Presentation on theme: "By Zach Andersen Jon Durrant Jayson Talakai"— Presentation transcript:
1 By Zach Andersen Jon Durrant Jayson Talakai Multilevel AnalysisByZach AndersenJon DurrantJayson Talakai
2 OUTLINEJon – What is Multilevel Regression Jayson – The Model Zach – R code applications / examples
3 WHAT IS MULTILEVEL REGRESSION Regression models at multiple levels, because of dependencies in nested data Not two stage, this occurs all at once
4 Employees in organizations Firms in various industries EXAMPLESStudents in schoolsIndividuals by areaEmployees in organizationsFirms in various industriesRepeated observations on a person
5 WHEN 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)
6 WHEN 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
7 DATA 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 independent
9 PROBLEMS CAUSED BY CORRELATION Imprecise parameter estimatesIncorrect standard errors
10 A SIMPLE 2-LEVEL HIERARCHY School 1School 2Student 1Student 2Student 3Student 1Student 2Student 3
11 A SIMPLE 2-LEVEL HIERARCHY School 1School 2Level 2Student 1Student 2Student 3Student 1Student 2Student 3Level 1
12 The first level of a hierarchy is not necessarily a person PEOPLE ARE AT LEVEL 1??The first level of a hierarchy is not necessarily a person
13 A SIMPLE 2-LEVEL HIERARCHY Industry 1Industry 2Level 2Firm 1Firm 2Firm 3Firm 1Firm 2Firm 3Level 1
14 A SIMPLE 2-LEVEL HIERARCHY Person 1Person 2Level 2Event 1Event 2Event 3Event 1Event 2Event 3Level 1
15 BRIEF HISTORYProblems of single level analysis, cross level inferences and ecological fallacy
16 DISCUSSION 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 differently
17 Also 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)
18 INTRACLASS 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
20 Random 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
21 Fixed vs random effects **Anytime that you see the word “population” substitute it with the word “processes.”
23 Types 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.
24 Types of Models: Random Slopes Model Slopes are different across groups.This model assumes that intercepts are fixed (the same across different contexts).
25 Types 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.
26 Assumptions 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.