2OUTLINEJon – What is Multilevel Regression Jayson – The Model Zach – R code applications / examples
3WHAT IS MULTILEVEL REGRESSION Regression models at multiple levels, because of dependencies in nested data Not two stage, this occurs all at once
4Employees in organizations Firms in various industries EXAMPLESStudents in schoolsIndividuals by areaEmployees in organizationsFirms in various industriesRepeated observations on a personhttps://www.youtube.com/watch?v=wom6uPdI-P4
5WHEN TO USE A MULTILEVEL MODEL? Individual units (often people), with group indicators (e.g. Schools, area).Dependent variable (level 1)More than one person per groupGenerally we need at least 5 groups, preferably more. (Ugly rule of thumb)https://www.youtube.com/watch?v=wom6uPdI-P4
6WHEN TO USE A MULTILEVEL MODEL? Use a multilevel model whenever your data is grouped (or nested) into categories (or clusters)Allows for the study of effects that vary by groupRegular regression ignores the average variation between groups and may lack the ability to generalize
7DATA STRUCTURE AND DEPENDENCE Independence makes sense sometimes and keeps statistical theory relatively simple.Eg; standard error(sample average) = s/n requires that the n observations are independentBut data often have structure, and observations have things in common; same area, same school, repeated observations on the same personObservations usually cannot be regarded as independenthttps://www.youtube.com/watch?v=wom6uPdI-P4
15BRIEF HISTORYProblems of single level analysis, cross level inferences and ecological fallacyhttps://www.youtube.com/watch?v=wom6uPdI-P4
16DISCUSSION AS TO WHY A NORMAL REGRESSION CAN BE A POOR MODEL Because Reality might not conform to the assumptions of linear regression (Independence)Because in nature observation tend to clusterA random person in Lubbock is more likely to be a student then a random person in another city (clustering of populations/not independent)Different clusters react differentlyhttps://www.youtube.com/watch?v=wom6uPdI-P4
17Also longitudinal, geographical studies EXTENSIONSFocus was initially on hierarchical structures and especially students in schoolsAlso longitudinal, geographical studiesMore recently moved to non hierarchical situations such as cross-classified models. (single level is part of more than one group)
18INTRACLASS CORRELATION Level 1 variance explained by the group (level 2)ICC is the proportion of group-level variance to the total varianceFormula for ICC:Variance in groupOverall variance
20Random or Fixed Effects MULTILEVEL MODELINGRandom or Fixed EffectsWhat are random and fixed effects?When should you use random and fixed effects?Types of random effects modelsThe ModelAssumptions of the modelBuilding a multilevel model
21Fixed vs random effects **Anytime that you see the word “population” substitute it with the word “processes.”
23Types of Models: Random Intercepts Model Intercepts are allowed to vary:The scores on the dependent variable for each individual observation are predicted by the intercept that varies across groups.
24Types of Models: Random Slopes Model Slopes are different across groups.This model assumes that intercepts are fixed (the same across different contexts).
25Types of Models: Random intercepts and slopes model Includes both random intercepts and random slopesIs likely the most realistic type of model, although it is also the most complex.
26Assumptions for Multilevel Models Modification of assumptionsLinearity and normality assumptions are retainedHomoscedasticity and independence of observations need to be adjusted.Observations within a group are more similar to observations in different groups.Groups are independent from other groups, but observations within a group are not.