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Questions and Answers

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.

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?

To ensure the validity of statistical tests and to prevent biased results.

When is it necessary to account for group dependence in a model?

<p>When you want to understand group-level effects.</p> Signup and view all the answers

Can MLM predict constructs at multiple levels, such as individuals nested in groups?

<p>Yes, MLM can predict constructs at multiple levels.</p> Signup and view all the answers

Provide an example of why we are interested in the dependency created by a group structure.

<p>Understanding how a teacher influences a child's learning or how a work environment affects employee productivity.</p> Signup and view all the answers

What is multi-stage sampling, and how does it relate to MLM?

<p>Multi-stage sampling is a sampling method where units are selected in multiple stages, which is often used in MLM.</p> Signup and view all the answers

What does the diagram suggest about the relationship between micro-level and macro-level variables?

<p>The diagram suggests that there is a macro-level variable not indicated by the dotted line, and MLM can be used to model this relationship.</p> Signup and view all the answers

What type of modeling is used to predict individual performance in a multi-level modeling approach?

<p>MLM (Multi-Level Modeling)</p> Signup and view all the answers

In Example 1, what does Maro predict?

<p>Micro-level individual performance</p> Signup and view all the answers

What is the focus of Example 2?

<p>Z predicts Y, holding constant score on X</p> Signup and view all the answers

In Example 3, what is the dependent variable?

<p>Individual results (Y)</p> Signup and view all the answers

What is the role of school (Z) in Example 3?

<p>School (Z) is a predictor of individual results (Y)</p> Signup and view all the answers

What is the relationship between verbal IQ and year 12 results?

<p>Verbal IQ predicts year 12 results</p> Signup and view all the answers

What is the advantage of using multi-level modeling?

<p>It takes into account the nested structure of the data</p> Signup and view all the answers

What is the goal of predicting Y from Z?

<p>To understand the relationship between Z and Y</p> Signup and view all the answers

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

<p>Pupils within classrooms, where variables such as test result and classroom size are measured at the individual level, but need to be aggregated to the classroom level.</p> Signup and view all the answers

How would you manage an aggregation in multilevel modeling?

<p>Calculate the means of the test results and then perform a regression at the macro level.</p> Signup and view all the answers

What is the definition of aggregation in multilevel modeling?

<p>Aggregation refers to the process of taking all data points at the lowest level and aggregating them into a single data point at a higher level.</p> Signup and view all the answers

When is it okay to use aggregation in multilevel modeling?

<p>Aggregation is okay if you are only interested in macro-level information.</p> Signup and view all the answers

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

<p>Ecological fallacy, where aggregated data is mistakenly interpreted at a lower level.</p> Signup and view all the answers

What is the definition of disaggregation in multilevel modeling?

<p>Disaggregation is not defined in the text, but it refers to the process of breaking down aggregated data into its individual components at a lower level.</p> Signup and view all the answers

Why would you use disaggregation in multilevel modeling?

<p>To examine individual-level data and avoid issues related to aggregation, such as the ecological fallacy.</p> Signup and view all the answers

What is an example of a research question that would require multilevel modeling?

<p>Do larger classes affect test results?</p> Signup and view all the answers

What is the correlation between randomly drawn individuals in one randomly drawn group, according to the ICC?

<p>True</p> Signup and view all the answers

What is the cut-off value for ICC to justify doing MLM?

<p>0.05</p> Signup and view all the answers

How do you interpret the ICC value of 0.147 in the context of a multilevel model?

<p>14.7% of the variance in the test score is due to the group structure.</p> Signup and view all the answers

What is the range of the ICC value?

<p>Between 0 and 1</p> Signup and view all the answers

How do you calculate the total variance in a multilevel model?

<p>Add the residual variance and the variance of the intercept.</p> Signup and view all the answers

What does the random intercept multilevel model attempt to explain?

<p>The variation in the outcome variable due to the group structure.</p> Signup and view all the answers

What is an example of a random intercept model?

<p>A model with a group of schools as the level 2 unit and SES as a predictor of math test results.</p> Signup and view all the answers

Does the computer generate MLM in two stages?

<p>Yes</p> Signup and view all the answers

What is the consequence of applying the class size effect to the pupil data in terms of test scores?

<p>We find a difference between the aggregated and disaggregated scores.</p> Signup and view all the answers

What are some issues associated with disaggregation?

<p>Measure of macro-level variable considered as micro-level, miraculous multiplication of the number of units, risks of type 1 errors, and not taking into account correlated observations within a macro-unit.</p> Signup and view all the answers

What is the purpose of combining a multilevel approach when analyzing both micro and macro level data?

<p>To minimize the risk of erroneous conclusions.</p> Signup and view all the answers

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

<p>Fixed effects ANOVA assumes groups refer to categories with distinct interpretations, while random effects ANOVA assumes groups are samples from a population of possible macro units.</p> Signup and view all the answers

What is the role of β0j in a random effects ANOVA model?

<p>β0j = γ00 + u0j, which includes both a fixed and random component.</p> Signup and view all the answers

What is the null hypothesis in a random effects ANOVA?

<p>The null hypothesis changes depending on the specific research question and the level of analysis.</p> Signup and view all the answers

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

<p>The equation is not provided in the text, but it is a combination of the variance of the random effect (u0j) and the variance of the residual error (εij).</p> Signup and view all the answers

What is the interpretation of the ICC (Intraclass Correlation Coefficient) in a random effects ANOVA?

<p>It is the correlation between two randomly drawn individuals in one randomly drawn group.</p> Signup and view all the answers

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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