University:
University of Michigan
Course:
STATS 605 | Advanced Topics in Modeling and Data Analysis
Academic year:

2019
Views:

113

Pages:

14
Author:

Koen D

A Practical Guide to Multilevel Modeling Usual caveat – this is what I know to be true as of Fall 2019, this is an area of statistics that is frequently updating Table of Contents • • • • • • • • What it is, when you need it (and when you don’t) Identifying the structure of your data Fixed and random effects Centering Covariance matrices Setting Up Data & Sample Syntax Interpreting Basic Output Other Topics • • • • • Mediation Moderation Time-Lagged Analyses Growth Curve Analyses Power and Sample Size Calculations • Resources Note: Click on a topic to go directly to that content MLM: What it is • An approach to dealing with non-independence between data points (i.e., clustered data) • Multilevel modeling (MLM) is also known as… • • • • Hierarchical Linear Modeling (HLM) Linear Mixed Modeling Random Coefficient Modeling Variance Component Modeling When do you need MLM? • If your data violates the “Assumption of Independence” required for basic statistical approaches Repeated measures nested within individuals • Event-contingent sampling, daily diary, longitudinal, multiple videos watched within a lab session, rating multiple targets on traits Individuals nested within groups - Students in a school, employees on teams, romantic partners, families • The basic problem: observations within a group are likely to be correlated, which leads us to underestimate the SEs for our effects, leading to Type I error. Do you need to use MLM? One reason you wouldn’t use MLM: Although your data may be clustered, it’s possible your data points are not actually interdependent • Strangers brought into the lab to interact likely to have similar hormonal profile? Students in classrooms (all from same grade) likely to have similar height? • You can test this with the Intraclass Correlation (ICC) • Amount of variance due to clustering • How correlated two random data points within a cluster are expected to be, are they more highly correlated than two data points from two different clusters? Testing for Interdependence • To test the strength of the ICC: • One-way ANOVA with clusters as grouping variable • possible to calculate ICC using MSbetween and Mserror • Intercept-only MLM • ρ (rho) = relative proportion of cluster variance to total variance A few caveats: • You must test each variable separately • Even if the ICC is low, it may make sense conceptually to treat the data as hierarchical • No hard and fast rules, but have seen ICC = .10 to be considered high enough that MLM should be used. Typically factors you think will be clustered are clustered. It’s just that occasionally you collect clustered data, but the variables you are interested in aren’t at all related to the clustering (e.g., brought randomly-paired strangers into the lab to interact but you are looking at their personality and not interested in interaction-related variables) Do you need to use MLM? • Another reason you wouldn’t use MLM: Although your data are clustered, you have a very small number of clusters and/or are interested in directly comparing the clusters to each other – Gender – Culture, Ethnicity – 4 classes in a school – 10 teams in a company • This is called the “Fixed Effects” approach Why not always use the fixed effects approach? • When you have a large number of clusters and you are not trying to meaningfully compare one cluster to another • If you have 100 participants – are you going to enter in 99 dummy codes to control for their differences? • MLM captures all of the variability of 99 dummy codes in one parameter: amount of variance due to cluster differences • Allows you to look at cluster-level variables (for individuals: gender, attachment, SES) without having to interact it with 99 dummy codes Other Ways to Deal with Non-Independence • Other ways you can deal with clustering without using MLM • Aggregation: take all data points at lowest level and aggregate them into a single data point • Average depressive mood across a year, proportion of time spent hanging out with friends during ESM study, number of conflicts with partner reported during two week diary • Disaggregation: take data point from high level and assign it to each data point at the lower level • Every time-point gets same score for P’s Gender; Depression Diagnosis • Statistical Problems with these approaches: • Over or underestimate sample size, SEs, may misrepresent population How to Deal with Non-Independence • It’s not just about these statistical limitations, there are also conceptual limitations • What is happening at the within-group level may not reflect what is happening between groups cluster cluster The Difference between MLM and Aggregation cluster cluster Aggregation Problems: An Example Linear Regression Multilevel Modeling Male = 1, Female = 0 Do you need to use MLM? 1. A principal rates the performance of his 50 teachers for competence in the classroom. 2. Data about recovery from 300 people in therapy. Data is drawn from the clientele of 50 different therapists. 3. 100 students report on their feelings of belonging several times a week for one month. 4. 1000 people from 5 different cultures report on their emotional experiences one time. 5. 300 Students complete questionnaires in random groups of 3-5. Students complete questions about their current GPA, class schedule, where they grew up, and other basic demographics. Creating a Multilevel Model 1. What is the structure of my nested data? 2. Are my effects fixed or random? 3. What type of centering should I use? 4. Which covariance matrices should I use?

Multilevel Modeling -1

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