.
- However, group dependence is necessary for understanding group-level effects.
Examples of MLM
- How a teacher influences a child.
- How a work environment influences employee productivity.
Multi-Stage Sampling
- A sampling method that selects clusters, then selects units within clusters.
Hierarchical Modeling
- Can model relationships between variables at multiple levels.
- Example 1: Marx predicts micro-level - higher resourced classrooms predict higher individual performance.
- Example 2: Z predicts Y (holding constant score on X).
- Example 3: X and Y depend on Z.
Aggregation
- Aggregation refers to combining lower-level data points into a single data point at a higher level.
- Aggregation is okay if you're only interested in macro-level information.
- Issues with aggregation: shift of meaning, neglect of original data structure, prevents examination of cross-level interactions, and ecological fallacy.
ICC (Intra-Class Correlation)
- Measures the proportion of variance in the outcome variable that is due to the group structure.
- ICC ranges from 0 to 1.
- A high ICC indicates that the group structure explains a significant amount of variance in the outcome variable.
Random Intercept Model
- Attempts to explain the variance in the outcome variable due to the group structure.
- The intercept is allowed to vary randomly across groups.
- The model includes a variance component at the group level.
Random Effects ANOVA
- A two-stage strategy to investigate variables at two levels of analysis.
- Level 1: relationships among level 1 variables are estimated separately for each higher-level unit.
- Level 2: the variance component at the group level is estimated.
Fixed vs. Random Effects ANOVA
- Fixed effects ANOVA assumes the groups refer to categories with distinct interpretations.
- Random effects ANOVA assumes the groups are samples from a population of possible macro units.
- Random effects ANOVA includes a random intercept and slope.
Key Concepts
- Disaggregation: the process of moving from a higher level to a lower level of analysis.
- Issues with disaggregation: measure of macro-level variable considered as micro-level, miraculous multiplication of the number of units, risks of type 1 errors, and neglect of correlations within macro-units.
- Multilevel modeling combines both micro and macro levels to minimize the risk of erroneous conclusions.
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