School of Veterinary Medicine and Science Multilevel modelling Chris Hudson.

Slides:

Advertisements

Similar presentations

Questions From Yesterday

Advertisements

Contextual effects In the previous sections we found that when regressing pupil attainment on pupil prior ability schools vary in both intercept and slope.

Multilevel modelling short course

What is multilevel modelling?

To go further: intra- versus interindividual variability.

Hierarchical Linear Modeling: An Introduction & Applications in Organizational Research Michael C. Rodriguez.

Structural Equation Modeling

By Zach Andersen Jon Durrant Jayson Talakai

Tests of Significance for Regression & Correlation b* will equal the population parameter of the slope rather thanbecause beta has another meaning with.

Multilevel Modeling in Health Research April 11, 2008.

BA 275 Quantitative Business Methods

1 SSS II Lecture 1: Correlation and Regression Graduate School 2008/2009 Social Science Statistics II Gwilym Pryce

Linear regression models

Multilevel modeling in R Tom Dunn and Thom Baguley, Psychology, Nottingham Trent University

2005 Hopkins Epi-Biostat Summer Institute1 Module 2: Bayesian Hierarchical Models Francesca Dominici Michael Griswold The Johns Hopkins University Bloomberg.

Simple Linear Regression

Advanced Methods and Models in Behavioral Research – 2014 Been there / done that: Stata Logistic regression (……) Conjoint analysis Coming up: Multi-level.

Lecture 4 Linear random coefficients models. Rats example 30 young rats, weights measured weekly for five weeks Dependent variable (Y ij ) is weight for.

Some Terms Y =  o +  1 X Regression of Y on X Regress Y on X X called independent variable or predictor variable or covariate or factor Which factors.

Psychology 202b Advanced Psychological Statistics, II

The Simple Linear Regression Model: Specification and Estimation

Chapter 10 Simple Regression.

1 BA 275 Quantitative Business Methods Residual Analysis Multiple Linear Regression Adjusted R-squared Prediction Dummy Variables Agenda.

Analysis of Covariance Goals: 1)Reduce error variance. 2)Remove sources of bias from experiment. 3)Obtain adjusted estimates of population means.

A multilevel approach to geography of innovation Martin Srholec TIK Centre University of Oslo DIME International Workshop.

Clustered or Multilevel Data

Chapter 11 Multiple Regression.

Foster Care Reunification: The use of hierarchical modeling to account for sibling and county correlation Emily Putnam-Hornstein, MSW Center for Social.

Relationships Among Variables

Unit 3b: From Fixed to Random Intercepts © Andrew Ho, Harvard Graduate School of EducationUnit 3b – Slide 1

Analysis of Clustered and Longitudinal Data

Introduction to Multilevel Modeling Using SPSS

Overview of Meta-Analytic Data Analysis

Advanced Business Research Method Intructor : Prof. Feng-Hui Huang Agung D. Buchdadi DA21G201.

Modelling non-independent random effects in multilevel models William Browne Harvey Goldstein University of Bristol.

BPS - 3rd Ed. Chapter 211 Inference for Regression.

Workshop 1 Specify a multilevel structure for EITHER a response variable of your choice OR for a model to explain house prices OR voting behaviour Template.

Advanced Methods and Models in Behavioral Research – 2010/2011 AMMBR course design CONTENT METHOD Y is 0/1 conjoint analysis logistic regression multi-level.

Hierarchical Linear Modeling (HLM): A Conceptual Introduction Jessaca Spybrook Educational Leadership, Research, and Technology.

Introduction Multilevel Analysis

Simple Linear Regression One reason for assessing correlation is to identify a variable that could be used to predict another variable If that is your.

Multilevel Data in Outcomes Research Types of multilevel data common in outcomes research Random versus fixed effects Statistical Model Choices “Shrinkage.

Linear correlation and linear regression + summary of tests

Inference for Regression Simple Linear Regression IPS Chapter 10.1 © 2009 W.H. Freeman and Company.

HLM Models. General Analysis Strategy Baseline Model - No Predictors Model 1- Level 1 Predictors Model 2 – Level 2 Predictors of Group Mean Model 3 –

Mixed Effects Models Rebecca Atkins and Rachel Smith March 30, 2015.

Analysis Overheads1 Analyzing Heterogeneous Distributions: Multiple Regression Analysis Analog to the ANOVA is restricted to a single categorical between.

Data Analysis in Practice- Based Research Stephen Zyzanski, PhD Department of Family Medicine Case Western Reserve University School of Medicine October.

Talk by William Browne Slides by Kelvyn Jones In memory of Jon Rasbash all University of Bristol Monday 5th July 2010, Session 2 WHAT IS: multilevel modelling?

Marshall University School of Medicine Department of Biochemistry and Microbiology BMS 617 Lecture 11: Models Marshall University Genomics Core Facility.

Advanced Methods and Models in Behavioral Research – 2009/2010 AMMBR course design CONTENT METHOD Y is 0/1 conjoint analysis logistic regression multi-level.

Sampling and Nested Data in Practice-Based Research Stephen Zyzanski, PhD Department of Family Medicine Case Western Reserve University School of Medicine.

1 Statistics 262: Intermediate Biostatistics Regression Models for longitudinal data: Mixed Models.

Kelvyn Jones, University of Bristol Wednesday 2nd July 2008, Session 29 WHAT IS: multilevel modelling?

Introduction to Multilevel Analysis Presented by Vijay Pillai.

BPS - 5th Ed. Chapter 231 Inference for Regression.

The “Big Picture” (from Heath 1995). Simple Linear Regression.

© Murnane & Willett, Harvard University Graduate School of Education, 6/28/2016S290/Class #09 – Slide 1 S052: Applied Data Analysis Everything in the.

Marshall University School of Medicine Department of Biochemistry and Microbiology BMS 617 Lecture 10: Comparing Models.

Multilevel modelling: general ideas and uses

The simple linear regression model and parameter estimation

B&A ; and REGRESSION - ANCOVA B&A ; and

Linear Mixed Models in JMP Pro

Lecture 4 - Model Selection

G Lecture 6 Multilevel Notation; Level 1 and Level 2 Equations

ELEMENTS OF HIERARCHICAL REGRESSION LINEAR MODELS

From GLM to HLM Working with Continuous Outcomes

Simple Linear Regression

Fixed, Random and Mixed effects

An Introductory Tutorial

Presentation transcript:

School of Veterinary Medicine and Science Multilevel modelling Chris Hudson

School of Veterinary Medicine and Science Regression models..with 1 predictor outcome predictor

School of Veterinary Medicine and Science Regression models y= x..with 1 predictor

School of Veterinary Medicine and Science Regression models..with >1 predictor

School of Veterinary Medicine and Science More complex data structures In real life, things are often less simple! Are your “units” of data really independent? –Repeated measures within individuals –Pupils within schools –Individuals within households within neighbourhoods These are “multilevel” structures –e.g. pupils from the same school are more likely to be similar than pupils from different schools

School of Veterinary Medicine and Science A real example… Using a multilevel/hierarchical structure… 2d

School of Veterinary Medicine and Science A real example… Using a multilevel/hierarchical structure…

Why should we use multilevel models? Slides from

How do we deal with this? Contextual analysis. Analysis individual-level data but include group-level predictors Problem: Assumes all group-level variance can be explained by group-level predictors; incorrect SE’s for group-level predictors Do pupils in single-sex school experience higher exam attainment? Structure: 4059 pupils in 65 schools Response: Normal score across all London pupils aged 16 Predictor: Girls and Boys School compared to Mixed school Parameter Single level Multilevel Intercept (Mixed school) (0.021) (0.070) Boy school (0.049) (0.149) Girl school (0.034) (0.117) Between school variance(  u 2 ) (0.030) Between student variance (  e 2 ) (0.022) (0.019) Parameter Single level Intercept (Mixed school) (0.021) Boy school (0.049) Girl school (0.034) Between school variance(  u 2 ) Between student variance (  e 2 ) (0.022)

How do we deal with this? Analysis of covariance (fixed effects model). Include dummy variables for each and every group Problems What if number of groups very large, eg households? No single parameter assesses between group differences Cannot make inferences beyond groups in sample Cannot include group-level predictors as all degrees of freedom at the group-level have been consumed Target of inference: individual School versus schools

How do we deal with this? Fit single-level model but adjust standard errors for clustering (GEE approach) Problems: Treats groups as a nuisance rather than of substantive interest; no estimate of between-group variance; not extendible to more levels and complex heterogeneity Multilevel (random effects) model –Partition residual variance into between- and within-group (level 2 and level 1) components –Allows for un-observables at each level, corrects standard errors –Micro AND macro models analysed simultaneously –Avoids ecological fallacy and atomistic fallacy

School of Veterinary Medicine and Science ML models… 1.Account appropriately for clustering (even in complex structured data) 2.Allow inferences to be made about differences between levels (including generalisation to wider popluations) –cf treating this as a “nuisance”

School of Veterinary Medicine and Science Random effects Random intercepts –Each higher-level unit has a different intercept –These are assumed to come from a Normal distribution

School of Veterinary Medicine and Science Random effects Random slopes –It’s also possible to let the slope of each line vary between higher-level units…

School of Veterinary Medicine and Science An example…

School of Veterinary Medicine and Science Resources