# Lecture 5 Three level variance component models

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Lecture 5 Three level variance component models

2 Three levels models In three levels models the clusters themselves are nested in superclusters, forming a hierarchical structure. For example, we might have repeated measurement occasions (units) for patients (clusters) who are clustered in hospitals (superclusters).

3

4 Which method is best for measuring respiratory flow? Peak respiratory flow (PEFR) is measured by two methods, the standard Wright peak flow and the Mini Wright meter, each on two occasions on 17 subjects.

5 Table 1.1: Peak respiratory flow rate measured on two occasions using both the Wright and the Mini Wright meter ( Bland and Altma, Lancet 1986) Level 1: occasion (i) Level 2: method (j) Level 3: individual (k)

6 Model 1: two-level We fitted a two-level model to all 4 measurements ignoring the fact the different methods were used Occasion i, method j, subject k y ijk = β 1 + ζ k (3) + ε ijk ε ijk ~ N(0,σ 2 ) ζ k (3) ~ N(0,τ 2 ) Variance of the measurements within subjects Variance of the measurements across subjects Here we made no distinction between the two methods

7 Model 2: two-level Occasion i, method j, subject k y ijk = β 1 + β 2 x j + ζ k (3) + ε ijk ε ijk ~ N(0,σ 2 ) ζ k (3) ~ N(0,τ 2 ) Here we might add a binary variable for estimating the methods effect - this variable allows for a systematic difference between the 2 methods

8 Intraclass correlation coefficient τ 2 τ 2 + σ 2 = = 0.95 Correlation between the 4 repeated measures on the same individual (the method used for the measurement Is ignored) The % of the total variance of the measurements (within + between) that is explained by the variance of the measurem individuals

9 Why we need three stage? occasion (i), method(j), individual (k) Both two-level variance component models assume that the four measurements using the two methods, were all mutually independent, conditional on the random intercept (that is, they ignore the possibility that the measurements obtained with the same method might be more similar to each other than the measurements obtained with two different methods). In other words the measurements are nested within the method To see if this appears reasonable, we can plot all four measurements against subject id

10 Fig 7.2: Scatterplot of peak-respiratory flow measured by two methods versus subject id The shift between the measurements taken from the 2 methods varies across subjects measurements on the same subjects are more similar than measurements on different subjects For a given subject, the measurements using the same method tend to resamble each other more than measurements using the other method

11 Why we need three-level models? As expected, measurements on the same subjects are more similar than measurements on different subjects. This between subject heterogeneity is modeled by the subject-level intercept ς (3) k.

12 Why we need three-level models The figure suggests that for a given subject, the measurements using the same method tend to be more similar to each other, violating the conditional independence assumption of model (1) The difference between methods is not due to some constant shift of the measurements using one method relative to the other, but due to shifts that vary between subjects, thus violating the assumption in model (2)

13 Model 3: three-level variance component models y = β + ζ (2) + ζ (3) + ε ijk 1 jk k ijk ε ijk ~ N(0,σ 2 ) ζ (2) ~ N(0,τ 2 ) jk 2 ζ k (3) ~ N(0,τ 3 2 ) account for between-method within-subject heterogeneity Variance of the measurements across the two methods for the same subject Variance of the measurements across subjects

14 Parameters interpretations y = β + ζ (2) + ζ (3) + ε ijk 1 jk k ijk β 1 Population average of all measurements (across occasions, methods, and subjects) β 1 + ζ k (3) β + ζ (2) + ζ (3) 1 jk k Average of the measurements for subject k (across occasions and methods) Average of the measurements for method j and for subject k (across occasions)

15 Model 4: three-level variance component models y = β + β x + ζ (2) + ζ (3) + ε ijk 1 2 j jk k ijk ε ijk ~ N(0,σ 2 ) ζ (2) ~ N(0,τ 2 ) jk 2 ζ k (3) ~ N(0,τ 3 2 )

16 Different types of intraclass correlation ρ(subject) = cor(y ijk, y i' j'k x j,x j' ) = = τ 3 2 τ τ σ 2 correlation between the 4 measurements within the subject (same subject, different method, and different occasion) ρ(method,subject) = cor(y ijk,y i' jk x j ) = = τ τ 3 2 τ τ σ 2 correlation between the measurements obtained with the same method and for the same subject (same subject, same method, different occasions)

17 Intraclass correlations Note that cor(method,subject)> cor(subject). This makes sense since, as we saw in Figure 7.2, measurements using the same method are more similar than measurements using different methods for the same person.

18 Three-stage formulation Random effect Fixed effect y ijk = η jk + β 2 x j + ε ijk η = π + ζ (2) jk k jk π = β + ζ (3) k 1 jk Stage 1 Stage 2 Stage 3 y = β + β x + ζ (2) + ζ (3) + ε ijk 1 2 j jk jk ijk

19

20 Television school and family smoking cessation project (TVSFP) The TVSFP is a study designed to determine the efficacy of a schoolbased smoking prevention program in conjunction with a television-based prevention program, in terms of preventing smoking onset and increasing smoking cessation (Flay et al 1995)

21 TVSFP: outcome Outcome: a tobacco and health knowledge scale (THKS) assessing the student s knowledge of tobacco and health Linear model for THKS postintervention, with THKS pre-intervention as a covariate

22 TVSFP: study design 2x2 factorial design, with four intervention conditions determined by cross-classification of a school-based social resistant curriculum (CC: coded as 0 or 1) with a television-based program (TV, coded as 0 or 1) Randomization to one of the four intervention conditions was at the school level Intervention was delivered at the classroom level 1600 seventh-grades students from 135 classes in 28 schools in Los Angeles

23 Three-level model for the TVSFP i (student), j (classroom), k (school) postthks Y ijk = β 1 + β 2 prethks + β 3 CC + β 4 TV + β 5 (CC TV ) + +b (3) k + b (2) jk + ε ijk ε ijk ~ N(0,σ 1 2 ) b (2) jk ~ N(0,σ 2 2 ) b k (3) ~ N(0,σ 3 2 ) Within classroom, across students Within school, across classrooms Across schools

24 Intraclass correlation coefficients Correlation among THKS scores for classmates (or children within the same class and same school) is σ σ 2 2 σ σ σ 1 2 =

25 Intraclass correlation coefficients Correlation among THKS scores for children for different classrooms within the same school is σ 3 2 σ σ σ 1 2 =

26

27 Should we ignore the intraclass correlation? The intraclass correlation coefficients were relatively small at both the school and at the classroom levels. We might be tempted to think that the clustering of the data would not affect the intervention effects Such conclusion would be erroneous Although the intraclass correlations are small, they have substantial impact on the inferences

28 Linear model for the TVSFP without random effects i (student), j (classroom), k (school) postthks Y ijk = β 1 + β 2 prethks + β 3 CC + β 4 TV + β 5 (CC TV ) + ε ijk ε ijk ~ N(0,σ 1 2 ) This model ignores clustering in the data at a classroom and school levels. This is a standard linear regression model and assumes that the responses are independent

29

30 Comparing results Model-based standard errors (assuming no clustering) and misleading small for the randomized intervention effects and lead to substantially different conclusions Bottom line: even a very modest intracluster correlation can have a discernable impact on the inferences

### Overview of Methods for Analyzing Cluster-Correlated Data. Garrett M. Fitzmaurice

Overview of Methods for Analyzing Cluster-Correlated Data Garrett M. Fitzmaurice Laboratory for Psychiatric Biostatistics, McLean Hospital Department of Biostatistics, Harvard School of Public Health Outline

### Introduction to Longitudinal Data Analysis

Introduction to Longitudinal Data Analysis Longitudinal Data Analysis Workshop Section 1 University of Georgia: Institute for Interdisciplinary Research in Education and Human Development Section 1: Introduction

### Lecture 4 Linear random coefficients models

Lecture 4 Linear random coefficients models Rats example 30 young rats, weights measured weekly for five weeks Dependent variable (Y ij ) is weight for rat i at week j Data: Multilevel: weights (observations)

### How do I analyse observer variation studies?

How do I analyse observer variation studies? This is based on work done for a long term project by Doug Altman and Martin Bland. I recommend that you first read our three Statistics Notes on measurement

### Homework 11. Part 1. Name: Score: / null

Name: Score: / Homework 11 Part 1 null 1 For which of the following correlations would the data points be clustered most closely around a straight line? A. r = 0.50 B. r = -0.80 C. r = 0.10 D. There is

### Power and sample size in multilevel modeling

Snijders, Tom A.B. Power and Sample Size in Multilevel Linear Models. In: B.S. Everitt and D.C. Howell (eds.), Encyclopedia of Statistics in Behavioral Science. Volume 3, 1570 1573. Chicester (etc.): Wiley,

### The 3-Level HLM Model

James H. Steiger Department of Psychology and Human Development Vanderbilt University Regression Modeling, 2009 1 2 Basic Characteristics of the 3-level Model Level-1 Model Level-2 Model Level-3 Model

### Designing Adequately Powered Cluster-Randomized Trials using Optimal Design

Designing Adequately Powered Cluster-Randomized Trials using Optimal Design Jessaca Spybrook, Western Michigan University March 4, 2010 *Joint work with Stephen Raudenbush and Andres Martinez CRT s Cluster-Randomized

### Using PROC MIXED in Hierarchical Linear Models: Examples from two- and three-level school-effect analysis, and meta-analysis research

Using PROC MIXED in Hierarchical Linear Models: Examples from two- and three-level school-effect analysis, and meta-analysis research Sawako Suzuki, DePaul University, Chicago Ching-Fan Sheu, DePaul University,

### Methods for the Analysis of Pretest-Posttest Binary Outcomes from Cluster Randomization Trials

Western University Scholarship@Western Electronic Thesis and Dissertation Repository August 2012 Methods for the Analysis of Pretest-Posttest Binary Outcomes from Cluster Randomization Trials ASM Borhan

### MS 2007-0081-RR Booil Jo. Supplemental Materials (to be posted on the Web)

MS 2007-0081-RR Booil Jo Supplemental Materials (to be posted on the Web) Table 2 Mplus Input title: Table 2 Monte Carlo simulation using externally generated data. One level CACE analysis based on eqs.

### Program Attendance in 41 Youth Smoking Cessation Programs in the U.S.

Program Attendance in 41 Youth Smoking Cessation Programs in the U.S. Zhiqun Tang, Robert Orwin, PhD, Kristie Taylor, PhD, Charles Carusi, PhD, Susan J. Curry, PhD, Sherry L. Emery, PhD, Amy K. Sporer,

### Design of Experiments and Experimental Data Processing

Design of Experiments and Experimental Data Processing Course plan October 9, 2008 Fall 2008 Prof. Ivan Kalaykov Room: T-1224, Tel. 019-303625, ivan.kalaykov@oru.se 1 Course objectives In order to discover

### Prediction for Multilevel Models

Prediction for Multilevel Models Sophia Rabe-Hesketh Graduate School of Education & Graduate Group in Biostatistics University of California, Berkeley Institute of Education, University of London Joint

### Assessing the Effectiveness of the Mass Media in Discouraging Smoking Behavior

12 Assessing the Effectiveness of the Mass Media in Discouraging Smoking Behavior Mass media have been used as a population-level strategy to reduce tobacco use for several decades. However, studies of

### Getting Started with HLM 5. For Windows

For Windows August 2012 Table of Contents Section 1: Overview... 3 1.1 About this Document... 3 1.2 Introduction to HLM... 3 1.3 Accessing HLM... 3 1.4 Getting Help with HLM... 4 Section 2: Accessing Data

### HLM software has been one of the leading statistical packages for hierarchical

Introductory Guide to HLM With HLM 7 Software 3 G. David Garson HLM software has been one of the leading statistical packages for hierarchical linear modeling due to the pioneering work of Stephen Raudenbush

### 10. Analysis of Longitudinal Studies Repeat-measures analysis

Research Methods II 99 10. Analysis of Longitudinal Studies Repeat-measures analysis This chapter builds on the concepts and methods described in Chapters 7 and 8 of Mother and Child Health: Research methods.

### Introduction to Multilevel Modeling Using HLM 6. By ATS Statistical Consulting Group

Introduction to Multilevel Modeling Using HLM 6 By ATS Statistical Consulting Group Multilevel data structure Students nested within schools Children nested within families Respondents nested within interviewers

### Longitudinal Data Analysis

Longitudinal Data Analysis Acknowledge: Professor Garrett Fitzmaurice INSTRUCTOR: Rino Bellocco Department of Statistics & Quantitative Methods University of Milano-Bicocca Department of Medical Epidemiology

### Correlation. What Is Correlation? Perfect Correlation. Perfect Correlation. Greg C Elvers

Correlation Greg C Elvers What Is Correlation? Correlation is a descriptive statistic that tells you if two variables are related to each other E.g. Is your related to how much you study? When two variables

### What s New in Econometrics? Lecture 8 Cluster and Stratified Sampling

What s New in Econometrics? Lecture 8 Cluster and Stratified Sampling Jeff Wooldridge NBER Summer Institute, 2007 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of Groups and

### A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models

A Composite Likelihood Approach to Analysis of Survey Data with Sampling Weights Incorporated under Two-Level Models Grace Y. Yi 13, JNK Rao 2 and Haocheng Li 1 1. University of Waterloo, Waterloo, Canada

### Introduction to Data Analysis in Hierarchical Linear Models

Introduction to Data Analysis in Hierarchical Linear Models April 20, 2007 Noah Shamosh & Frank Farach Social Sciences StatLab Yale University Scope & Prerequisites Strong applied emphasis Focus on HLM

### CHAPTER 6 EXAMPLES: GROWTH MODELING AND SURVIVAL ANALYSIS

Examples: Growth Modeling And Survival Analysis CHAPTER 6 EXAMPLES: GROWTH MODELING AND SURVIVAL ANALYSIS Growth models examine the development of individuals on one or more outcome variables over time.

### Models of binary outcomes with 3-level data: A comparison of some options within SAS. CAPS Methods Core Seminar April 19, 2013.

Models of binary outcomes with 3-level data: A comparison of some options within SAS CAPS Methods Core Seminar April 19, 2013 Steve Gregorich SEGregorich 1 April 19, 2013 Designs I. Cluster Randomized

### CLUSTER SAMPLE SIZE CALCULATOR USER MANUAL

1 4 9 5 CLUSTER SAMPLE SIZE CALCULATOR USER MANUAL Health Services Research Unit University of Aberdeen Polwarth Building Foresterhill ABERDEEN AB25 2ZD UK Tel: +44 (0)1224 663123 extn 53909 May 1999 1

### 12/31/2016. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Understand linear regression with a single predictor Understand how we assess the fit of a regression model Total Sum of Squares

UCL DEPARTMENT OF SECURITY AND CRIME SCIENCE Advanced time-series analysis Lisa Tompson Research Associate UCL Jill Dando Institute of Crime Science l.tompson@ucl.ac.uk Overview Fundamental principles

### CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA

Examples: Multilevel Modeling With Complex Survey Data CHAPTER 9 EXAMPLES: MULTILEVEL MODELING WITH COMPLEX SURVEY DATA Complex survey data refers to data obtained by stratification, cluster sampling and/or

### Lecture 18 Linear Regression

Lecture 18 Statistics Unit Andrew Nunekpeku / Charles Jackson Fall 2011 Outline 1 1 Situation - used to model quantitative dependent variable using linear function of quantitative predictor(s). Situation

### Elements of statistics (MATH0487-1)

Elements of statistics (MATH0487-1) Prof. Dr. Dr. K. Van Steen University of Liège, Belgium December 10, 2012 Introduction to Statistics Basic Probability Revisited Sampling Exploratory Data Analysis -

### Cluster Randomised Controlled Trials

Cluster Randomised Controlled Trials STATS 773: DESIGN AND ANALYSIS OF CLINICAL TRIALS Dr Yannan Jiang Department of Statistics May 14 th 2012, Monday, 09:00-10:30 Cluster Randomised Trial A group of individuals

### Models for Longitudinal and Clustered Data

Models for Longitudinal and Clustered Data Germán Rodríguez December 9, 2008, revised December 6, 2012 1 Introduction The most important assumption we have made in this course is that the observations

### CHAPTER 8 EXAMPLES: MIXTURE MODELING WITH LONGITUDINAL DATA

Examples: Mixture Modeling With Longitudinal Data CHAPTER 8 EXAMPLES: MIXTURE MODELING WITH LONGITUDINAL DATA Mixture modeling refers to modeling with categorical latent variables that represent subpopulations

### Simple linear regression

Simple linear regression Introduction Simple linear regression is a statistical method for obtaining a formula to predict values of one variable from another where there is a causal relationship between

### LMM: Linear Mixed Models and FEV1 Decline

LMM: Linear Mixed Models and FEV1 Decline We can use linear mixed models to assess the evidence for differences in the rate of decline for subgroups defined by covariates. S+ / R has a function lme().

### Running head: ASSUMPTIONS IN MULTIPLE REGRESSION 1. Assumptions in Multiple Regression: A Tutorial. Dianne L. Ballance ID#

Running head: ASSUMPTIONS IN MULTIPLE REGRESSION 1 Assumptions in Multiple Regression: A Tutorial Dianne L. Ballance ID#00939966 University of Calgary APSY 607 ASSUMPTIONS IN MULTIPLE REGRESSION 2 Assumptions

### Individual Growth Analysis Using PROC MIXED Maribeth Johnson, Medical College of Georgia, Augusta, GA

Paper P-702 Individual Growth Analysis Using PROC MIXED Maribeth Johnson, Medical College of Georgia, Augusta, GA ABSTRACT Individual growth models are designed for exploring longitudinal data on individuals

### STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT

STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT J. Martin Bland, Douglas G. Altman Department of Clinical Epidemiology and Social Medicine, St. George's Hospital

### Hedonism example. Our questions in the last session. Our questions in this session

Random Slope Models Hedonism example Our questions in the last session Do differences between countries in hedonism remain after controlling for individual age? How much of the variation in hedonism is

### The Basic Two-Level Regression Model

2 The Basic Two-Level Regression Model The multilevel regression model has become known in the research literature under a variety of names, such as random coefficient model (de Leeuw & Kreft, 1986; Longford,

### A brush-up on residuals

A brush-up on residuals Going back to a single level model... y i = β 0 + β 1 x 1i + ε i The residual for each observation is the difference between the value of y predicted by the equation and the actual

### Getting Correct Results from PROC REG

Getting Correct Results from PROC REG Nathaniel Derby, Statis Pro Data Analytics, Seattle, WA ABSTRACT PROC REG, SAS s implementation of linear regression, is often used to fit a line without checking

### Algebra I: Lesson 5-4 (5074) SAS Curriculum Pathways

Two-Variable Quantitative Data: Lesson Summary with Examples Bivariate data involves two quantitative variables and deals with relationships between those variables. By plotting bivariate data as ordered

### Review Jeopardy. Blue vs. Orange. Review Jeopardy

Review Jeopardy Blue vs. Orange Review Jeopardy Jeopardy Round Lectures 0-3 Jeopardy Round \$200 How could I measure how far apart (i.e. how different) two observations, y 1 and y 2, are from each other?

### Overview. Longitudinal Data Variation and Correlation Different Approaches. Linear Mixed Models Generalized Linear Mixed Models

Overview 1 Introduction Longitudinal Data Variation and Correlation Different Approaches 2 Mixed Models Linear Mixed Models Generalized Linear Mixed Models 3 Marginal Models Linear Models Generalized Linear

### Techniques of Statistical Analysis II second group

Techniques of Statistical Analysis II second group Bruno Arpino Office: 20.182; Building: Jaume I bruno.arpino@upf.edu 1. Overview The course is aimed to provide advanced statistical knowledge for the

### Business Statistics. Successful completion of Introductory and/or Intermediate Algebra courses is recommended before taking Business Statistics.

Business Course Text Bowerman, Bruce L., Richard T. O'Connell, J. B. Orris, and Dawn C. Porter. Essentials of Business, 2nd edition, McGraw-Hill/Irwin, 2008, ISBN: 978-0-07-331988-9. Required Computing

### What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers

What Is an Intracluster Correlation Coefficient? Crucial Concepts for Primary Care Researchers Shersten Killip, MD, MPH 1 Ziyad Mahfoud, PhD 2 Kevin Pearce, MD, MPH 1 1 Department of Family Practice and

### An introduction to hierarchical linear modeling

Tutorials in Quantitative Methods for Psychology 2012, Vol. 8(1), p. 52-69. An introduction to hierarchical linear modeling Heather Woltman, Andrea Feldstain, J. Christine MacKay, Meredith Rocchi University

### Partitioning of Variance in Multilevel Models. Dr William J. Browne

Partitioning of Variance in Multilevel Models Dr William J. Browne University of Nottingham with thanks to Harvey Goldstein (Institute of Education) & S.V. Subramanian (Harvard School of Public Health)

### Chapter 23. Inferences for Regression

Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily

### Statistical Analysis RSCH 665 Eagle Vision Classroom - Blended Course Syllabus

Statistical Analysis RSCH 665 Eagle Vision Classroom - Blended Course Syllabus Credit Hours: 3 Credits Academic Term: May 2016; 31 May 2016 01 August 2016 Meetings: Fri 1800-2200 Sat/Sun 0900-1400 (GMT+1)

### When to Use Which Statistical Test

When to Use Which Statistical Test Rachel Lovell, Ph.D., Senior Research Associate Begun Center for Violence Prevention Research and Education Jack, Joseph, and Morton Mandel School of Applied Social Sciences

### Analyzing Data from Nonrandomized Group Studies

Methods Report Analyzing Data from Nonrandomized Group Studies Jeremy W. Bray, William E. Schlenger, Gary A. Zarkin, and Deborah Galvin November 2008 RTI Press About the Author Jeremy W. Bray, PhD, is

### Fixed-Effect Versus Random-Effects Models

CHAPTER 13 Fixed-Effect Versus Random-Effects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval

### Analysis of Correlated Data. Patrick J. Heagerty PhD Department of Biostatistics University of Washington

Analysis of Correlated Data Patrick J Heagerty PhD Department of Biostatistics University of Washington Heagerty, 6 Course Outline Examples of longitudinal data Correlation and weighting Exploratory data

### Chapter 1. Longitudinal Data Analysis. 1.1 Introduction

Chapter 1 Longitudinal Data Analysis 1.1 Introduction One of the most common medical research designs is a pre-post study in which a single baseline health status measurement is obtained, an intervention

### Univariate Regression

Univariate Regression Correlation and Regression The regression line summarizes the linear relationship between 2 variables Correlation coefficient, r, measures strength of relationship: the closer r is

### AMS7: WEEK 8. CLASS 1. Correlation Monday May 18th, 2015

AMS7: WEEK 8. CLASS 1 Correlation Monday May 18th, 2015 Type of Data and objectives of the analysis Paired sample data (Bivariate data) Determine whether there is an association between two variables This

### The aspect of the data that we want to describe/measure is the degree of linear relationship between and The statistic r describes/measures the degree

PS 511: Advanced Statistics for Psychological and Behavioral Research 1 Both examine linear (straight line) relationships Correlation works with a pair of scores One score on each of two variables ( and

### Chapter 11: Two Variable Regression Analysis

Department of Mathematics Izmir University of Economics Week 14-15 2014-2015 In this chapter, we will focus on linear models and extend our analysis to relationships between variables, the definitions

### Elementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination

Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used

### Arbeitspapiere Working papers

Politicisation and Political Interest in Europe: A Multi-Level Approach Arbeitspapiere Working papers Jan W. van Deth Martin Elff Arbeitspapiere - Mannheimer Zentrum für Europäische Sozialforschung Nr.

### What is correlational research?

Key Ideas Purpose and use of correlational designs How correlational research developed Types of correlational designs Key characteristics of correlational designs Procedures used in correlational studies

### Teaching model: C1 a. General background: 50% b. Theory-into-practice/developmental 50% knowledge-building: c. Guided academic activities:

1. COURSE DESCRIPTION Degree: Double Degree: Derecho y Finanzas y Contabilidad (English teaching) Course: STATISTICAL AND ECONOMETRIC METHODS FOR FINANCE (Métodos Estadísticos y Econométricos en Finanzas

### Homework 8 Solutions

Math 17, Section 2 Spring 2011 Homework 8 Solutions Assignment Chapter 7: 7.36, 7.40 Chapter 8: 8.14, 8.16, 8.28, 8.36 (a-d), 8.38, 8.62 Chapter 9: 9.4, 9.14 Chapter 7 7.36] a) A scatterplot is given below.

### Course Text. Required Computing Software. Course Description. Course Objectives. StraighterLine. Business Statistics

Course Text Business Statistics Lind, Douglas A., Marchal, William A. and Samuel A. Wathen. Basic Statistics for Business and Economics, 7th edition, McGraw-Hill/Irwin, 2010, ISBN: 9780077384470 [This

### Assignments Analysis of Longitudinal data: a multilevel approach

Assignments Analysis of Longitudinal data: a multilevel approach Frans E.S. Tan Department of Methodology and Statistics University of Maastricht The Netherlands Maastricht, Jan 2007 Correspondence: Frans

### Illustration (and the use of HLM)

Illustration (and the use of HLM) Chapter 4 1 Measurement Incorporated HLM Workshop The Illustration Data Now we cover the example. In doing so we does the use of the software HLM. In addition, we will

### Experimental Designs leading to multiple regression analysis

Experimental Designs leading to multiple regression analysis 1. (Randomized) designed experiments. 2. Randomized block experiments. 3. Observational studies: probability based sample surveys 4. Observational

### A Hierarchical Linear Modeling Approach to Higher Education Instructional Costs

A Hierarchical Linear Modeling Approach to Higher Education Instructional Costs Qin Zhang and Allison Walters University of Delaware NEAIR 37 th Annual Conference November 15, 2010 Cost Factors Middaugh,

### Test Bias. As we have seen, psychological tests can be well-conceived and well-constructed, but

Test Bias As we have seen, psychological tests can be well-conceived and well-constructed, but none are perfect. The reliability of test scores can be compromised by random measurement error (unsystematic

### 2009 Mississippi Youth Tobacco Survey. Office of Health Data and Research Office of Tobacco Control Mississippi State Department of Health

9 Mississippi Youth Tobacco Survey Office of Health Data and Research Office of Tobacco Control Mississippi State Department of Health Acknowledgements... 1 Glossary... 2 Introduction... 3 Sample Design

### Geostatistics Exploratory Analysis

Instituto Superior de Estatística e Gestão de Informação Universidade Nova de Lisboa Master of Science in Geospatial Technologies Geostatistics Exploratory Analysis Carlos Alberto Felgueiras cfelgueiras@isegi.unl.pt

### Using Mplus individual residual plots for. diagnostics and model evaluation in SEM

Using Mplus individual residual plots for diagnostics and model evaluation in SEM Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 20 October 6, 2014 1 Introduction A variety of plots are available

### Chapter 15 Multiple Choice Questions (The answers are provided after the last question.)

Chapter 15 Multiple Choice Questions (The answers are provided after the last question.) 1. What is the median of the following set of scores? 18, 6, 12, 10, 14? a. 10 b. 14 c. 18 d. 12 2. Approximately

### The Comparisons. Grade Levels Comparisons. Focal PSSM K-8. Points PSSM CCSS 9-12 PSSM CCSS. Color Coding Legend. Not Identified in the Grade Band

Comparison of NCTM to Dr. Jim Bohan, Ed.D Intelligent Education, LLC Intel.educ@gmail.com The Comparisons Grade Levels Comparisons Focal K-8 Points 9-12 pre-k through 12 Instructional programs from prekindergarten

### Analyzing Intervention Effects: Multilevel & Other Approaches. Simplest Intervention Design. Better Design: Have Pretest

Analyzing Intervention Effects: Multilevel & Other Approaches Joop Hox Methodology & Statistics, Utrecht Simplest Intervention Design R X Y E Random assignment Experimental + Control group Analysis: t

### Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM. Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών

Εισαγωγή στην πολυεπίπεδη μοντελοποίηση δεδομένων με το HLM Βασίλης Παυλόπουλος Τμήμα Ψυχολογίας, Πανεπιστήμιο Αθηνών Το υλικό αυτό προέρχεται από workshop που οργανώθηκε σε θερινό σχολείο της Ευρωπαϊκής

### ICOTS6, 2002: O Connell HIERARCHICAL LINEAR MODELS FOR THE ANALYSIS OF LONGITUDINAL DATA WITH APPLICATIONS FROM HIV/AIDS PROGRAM EVALUATION

HIERARCHICAL LINEAR MODELS FOR THE ANALYSIS OF LONGITUDINAL DATA WITH APPLICATIONS FROM HIV/AIDS PROGRAM EVALUATION Ann A. O Connell University of Connecticut USA In this paper, two examples of multilevel

### ANOVA Analysis of Variance

ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,

### Systematic Reviews and Meta-analyses

Systematic Reviews and Meta-analyses Introduction A systematic review (also called an overview) attempts to summarize the scientific evidence related to treatment, causation, diagnosis, or prognosis of

### Regents Exam Questions A2.S.8: Correlation Coefficient

A2.S.8: Correlation Coefficient: Interpret within the linear regression model the value of the correlation coefficient as a measure of the strength of the relationship 1 Which statement regarding correlation

### Introducing the Multilevel Model for Change

Department of Psychology and Human Development Vanderbilt University GCM, 2010 1 Multilevel Modeling - A Brief Introduction 2 3 4 5 Introduction In this lecture, we introduce the multilevel model for change.

### Chapter 7 Factor Analysis SPSS

Chapter 7 Factor Analysis SPSS Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often

### Family economics data: total family income, expenditures, debt status for 50 families in two cohorts (A and B), annual records from 1990 1995.

Lecture 18 1. Random intercepts and slopes 2. Notation for mixed effects models 3. Comparing nested models 4. Multilevel/Hierarchical models 5. SAS versions of R models in Gelman and Hill, chapter 12 1

### Class 6: Chapter 12. Key Ideas. Explanatory Design. Correlational Designs

Class 6: Chapter 12 Correlational Designs l 1 Key Ideas Explanatory and predictor designs Characteristics of correlational research Scatterplots and calculating associations Steps in conducting a correlational

### , then the form of the model is given by: which comprises a deterministic component involving the three regression coefficients (

Multiple regression Introduction Multiple regression is a logical extension of the principles of simple linear regression to situations in which there are several predictor variables. For instance if we

### Data analysis process

Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Introduction to latent variable models

Introduction to latent variable models lecture 1 Francesco Bartolucci Department of Economics, Finance and Statistics University of Perugia, IT bart@stat.unipg.it Outline [2/24] Latent variables and their

### ANSWERS TO EXERCISES AND REVIEW QUESTIONS

ANSWERS TO EXERCISES AND REVIEW QUESTIONS PART FIVE: STATISTICAL TECHNIQUES TO COMPARE GROUPS Before attempting these questions read through the introduction to Part Five and Chapters 16-21 of the SPSS

### Statistical Rules of Thumb

Statistical Rules of Thumb Second Edition Gerald van Belle University of Washington Department of Biostatistics and Department of Environmental and Occupational Health Sciences Seattle, WA WILEY AJOHN

### Handling attrition and non-response in longitudinal data

Longitudinal and Life Course Studies 2009 Volume 1 Issue 1 Pp 63-72 Handling attrition and non-response in longitudinal data Harvey Goldstein University of Bristol Correspondence. Professor H. Goldstein

### Misconceptions, Problems, and Fallacies in Correlational Analysis

Misconceptions, Problems, and Fallacies in Correlational Analysis James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) Misconceptions,