Advanced Statistical Analysis Lecture 10

Advanced Statistical Analysis Lecture 10 Introduction to Multilevel Modelling Dr. Mark van Duijn Department of Economic Geography Department of DemographyUniversity of Groningen [email protected] 13 Mar, 2023 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Ag...

Advanced Statistical Analysis Lecture 10 Introduction to Multilevel Modelling Dr. Mark van Duijn Department of Economic Geography Department of DemographyUniversity of Groningen [email protected] 13 Mar, 2023 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Agenda Introduction to Multilevel modelling Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20232 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Literature on multilevel modelling Main literature (remember no exam material) Mehmetoglu & Jakobsen (2022). Chapter 10: Multilevel Analysis, Applied Statistics using STATA Sommet & Morselli (2017). Keep Calm and Learn Multilevel Logistic Modelling Background literature (self-study) Snijders & Bosker (2012). Multilevel Analysis: An introduction to basic and advanced multilevel modeling : weblinkConcise explanation on multilevel analysis (by Tom A.B. Snijders) Srholec (2010). A Multilevel Approach to Geography of Innovation. Regional Studies , 44(9), 1207-1220Centre for Multilevel Modelling (University of Bristol): weblink Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20233 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel modelling Unit of analysis is mostly based on one type (e.g., sample of individuals, sample of countries, sample of schools) However, people are not independent of the groups they belong to. . . (violation of independent and identically distributed errors) MLM corrects for bias in parameters and standard errors by accounting for nesting if one observes the hierarchical structure of the data MLM is also known as . . . Mixed model Hierarchical model Random coefficient model Random effects model Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20234 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel modelling Examples of MLM settings Cross-sectional: People - neighborhoods - regions - countries Cross-sectional: Workers - departments - organizations - regions - countries Longitudinal: People who are observed at several time points Meta-analysis: Subjects - Different studies All regression models can be extended to multilevel models (if data allows) Multilevel linear regression model Multilevel logistic regression model . . . Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20235 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel modelling Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20236 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel modelling Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20237 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel regression models Linear regression model with one level (individual i) y i = b 0 + b 1x i + e i Linear (fixed effect) regression model with two levels (individual iand group j) y ij = b 0j + b 1x ij + e ij Multilevel regression model with two levels (individual iand group j) y ij = b 0j + b 1jx ij + e ij where b 0j = b 0 + u 0j and b 1j = b 1 + u 1j y ij = b 0 + u 0j + b 1x ij + u 1jx ij + e ij a.k.a. hierarchical linear model (HLM) Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20238 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Important statistic (VPC/ICC) Variance partition coefficient / Intraclass correlation coefficient VPC = var (u 0) ( var (e ) + var(u 0)) Rule of thumb: Do not ignore the hierarchical structure of the data if VPC/ICC >5% Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 20239 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Random intercept model y ij = b 0j + b 1x ij + e ij b 0j = b 0 + u 0j y ij = b 0 + u 0j + b 1x ij + e ij Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202310 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Random intercept model y ij = b 0 + u 0j + b 1x ij + e ij Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202311 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Random coefficient model y ij = b 0j + b 1x ij + e ij y ij = b 0j + b 1jx ij + e ij where b 0j = b 0 + u 0j and b 1j = b 1 + u 1j y ij = b 0 + u 0j + b 1x ij + u 1jx ij + e ij Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202312 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Random coefficient model y ij = b 0 + u 0j + b 1x ij + u 1jx ij + e ij Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202313 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Multilevel vs fixed effects Multilevel analysis has in particular one strong assumption in order to make causal inferences: Random allocation of people within the different higher unit levels (representative) One must have enough higher level units for the multilevel approach to be appropriate Solution is to use ’fixed effects’ models that remove all variation between higher level units from parameter estimation (e.g. neighborhood dummies, country dummies, school dummies) One drawback: No estimates for time-invariant variables on the higher level units. Useful and/or interesting variation is removed from the model Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202314 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions When to use MLM? Hierarchical data structure Theoretical setup implies MLM Sample size requirements are met When you are interested in interaction effects of variables on different levels Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202315 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions When not to use MLM? Hierarchical data structure, but. . . Number of groups (e.g. spatial units) is very small No significant variation of the intercept (PVC/ICC very small) When only fixed effects are of importance When only group-level associations are of interest When you have a low number (or non-representative set) of level-1 observations for levels-2 or 3 Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202316 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Discuss paper of Sommet &Morselli (2017) For a more detailed application, study Sommet &Morselli (2017): Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS, International Review of Social Psychology , 30(1), 203-218Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202317 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Discuss paper of Srholec (2010) For an application in the field of (Economic) Geography, study Srholec (2010): A Multilevel Approach to Geography of Innovation, Regional Studies , 44(9), 1207-1220Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202318 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Practice and discuss an exam question Groups of 2 Whispering only please! 20 minutes and discuss answers after Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202319 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions What did we learn? Describe multilevel modelling Describe the underlying assumptions of multilevel modelling Know when to and when not to perform multilevel modelling A selection of published papers that apply multilevel modelling Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202320 / 21 Introduction Multilevel modelling Papers using MLM Formative assessment Conclusions Next lecture Thursday from 15h00-17h00 on Event History Analysis See announcement by Prof. dr. Clara Mulder: Prepare yourself ! Dr. Mark van Duijn (RUG) Advanced Statistical Analysis Lecture 10 13 Mar 202321 / 21