Introduction to Longitudinal Data Analysis

Save this PDF as:
Size: px
Start display at page:

Transcription

1 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 to Longitudinal Data Analysis

2 Covered This Section Features of multilevel models The general class of models we will be using to investigate longitudinal data Features of longitudinal data Features of longitudinal models What can multilevel models do for you? Workshop overview Section 1: Introduction to Longitudinal Data Analysis 2

3 HIERARCHICAL/MULTILEVEL DATA STRUCTURES Section 1: Introduction to Longitudinal Data Analysis 3

4 Multilevel or Hierarchical Data Structures In the social and educational sciences there are many examples of Hierarchical Data I will use the terms Hierarchical and Multilevel synonymously Hierarchical is often used in educational sciences Multilevel is often used in the social sciences Natural question: What are Hierarchical Data? Two or more different dimensions of sampling units Unit are nested within the other units Later we will call units levels Section 1: Introduction to Longitudinal Data Analysis 4

5 Multilevel Data An educational example is when the two different units are classes and students For any given classroom We will have students Here we would say that students are nested within classroom. We could have variables at the classroom level and at the student level Section 1: Introduction to Longitudinal Data Analysis 5

6 Multilevel Data In this particular example we may be interested in Performance of each student as predicted by a set of variables such as gender, socio economic status (SES), But it also makes sense that different classroom characteristics can have an impact It could also be the case that students from the same classroom have observations that are more highly related to each other than students from different classrooms Literally: a non zero intraclass correlation In practice: these data have additional dependencies Section 1: Introduction to Longitudinal Data Analysis 6

7 Multilevel Data So we could have several different classes with different characteristics that impact the students differently Section 1: Introduction to Longitudinal Data Analysis 7

8 LONGITUDINAL DATA FROM A MULTILEVEL PERSPECTIVE Section 1: Introduction to Longitudinal Data Analysis 8

9 Longitudinal Data: A Different Type of Nesting We could have subject variables e.g., gender, job, And we could have variables about each time point e.g., energy level, stress level T1 T1 T3 T5 T2 T3 T4 T5 T1 T2 T4 T5 Section 1: Introduction to Longitudinal Data Analysis 9

10 Multilevel Data and Models Repeated measures models and longitudinal models are different types of multilevel models Trials/observations are nested with in subjects In this case the subjects may also be nested within classes We would have three levels of data Time (1), Subject (2), Class (3) Section 1: Introduction to Longitudinal Data Analysis 10

11 Data Requirements for Models Featured in Workshop We need multiple OUTCOMES from the same sampling unit 2 is the minimum (think pre/post tests), but just 2 can lead to problems: Only 1 kind of change is observable (1 difference) Can t distinguish real individual differences in change from error Repeated measures ANOVA (our baseline) is just fine for 2 observations Necessary assumption of sphericity is satisfied with only 2 observations even if compound symmetry doesn t hold More data is better (with diminishing returns) More occasions means we can get a better description of the form of change More persons means we can get better estimates of amount of individual differences in change; better prediction of those individual differences More items/stimuli means we have more power to show effects of differences between items/stimuli/conditions Section 1: Introduction to Longitudinal Data Analysis 11

12 What this Workshop is About Longitudinal data Same individual units of analysis measured at different occasions (which can range from milliseconds to decades) Repeated measures data Same individual units of analysis measured via different items, using different stimuli, or under different conditions Both of these fall under a more general category of multivariate data of varying complexity The link between them is the use of random effects to describe covariance of outcomes from the same unit Section 1: Introduction to Longitudinal Data Analysis 12

13 Types of Outcome Data Covered in this Workshop For our workshop, an outcome (dependent) variable: Has an interval scale A one unit difference means the same thing across all scale points Has scores with the same meaning over observations Includes meaning of construct Includes how items relate to the scale Implies measurement invariance We will note the following up front: FANCY STATISTICAL MODELS CANNOT SAVE BADLY MEASURED VARIABLES or BADLY DESIGNED LONGITUDINAL STUDIES Section 1: Introduction to Longitudinal Data Analysis 13

14 Levels of Analysis in Longitudinal Data Between Person (BP) Variation: Level 2 INTER individual Differences Time Invariant All longitudinal studies begin as cross sectional studies Within Person (WP) Variation: Level 1 INTRA individual Differences Time Varying Only longitudinal studies can provide this extra information Longitudinal studies allow examination of both types of relationships simultaneously (and their interactions) Any variable measured over time usually has both BP and WP variation BP = more/less than other people; WP = more/less than one s average Section 1: Introduction to Longitudinal Data Analysis 14

15 A Longitudinal Data Continuum Within Person Change: Systematic change Magnitude or direction of change can be different across individuals Growth curve models where time is meaningfully sampled Within Person Fluctuation: No systematic change Outcome just varies/fluctuates over time (e.g., emotion, stress) Time is just a way to get lots of data per individual Pure WP Change Pure WP Fluctuation Time Time Section 1: Introduction to Longitudinal Data Analysis 15

16 Options for Longitudinal Models Although models and software are logically separate, longitudinal data can be analyzed via multiple analytic frameworks: Multilevel/Mixed Models Dependency over time, persons, groups, etc. is modeled via random effects (multivariate through levels using stacked/long data) Builds on GLM, generalizes easier to additional levels of analysis Structural Equation Models Dependency over time only is modeled via latent variables (single level analysis using multivariate/wide data) Generalizes easier to broader analysis of latent constructs, mediation Because random effects and latent variables are the same thing, many longitudinal models can be specified/estimated either way And now Multilevel Structural Equation Models can do it all Section 1: Introduction to Longitudinal Data Analysis 16

17 WHAT CAN MLM DO FOR YOU? Section 1: Introduction to Longitudinal Data Analysis 17

18 What can MLM do for you? Model dependency across observations Longitudinal, clustered, and/or cross classified data? No problem! Tailor your model of sources of correlation to your data Include categorical or continuous predictors at any level Time varying, person level, group level predictors for each variance Explore reasons for dependency, don t just control for dependency Does not require same data structure for each person Unbalanced or missing data? No problem! You already know how (or you will soon)! Use SPSS Mixed, SAS Mixed, Stata, Mplus, R, HLM, MlwiN What s an intercept? What s a slope? What s a variance component? Section 1: Introduction to Longitudinal Data Analysis 18

19 1. Model Dependency Sources of dependency depend on the sources of variation created by your sampling design: residuals for outcomes from the same unit are likely to be related, which violates the general linear model independence assumption Levels for dependency = levels of random effects Sampling dimensions can be nested e.g., time within person, person within group, school within district If you can t figure out the direction of your nesting structure, odds are good you have a crossed sampling design instead e.g., persons crossed with items, raters crossed with targets To have a level, there must be random outcome variation due to sampling that remains after including the model s fixed effects e.g., treatment vs. control does not create another level of group Section 1: Introduction to Longitudinal Data Analysis 19

20 Longitudinal dependency comes from Mean differences across sampling units (e.g., persons) Creates constant dependency over time Will be represented by a random intercept in our models Individual differences in effects of predictors e.g., individual differences in growth Creates non constant dependency, the size of which depends on the value of the predictor at each occasion Will be represented by random slopes in our models Non constant within person correlation for unknown reasons (timedependent autocorrelation) Can add other patterns of correlation as needed for this Section 1: Introduction to Longitudinal Data Analysis 20

21 Why care about dependency? In other words, what happens if we have how we model dependencies wrong? Validity of the tests of the predictors depends on having the most right dependency model (right random effects in the model) Estimates will usually be ok as the come from fixed effects Standard errors (and thus p values) can be compromised The sources of variation that exist in your outcome will dictate what kinds of predictors will be useful Between Person variation needs Between Person predictors Within Person variation needs Within Person predictors Section 1: Introduction to Longitudinal Data Analysis 21

22 2. Include categorical or continuous predictors at any level of analysis ANOVA: test differences among discrete independent variable factor levels Between Groups: Gender, Intervention, Age Groups Within Subjects (Repeated Measures): Condition, Time Test main effects of continuous covariates (ANCOVA) Regression: test whether slopes relating predictors to outcomes are different from zero Persons measured once, differ categorically or continuously on a set of time invariant (person level) covariates What if a predictor is assessed repeatedly (time varying predictors) but can t be characterized by conditions? ANOVA or Regression won t work per se, so there is a need for MLM Section 1: Introduction to Longitudinal Data Analysis 22

23 2. Include categorical or continuous predictors at any level of analysis Some things don t change over measurements Sex, Ethnicity Time Invariant Predictor = Person Level Some things do change over measurements Health Status, Stress Levels, Living Arrangements Time Varying Predictor = Time Level Some predictors might be measured at higher levels Family SES, length of marriage, school size Interactions between levels may be included, too Does the effect of health status differ by gender and SES? Level: Time Person Family Section 1: Introduction to Longitudinal Data Analysis 23

24 3. Does not require same data structure per person (by accident or by design) RM ANOVA: uses multivariate (wide) data structure: ID Sex T1 T2 T3 T People missing any data are excluded (data from ID 101 are not included at all) MLM: uses stacked (long) data structure: Only rows missing data are excluded 100 uses 4 cases 101 uses 3 cases ID Sex Time Y Time can also be unbalanced across people such that each person can have his or her own measurement schedule: Time Section 1: Introduction to Longitudinal Data Analysis 24

25 4. You most likely already know how to use MLMs If you can do general linear models (ANOVA and Regression) then you can do MLM. How do you interpret an estimate for the intercept? the effect of a continuous variable? the effect of a categorical variable? a variance component (think residual variance)? Section 1: Introduction to Longitudinal Data Analysis 25

26 WORKSHOP OVERVIEW Section 1: Introduction to Longitudinal Data Analysis 26

27 Longitudinal Data Analysis: A 7 Step Program 1. Calculate nature of dependency (intraclass correlation or ICC) from an empty model 2. Decide on a metric of time to use 3. Decide on a centering point 4. Estimate a saturated means model and plot individual trajectories 5. If systematic change is present: evaluate fixed and random effects of time; otherwise evaluate alternative models for the variances 6. Consider possible alternative models for the residuals 7. (very seldom done) Evaluate remaining heterogeneity (not in workshop) Section 1: Introduction to Longitudinal Data Analysis 27

28 Computing Information We will use SAS PROC MIXED for all analyses in this workshop All examples have detailed syntax available online and in your course packet Section 1: Introduction to Longitudinal Data Analysis 28

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

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

Qualitative vs Quantitative research & Multilevel methods

Qualitative vs Quantitative research & Multilevel methods How to include context in your research April 2005 Marjolein Deunk Content What is qualitative analysis and how does it differ from quantitative

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

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

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

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 Analyses Using Linear Mixed Models in SPSS: Concepts, Procedures and Illustrations

Research Article TheScientificWorldJOURNAL (2011) 11, 42 76 TSW Child Health & Human Development ISSN 1537-744X; DOI 10.1100/tsw.2011.2 Longitudinal Data Analyses Using Linear Mixed Models in SPSS: Concepts,

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.

1/27/2013. PSY 512: Advanced Statistics for Psychological and Behavioral Research 2

PSY 512: Advanced Statistics for Psychological and Behavioral Research 2 Introduce moderated multiple regression Continuous predictor continuous predictor Continuous predictor categorical predictor Understand

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.

SAS Syntax and Output for Data Manipulation:

Psyc 944 Example 5 page 1 Practice with Fixed and Random Effects of Time in Modeling Within-Person Change The models for this example come from Hoffman (in preparation) chapter 5. We will be examining

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

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

Moderation. Moderation

Stats - Moderation Moderation A moderator is a variable that specifies conditions under which a given predictor is related to an outcome. The moderator explains when a DV and IV are related. Moderation

Linear Mixed-Effects Modeling in SPSS: An Introduction to the MIXED Procedure

Technical report Linear Mixed-Effects Modeling in SPSS: An Introduction to the MIXED Procedure Table of contents Introduction................................................................ 1 Data preparation

4. Simple regression. QBUS6840 Predictive Analytics. https://www.otexts.org/fpp/4

4. Simple regression QBUS6840 Predictive Analytics https://www.otexts.org/fpp/4 Outline The simple linear model Least squares estimation Forecasting with regression Non-linear functional forms Regression

Consider a study in which. How many subjects? The importance of sample size calculations. An insignificant effect: two possibilities.

Consider a study in which How many subjects? The importance of sample size calculations Office of Research Protections Brown Bag Series KB Boomer, Ph.D. Director, boomer@stat.psu.edu A researcher conducts

Simple Predictive Analytics Curtis Seare

Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use

A course on Longitudinal data analysis : what did we learn? COMPASS 11/03/2011

A course on Longitudinal data analysis : what did we learn? COMPASS 11/03/2011 1 Abstract We report back on methods used for the analysis of longitudinal data covered by the course We draw lessons for

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9

DEPARTMENT OF PSYCHOLOGY UNIVERSITY OF LANCASTER MSC IN PSYCHOLOGICAL RESEARCH METHODS ANALYSING AND INTERPRETING DATA 2 PART 1 WEEK 9 Analysis of covariance and multiple regression So far in this course,

Applied Multivariate Analysis

Neil H. Timm Applied Multivariate Analysis With 42 Figures Springer Contents Preface Acknowledgments List of Tables List of Figures vii ix xix xxiii 1 Introduction 1 1.1 Overview 1 1.2 Multivariate Models

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

Interactions involving Categorical Predictors

Interactions involving Categorical Predictors Today s Class: To CLASS or not to CLASS: Manual vs. program-created differences among groups Interactions of continuous and categorical predictors Interactions

Lecture 5 Three level variance component models

Lecture 5 Three level variance component models Three levels models In three levels models the clusters themselves are nested in superclusters, forming a hierarchical structure. For example, we might have

Chapter 15. Mixed Models. 15.1 Overview. A flexible approach to correlated data.

Chapter 15 Mixed Models A flexible approach to correlated data. 15.1 Overview Correlated data arise frequently in statistical analyses. This may be due to grouping of subjects, e.g., students within classrooms,

January 26, 2009 The Faculty Center for Teaching and Learning

THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i

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,

The Latent Variable Growth Model In Practice. Individual Development Over Time

The Latent Variable Growth Model In Practice 37 Individual Development Over Time y i = 1 i = 2 i = 3 t = 1 t = 2 t = 3 t = 4 ε 1 ε 2 ε 3 ε 4 y 1 y 2 y 3 y 4 x η 0 η 1 (1) y ti = η 0i + η 1i x t + ε ti

Department of Epidemiology and Public Health Miller School of Medicine University of Miami

Department of Epidemiology and Public Health Miller School of Medicine University of Miami BST 630 (3 Credit Hours) Longitudinal and Multilevel Data Wednesday-Friday 9:00 10:15PM Course Location: CRB 995

Joseph Twagilimana, University of Louisville, Louisville, KY

ST14 Comparing Time series, Generalized Linear Models and Artificial Neural Network Models for Transactional Data analysis Joseph Twagilimana, University of Louisville, Louisville, KY ABSTRACT The aim

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.

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus

Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus Tihomir Asparouhov and Bengt Muthén Mplus Web Notes: No. 15 Version 8, August 5, 2014 1 Abstract This paper discusses alternatives

SPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg

SPSS TRAINING SESSION 3 ADVANCED TOPICS (PASW STATISTICS 17.0) Sun Li Centre for Academic Computing lsun@smu.edu.sg IN SPSS SESSION 2, WE HAVE LEARNT: Elementary Data Analysis Group Comparison & One-way

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

Chapter 5 Analysis of variance SPSS Analysis of variance

Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means One-way ANOVA To test the null hypothesis that several population means are equal,

Multilevel Modeling Tutorial. Using SAS, Stata, HLM, R, SPSS, and Mplus

Using SAS, Stata, HLM, R, SPSS, and Mplus Updated: March 2015 Table of Contents Introduction... 3 Model Considerations... 3 Intraclass Correlation Coefficient... 4 Example Dataset... 4 Intercept-only Model

10. Comparing Means Using Repeated Measures ANOVA

10. Comparing Means Using Repeated Measures ANOVA Objectives Calculate repeated measures ANOVAs Calculate effect size Conduct multiple comparisons Graphically illustrate mean differences Repeated measures

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

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION

HYPOTHESIS TESTING: CONFIDENCE INTERVALS, T-TESTS, ANOVAS, AND REGRESSION HOD 2990 10 November 2010 Lecture Background This is a lightning speed summary of introductory statistical methods for senior undergraduate

A Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution

A Primer on Mathematical Statistics and Univariate Distributions; The Normal Distribution; The GLM with the Normal Distribution PSYC 943 (930): Fundamentals of Multivariate Modeling Lecture 4: September

Silvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com

SPSS-SA Silvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com SPSS-SA Training Brochure 2009 TABLE OF CONTENTS 1 SPSS TRAINING COURSES FOCUSING

MISSING DATA TECHNIQUES WITH SAS. IDRE Statistical Consulting Group

MISSING DATA TECHNIQUES WITH SAS IDRE Statistical Consulting Group ROAD MAP FOR TODAY To discuss: 1. Commonly used techniques for handling missing data, focusing on multiple imputation 2. Issues that could

Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

Introduction to Hierarchical Linear Modeling with R

Introduction to Hierarchical Linear Modeling with R 5 10 15 20 25 5 10 15 20 25 13 14 15 16 40 30 20 10 0 40 30 20 10 9 10 11 12-10 SCIENCE 0-10 5 6 7 8 40 30 20 10 0-10 40 1 2 3 4 30 20 10 0-10 5 10 15

Specifications for this HLM2 run

One way ANOVA model 1. How much do U.S. high schools vary in their mean mathematics achievement? 2. What is the reliability of each school s sample mean as an estimate of its true population mean? 3. Do

Chapter 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

Multilevel Models for Longitudinal Data. Fiona Steele

Multilevel Models for Longitudinal Data Fiona Steele Aims of Talk Overview of the application of multilevel (random effects) models in longitudinal research, with examples from social research Particular

Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

Better decision making under uncertain conditions using Monte Carlo Simulation

IBM Software Business Analytics IBM SPSS Statistics Better decision making under uncertain conditions using Monte Carlo Simulation Monte Carlo simulation and risk analysis techniques in IBM SPSS Statistics

Using SAS Proc Mixed for the Analysis of Clustered Longitudinal Data

Using SAS Proc Mixed for the Analysis of Clustered Longitudinal Data Kathy Welch Center for Statistical Consultation and Research The University of Michigan 1 Background ProcMixed can be used to fit Linear

Binary Logistic Regression

Binary Logistic Regression Main Effects Model Logistic regression will accept quantitative, binary or categorical predictors and will code the latter two in various ways. Here s a simple model including

New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Introduction

Introduction New Work Item for ISO 3534-5 Predictive Analytics (Initial Notes and Thoughts) Predictive analytics encompasses the body of statistical knowledge supporting the analysis of massive data sets.

College Readiness LINKING STUDY A Study of the Alignment of the RIT Scales of NWEA s MAP Assessments with the College Readiness Benchmarks of EXPLORE, PLAN, and ACT December 2011 (updated January 17, 2012)

Multivariate Normal Distribution

Multivariate Normal Distribution Lecture 4 July 21, 2011 Advanced Multivariate Statistical Methods ICPSR Summer Session #2 Lecture #4-7/21/2011 Slide 1 of 41 Last Time Matrices and vectors Eigenvalues

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

16 : Demand Forecasting

16 : Demand Forecasting 1 Session Outline Demand Forecasting Subjective methods can be used only when past data is not available. When past data is available, it is advisable that firms should use statistical

(and sex and drugs and rock 'n' roll) ANDY FIELD

DISCOVERING USING SPSS STATISTICS THIRD EDITION (and sex and drugs and rock 'n' roll) ANDY FIELD CONTENTS Preface How to use this book Acknowledgements Dedication Symbols used in this book Some maths revision

International Statistical Institute, 56th Session, 2007: Phil Everson

Teaching Regression using American Football Scores Everson, Phil Swarthmore College Department of Mathematics and Statistics 5 College Avenue Swarthmore, PA198, USA E-mail: peverso1@swarthmore.edu 1. Introduction

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

data visualization and regression

data visualization and regression Sepal.Length 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 I. setosa I. versicolor I. virginica I. setosa I. versicolor I. virginica Species Species

Regression Analysis: A Complete Example

Regression Analysis: A Complete Example This section works out an example that includes all the topics we have discussed so far in this chapter. A complete example of regression analysis. PhotoDisc, Inc./Getty

IBM SPSS Direct Marketing 23

IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release

IBM SPSS Direct Marketing 22

IBM SPSS Direct Marketing 22 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 22, release

Technical report. in SPSS AN INTRODUCTION TO THE MIXED PROCEDURE

Linear mixedeffects modeling in SPSS AN INTRODUCTION TO THE MIXED PROCEDURE Table of contents Introduction................................................................3 Data preparation for MIXED...................................................3

Tips for surviving the analysis of survival data. Philip Twumasi-Ankrah, PhD

Tips for surviving the analysis of survival data Philip Twumasi-Ankrah, PhD Big picture In medical research and many other areas of research, we often confront continuous, ordinal or dichotomous outcomes

SPSS Resources. 1. See website (readings) for SPSS tutorial & Stats handout

Analyzing Data SPSS Resources 1. See website (readings) for SPSS tutorial & Stats handout Don t have your own copy of SPSS? 1. Use the libraries to analyze your data 2. Download a trial version of SPSS

When to Use a Particular Statistical Test

When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the

I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN

Beckman HLM Reading Group: Questions, Answers and Examples Carolyn J. Anderson Department of Educational Psychology I L L I N O I S UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Linear Algebra Slide 1 of

Service courses for graduate students in degree programs other than the MS or PhD programs in Biostatistics.

Course Catalog In order to be assured that all prerequisites are met, students must acquire a permission number from the education coordinator prior to enrolling in any Biostatistics course. Courses are

861 Example SPLH. 5 page 1. prefer to have. New data in. SPSS Syntax FILE HANDLE. VARSTOCASESS /MAKE rt. COMPUTE mean=2. COMPUTE sal=2. END IF.

SPLH 861 Example 5 page 1 Multivariate Models for Repeated Measures Response Times in Older and Younger Adults These data were collected as part of my masters thesis, and are unpublished in this form (to

: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

Statistical Models in R

Statistical Models in R Some Examples Steven Buechler Department of Mathematics 276B Hurley Hall; 1-6233 Fall, 2007 Outline Statistical Models Structure of models in R Model Assessment (Part IA) Anova

GLM I An Introduction to Generalized Linear Models

GLM I An Introduction to Generalized Linear Models CAS Ratemaking and Product Management Seminar March 2009 Presented by: Tanya D. Havlicek, Actuarial Assistant 0 ANTITRUST Notice The Casualty Actuarial

Use of deviance statistics for comparing models

A likelihood-ratio test can be used under full ML. The use of such a test is a quite general principle for statistical testing. In hierarchical linear models, the deviance test is mostly used for multiparameter

Problem of Missing Data

VASA Mission of VA Statisticians Association (VASA) Promote & disseminate statistical methodological research relevant to VA studies; Facilitate communication & collaboration among VA-affiliated statisticians;

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

17. SIMPLE LINEAR REGRESSION II

17. SIMPLE LINEAR REGRESSION II The Model In linear regression analysis, we assume that the relationship between X and Y is linear. This does not mean, however, that Y can be perfectly predicted from X.

Overview Classes. 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7)

Overview Classes 12-3 Logistic regression (5) 19-3 Building and applying logistic regression (6) 26-3 Generalizations of logistic regression (7) 2-4 Loglinear models (8) 5-4 15-17 hrs; 5B02 Building and

BIO 226: APPLIED LONGITUDINAL ANALYSIS COURSE SYLLABUS. Spring 2015

BIO 226: APPLIED LONGITUDINAL ANALYSIS COURSE SYLLABUS Spring 2015 Instructor: Teaching Assistants: Dr. Brent Coull HSPH Building II, Room 413 Phone: (617) 432-2376 E-mail: bcoull@hsph.harvard.edu Office

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

1 Theory: The General Linear Model

QMIN GLM Theory - 1.1 1 Theory: The General Linear Model 1.1 Introduction Before digital computers, statistics textbooks spoke of three procedures regression, the analysis of variance (ANOVA), and the

IBM SPSS Direct Marketing 19

IBM SPSS Direct Marketing 19 Note: Before using this information and the product it supports, read the general information under Notices on p. 105. This document contains proprietary information of SPSS

RMTD 404 Introduction to Linear Models

RMTD 404 Introduction to Linear Models Instructor: Ken A., Assistant Professor E-mail: kfujimoto@luc.edu Phone: (312) 915-6852 Office: Lewis Towers, Room 1037 Office hour: By appointment Course Content

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

MRes Psychological Research Methods

MRes Psychological Research Methods Module list Modules may include: Advanced Experimentation and Statistics (One) Advanced Experimentation and Statistics One examines the theoretical and philosophical

Using Mixture Latent Markov Models for Analyzing Change with Longitudinal Data

Using Mixture Latent Markov Models for Analyzing Change with Longitudinal Data Jay Magidson, Ph.D. President, Statistical Innovations Inc. Belmont, MA., U.S. Presented at Modern Modeling Methods (M3) 2013,

Including the Salesperson Effect in Purchasing Behavior Models Using PROC GLIMMIX

Paper 350-2012 Including the Salesperson Effect in Purchasing Behavior Models Using PROC GLIMMIX Philippe Baecke Faculty of Economics and Business Administration, Department of Marketing, Ghent University,

Using Excel for Statistics Tips and Warnings

Using Excel for Statistics Tips and Warnings November 2000 University of Reading Statistical Services Centre Biometrics Advisory and Support Service to DFID Contents 1. Introduction 3 1.1 Data Entry and

Module 4 - Multiple Logistic Regression

Module 4 - Multiple Logistic Regression Objectives Understand the principles and theory underlying logistic regression Understand proportions, probabilities, odds, odds ratios, logits and exponents Be

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,

DISCRIMINANT FUNCTION ANALYSIS (DA)

DISCRIMINANT FUNCTION ANALYSIS (DA) John Poulsen and Aaron French Key words: assumptions, further reading, computations, standardized coefficents, structure matrix, tests of signficance Introduction Discriminant

EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION

EDUCATION AND VOCABULARY MULTIPLE REGRESSION IN ACTION EDUCATION AND VOCABULARY 5-10 hours of input weekly is enough to pick up a new language (Schiff & Myers, 1988). Dutch children spend 5.5 hours/day

Electronic Thesis and Dissertations UCLA

Electronic Thesis and Dissertations UCLA Peer Reviewed Title: A Multilevel Longitudinal Analysis of Teaching Effectiveness Across Five Years Author: Wang, Kairong Acceptance Date: 2013 Series: UCLA Electronic

" Y. Notation and Equations for Regression Lecture 11/4. Notation:

Notation: Notation and Equations for Regression Lecture 11/4 m: The number of predictor variables in a regression Xi: One of multiple predictor variables. The subscript i represents any number from 1 through

Latent Growth Curve Analysis: A Gentle Introduction. Alan C. Acock* Department of Human Development and Family Sciences. Oregon State University

Latent Growth Curves: A Gentle Introduction 1 Latent Growth Curve Analysis: A Gentle Introduction Alan C. Acock* Department of Human Development and Family Sciences Oregon State University Fuzhong Li Oregon