# Missing Data Dr Eleni Matechou

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 1 Statistical Methods Principles Missing Data Dr Eleni Matechou References: R.J.A. Little and D.B. Rubin 2nd edition Statistical Analysis with Missing Data J.L. Schafer and J.W. Graham 2002 Missing Data: Our View of the State of the Art

2 2 Missing data indicator matrix Usually, the data set consists of a matrix Y with n rows and p columns. A row traditionally corresponds to a case and a column to a variable i.e. y ij is the value of variable j for individual i. With real data sets, it is not uncommon for an entry to be missing. Denote by M the missing data indicator matrix with entry M ij equal to 1 if observation y ij is missing and 0 otherwise.

3 3 Missing data mechanisms Question: Are the missing values related to the underlying values of the variables in the data set? The data can be: missing completely at random (MCAR) missing at random (MAR) not missing at random (NMAR) Denote by P (M Y, θ) the distribution of M, where θ are unknown parameters.

4 MCAR If missingness does not depend on the values of the data set, observed or unobserved, then: and the data are MCAR. P (M Y, θ) = P (M θ) Example: n individuals had their blood pressure measured and a random sample of size n < n also had their weight measured.

5 MAR If missingness does not depend on the unobserved values of the data set but does depend on the observed then: and the data are MAR. P (M Y, θ) = P (M Y obs, θ) Example: n individuals had their blood pressure measured and only those individuals with high blood pressure also had their weight measured.

6 NMAR If missingness depends on the unobserved values of the data set then: and the data are NMAR. P (M Y, θ) = P (M Y miss, θ) Example: n individuals had their blood pressure measured but only overweight individuals also had their weight measured.

7 Example Suppose Y i1 is the age and Y i2 is the income of individual i. Define M i = 1 if information on income of individual i is missing and 0 otherwise. If the probability that M i = 1 is the same for all individuals MCAR. depends on Y i1 then MAR (given Y i1 is observed). depends on Y i2 then NMAR.

8 8 Before collecting the data In the design of the data collection, take care that missingness is avoided/minimized; but missingness by design is allowed. If missingness is unavoidable, then collect variables that are predictive of missingness, and of the unobserved values. This helps for the plausibility of the MAR assumption. If there are missing values, try to understand how they arose, and describe their frequency and patterns.

9 When there are missing data Part of the descriptive analysis of the data set should always be an informal investigation of the missingness patterns: how many missing values are there? how are they clustered for certain variables? are there systematic differences with respect to observed variables between cases with and without missing values? Knowing what is predictive for missingness within the available data can help understand the processes leading to missingness.

10 How to deal with the missing values? A naive approach is to delete the cases that have missing values and only analyse the complete data set. If the data are not MCAR the results can be seriously biased because the complete cases are probably not a representative sample of the population. Even if the data are MCAR, case deletion can result in a large portion of the data set to be discarded even if the proportion of missingness is not that high.

11 How to deal with the missing values? A frequently used approach is to base inference on the likelihood function for the incomplete data by treating M as a random variable and specifying the joint distribution of M and Y. Generally, closed form expressions for the maximum likelihood estimates cannot be found and iterative processes are required. The Expectation-Maximisation algorithm is usually the method of choice. If MAR holds then the missingness mechanism does not need to be explicitly modelled.

12 How to deal with the missing values? An attractive approach is to impute the missing values i.e. to fill them in, but with what? In mean substitution the missing values are replaced by the average of the observed values. In hot deck imputation the missing values of one or more variables for a nonrespondent (called the recipient) are replaced with observed values from a respondent (the donor) that is similar to the non-respondent with respect to characteristics observed by both cases. In conditional mean imputation the missing values are predicted using a model which has as a response the variable with missing values and the rest of the variables as predictors (of course using only the complete cases). In conditional distribution imputation the missing values are replaced by random draws from the conditional distribution of the variable to be imputed on the other variables.

13 13 How do these imputation methods perform? Schafer and Graham report on their simulations: Mean substitution and the hot deck produce biased estimates for many parameters under any type of missingness. Conditional mean imputation performs slightly better but still may introduce bias. Imputing from a conditional distribution is essentially unbiased under MCAR or MAR but potentially biased under NMAR

14 14 Conditional distribution imputation Adds random variability to reflect the additional uncertainty caused by the imputation. For example, if Y has a multivariate normal distribution, then for each case i we may substitute missing values by random draws from the conditional normal distribution of the missing data, given the observed data. If MAR holds, then this will be a reasonable procedure; The multivariate normality assumption is not very critical if the number of missing values is not too high.

15 Multiple imputation For a given incomplete data set, the missing data is imputed independently D times by drawing from the conditional distribution of the missing data given the observed data. This leads to D complete data sets, that differ only with respect to the imputed values. For each complete data set the desired analysis is executed; standard errors of parameters are a combination of the within-data set standard errors, and the variability of estimates between the data sets.

16 16 How are the data sets combined? Suppose the parameter of interest is a scalar γ. The estimate obtained for the parameter of interest from the d th data set is γ d and its standard error is U d. The overall estimate is simply the average over the D data sets: γ = D i=1 γ i D The uncertainty in γ is: T D = ŪD + (1 + D 1 )B D

17 17 Where ŪD is the average within imputation variance: D i=1 Ū D = U i D and B D is the between-imputations variance: B D = D i=1 ( γ i γ) 2 D 1 See MissingData.R for an example.

18 What about NMAR data? In this case the distribution of the missingness must be explicitly specified. In selection models a distribution for the complete data is specified first and then a distribution for the missingness is specified conditional on that of the complete data. In pattern-mixture models individuals are classified by their missingness and the observed data are fitted within each missing group.

19 R packages useful for inference with missing data Amelia II: Bootstrap EM imputation. cat: Missing data methods for categorical data. mi: Missing Data Imputation and Model Checking. mice: Multiple Imputation and generalized linear regression by Chained Equations. mix: Missing data methods for mixed categorical and continuous data. mlmmm: Estimation for mixed linear models with missing data. mvnmle: MLE for multivariate normal with missing data. norm: Estimation and imputation for multivariate normal data with missings. VIM: Visualization and Imputation of Missing Values. There are many more! 19

### Handling missing data in large data sets. Agostino Di Ciaccio Dept. of Statistics University of Rome La Sapienza

Handling missing data in large data sets Agostino Di Ciaccio Dept. of Statistics University of Rome La Sapienza The problem Often in official statistics we have large data sets with many variables and

### Missing Data in Longitudinal Studies: To Impute or not to Impute? Robert Platt, PhD McGill University

Missing Data in Longitudinal Studies: To Impute or not to Impute? Robert Platt, PhD McGill University 1 Outline Missing data definitions Longitudinal data specific issues Methods Simple methods Multiple

### Dealing with Missing Data

Res. Lett. Inf. Math. Sci. (2002) 3, 153-160 Available online at http://www.massey.ac.nz/~wwiims/research/letters/ Dealing with Missing Data Judi Scheffer I.I.M.S. Quad A, Massey University, P.O. Box 102904

### A REVIEW OF CURRENT SOFTWARE FOR HANDLING MISSING DATA

123 Kwantitatieve Methoden (1999), 62, 123-138. A REVIEW OF CURRENT SOFTWARE FOR HANDLING MISSING DATA Joop J. Hox 1 ABSTRACT. When we deal with a large data set with missing data, we have to undertake

### Review of the Methods for Handling Missing Data in. Longitudinal Data Analysis

Int. Journal of Math. Analysis, Vol. 5, 2011, no. 1, 1-13 Review of the Methods for Handling Missing Data in Longitudinal Data Analysis Michikazu Nakai and Weiming Ke Department of Mathematics and Statistics

### 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;

### A Basic Introduction to Missing Data

John Fox Sociology 740 Winter 2014 Outline Why Missing Data Arise Why Missing Data Arise Global or unit non-response. In a survey, certain respondents may be unreachable or may refuse to participate. Item

### Multiple Imputation for Missing Data: A Cautionary Tale

Multiple Imputation for Missing Data: A Cautionary Tale Paul D. Allison University of Pennsylvania Address correspondence to Paul D. Allison, Sociology Department, University of Pennsylvania, 3718 Locust

### Analyzing Structural Equation Models With Missing Data

Analyzing Structural Equation Models With Missing Data Craig Enders* Arizona State University cenders@asu.edu based on Enders, C. K. (006). Analyzing structural equation models with missing data. In G.

### Missing Data. A Typology Of Missing Data. Missing At Random Or Not Missing At Random

[Leeuw, Edith D. de, and Joop Hox. (2008). Missing Data. Encyclopedia of Survey Research Methods. Retrieved from http://sage-ereference.com/survey/article_n298.html] Missing Data An important indicator

### Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13

Missing Data: Part 1 What to Do? Carol B. Thompson Johns Hopkins Biostatistics Center SON Brown Bag 3/20/13 Overview Missingness and impact on statistical analysis Missing data assumptions/mechanisms Conventional

### Dealing with Missing Data

Dealing with Missing Data Roch Giorgi email: roch.giorgi@univ-amu.fr UMR 912 SESSTIM, Aix Marseille Université / INSERM / IRD, Marseille, France BioSTIC, APHM, Hôpital Timone, Marseille, France January

### Challenges in Longitudinal Data Analysis: Baseline Adjustment, Missing Data, and Drop-out

Challenges in Longitudinal Data Analysis: Baseline Adjustment, Missing Data, and Drop-out Sandra Taylor, Ph.D. IDDRC BBRD Core 23 April 2014 Objectives Baseline Adjustment Introduce approaches Guidance

### Combining Multiple Imputation and Inverse Probability Weighting

Combining Multiple Imputation and Inverse Probability Weighting Shaun Seaman 1, Ian White 1, Andrew Copas 2,3, Leah Li 4 1 MRC Biostatistics Unit, Cambridge 2 MRC Clinical Trials Unit, London 3 UCL Research

### Handling missing data in Stata a whirlwind tour

Handling missing data in Stata a whirlwind tour 2012 Italian Stata Users Group Meeting Jonathan Bartlett www.missingdata.org.uk 20th September 2012 1/55 Outline The problem of missing data and a principled

### MISSING DATA IMPUTATION IN CARDIAC DATA SET (SURVIVAL PROGNOSIS)

MISSING DATA IMPUTATION IN CARDIAC DATA SET (SURVIVAL PROGNOSIS) R.KAVITHA KUMAR Department of Computer Science and Engineering Pondicherry Engineering College, Pudhucherry, India DR. R.M.CHADRASEKAR Professor,

### Dealing with missing data: Key assumptions and methods for applied analysis

Technical Report No. 4 May 6, 2013 Dealing with missing data: Key assumptions and methods for applied analysis Marina Soley-Bori msoley@bu.edu This paper was published in fulfillment of the requirements

### Imputation and Analysis. Peter Fayers

Missing Data in Palliative Care Research Imputation and Analysis Peter Fayers Department of Public Health University of Aberdeen NTNU Det medisinske fakultet Missing data Missing data is a major problem

### Missing Data. Paul D. Allison INTRODUCTION

4 Missing Data Paul D. Allison INTRODUCTION Missing data are ubiquitous in psychological research. By missing data, I mean data that are missing for some (but not all) variables and for some (but not all)

### 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

### Missing data and net survival analysis Bernard Rachet

Workshop on Flexible Models for Longitudinal and Survival Data with Applications in Biostatistics Warwick, 27-29 July 2015 Missing data and net survival analysis Bernard Rachet General context Population-based,

### Visualization of missing values using the R-package VIM

Institut f. Statistik u. Wahrscheinlichkeitstheorie 040 Wien, Wiedner Hauptstr. 8-0/07 AUSTRIA http://www.statistik.tuwien.ac.at Visualization of missing values using the R-package VIM M. Templ and P.

### Data Cleaning and Missing Data Analysis

Data Cleaning and Missing Data Analysis Dan Merson vagabond@psu.edu India McHale imm120@psu.edu April 13, 2010 Overview Introduction to SACS What do we mean by Data Cleaning and why do we do it? The SACS

### Imputing Missing Data using SAS

ABSTRACT Paper 3295-2015 Imputing Missing Data using SAS Christopher Yim, California Polytechnic State University, San Luis Obispo Missing data is an unfortunate reality of statistics. However, there are

### Modern Methods for Missing Data

Modern Methods for Missing Data Paul D. Allison, Ph.D. Statistical Horizons LLC www.statisticalhorizons.com 1 Introduction Missing data problems are nearly universal in statistical practice. Last 25 years

### Title: Categorical Data Imputation Using Non-Parametric or Semi-Parametric Imputation Methods

Masters by Coursework and Research Report Mathematical Statistics School of Statistics and Actuarial Science Title: Categorical Data Imputation Using Non-Parametric or Semi-Parametric Imputation Methods

### Nonrandomly Missing Data in Multiple Regression Analysis: An Empirical Comparison of Ten Missing Data Treatments

Brockmeier, Kromrey, & Hogarty Nonrandomly Missing Data in Multiple Regression Analysis: An Empirical Comparison of Ten s Lantry L. Brockmeier Jeffrey D. Kromrey Kristine Y. Hogarty Florida A & M University

### Data fusion with international large scale assessments: a case study using the OECD PISA and TALIS surveys

Kaplan and McCarty Large-scale Assessments in Education 2013, 1:6 RESEARCH Open Access Data fusion with international large scale assessments: a case study using the OECD PISA and TALIS surveys David Kaplan

### An introduction to modern missing data analyses

Journal of School Psychology 48 (2010) 5 37 An introduction to modern missing data analyses Amanda N. Baraldi, Craig K. Enders Arizona State University, United States Received 19 October 2009; accepted

### Missing Data & How to Deal: An overview of missing data. Melissa Humphries Population Research Center

Missing Data & How to Deal: An overview of missing data Melissa Humphries Population Research Center Goals Discuss ways to evaluate and understand missing data Discuss common missing data methods Know

### 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

### Quantitative Methods Workshop. Graphical Methods for Investigating Missing Data

Quantitative Methods Workshop Graphical Methods for Investigating Missing Data Graeme Hutcheson School of Education University of Manchester missing data data imputation missing data Data sets with missing

### Workpackage 11 Imputation and Non-Response. Deliverable 11.2

Workpackage 11 Imputation and Non-Response Deliverable 11.2 2004 II List of contributors: Seppo Laaksonen, Statistics Finland; Ueli Oetliker, Swiss Federal Statistical Office; Susanne Rässler, University

### Item Imputation Without Specifying Scale Structure

Original Article Item Imputation Without Specifying Scale Structure Stef van Buuren TNO Quality of Life, Leiden, The Netherlands University of Utrecht, The Netherlands Abstract. Imputation of incomplete

### A Review of Missing Data Treatment Methods

A Review of Missing Data Treatment Methods Liu Peng, Lei Lei Department of Information Systems, Shanghai University of Finance and Economics, Shanghai, 200433, P.R. China ABSTRACT Missing data is a common

ALLISON 1 TABLE OF CONTENTS 1. INTRODUCTION... 3 2. ASSUMPTIONS... 6 MISSING COMPLETELY AT RANDOM (MCAR)... 6 MISSING AT RANDOM (MAR)... 7 IGNORABLE... 8 NONIGNORABLE... 8 3. CONVENTIONAL METHODS... 10

### Analysis of Longitudinal Data with Missing Values.

Analysis of Longitudinal Data with Missing Values. Methods and Applications in Medical Statistics. Ingrid Garli Dragset Master of Science in Physics and Mathematics Submission date: June 2009 Supervisor:

### Missing data are ubiquitous in clinical research.

Advanced Statistics: Missing Data in Clinical Research Part 1: An Introduction and Conceptual Framework Jason S. Haukoos, MD, MS, Craig D. Newgard, MD, MPH Abstract Missing data are commonly encountered

### 2. Making example missing-value datasets: MCAR, MAR, and MNAR

Lecture 20 1. Types of missing values 2. Making example missing-value datasets: MCAR, MAR, and MNAR 3. Common methods for missing data 4. Compare results on example MCAR, MAR, MNAR data 1 Missing Data

### Best Practices for Missing Data Management in Counseling Psychology

Journal of Counseling Psychology 2010 American Psychological Association 2010, Vol. 57, No. 1, 1 10 0022-0167/10/\$12.00 DOI: 10.1037/a0018082 Best Practices for Missing Data Management in Counseling Psychology

### Imputation of missing network data: Some simple procedures

Imputation of missing network data: Some simple procedures Mark Huisman Dept. of Psychology University of Groningen Abstract Analysis of social network data is often hampered by non-response and missing

### IBM SPSS Missing Values 22

IBM SPSS Missing Values 22 Note Before using this information and the product it supports, read the information in Notices on page 23. Product Information This edition applies to version 22, release 0,

### Introduction to mixed model and missing data issues in longitudinal studies

Introduction to mixed model and missing data issues in longitudinal studies Hélène Jacqmin-Gadda INSERM, U897, Bordeaux, France Inserm workshop, St Raphael Outline of the talk I Introduction Mixed models

### A Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values

Methods Report A Mixed Model Approach for Intent-to-Treat Analysis in Longitudinal Clinical Trials with Missing Values Hrishikesh Chakraborty and Hong Gu March 9 RTI Press About the Author Hrishikesh Chakraborty,

### CHOOSING APPROPRIATE METHODS FOR MISSING DATA IN MEDICAL RESEARCH: A DECISION ALGORITHM ON METHODS FOR MISSING DATA

CHOOSING APPROPRIATE METHODS FOR MISSING DATA IN MEDICAL RESEARCH: A DECISION ALGORITHM ON METHODS FOR MISSING DATA Hatice UENAL Institute of Epidemiology and Medical Biometry, Ulm University, Germany

### A General Approach to Variance Estimation under Imputation for Missing Survey Data

A General Approach to Variance Estimation under Imputation for Missing Survey Data J.N.K. Rao Carleton University Ottawa, Canada 1 2 1 Joint work with J.K. Kim at Iowa State University. 2 Workshop on Survey

### The treatment of missing values and its effect in the classifier accuracy

The treatment of missing values and its effect in the classifier accuracy Edgar Acuña 1 and Caroline Rodriguez 2 1 Department of Mathematics, University of Puerto Rico at Mayaguez, Mayaguez, PR 00680 edgar@cs.uprm.edu

### On Treatment of the Multivariate Missing Data

On Treatment of the Multivariate Missing Data Peter J. Foster, Ahmed M. Mami & Ali M. Bala First version: 3 September 009 Research Report No. 3, 009, Probability and Statistics Group School of Mathematics,

### Missing Data: Patterns, Mechanisms & Prevention. Edith de Leeuw

Missing Data: Patterns, Mechanisms & Prevention Edith de Leeuw Thema middag Nonresponse en Missing Data, Universiteit Groningen, 30 Maart 2006 Item-Nonresponse Pattern General pattern: various variables

### Missing Data. Katyn & Elena

Missing Data Katyn & Elena What to do with Missing Data Standard is complete case analysis/listwise dele;on ie. Delete cases with missing data so only complete cases are le> Two other popular op;ons: Mul;ple

### HANDLING DROPOUT AND WITHDRAWAL IN LONGITUDINAL CLINICAL TRIALS

HANDLING DROPOUT AND WITHDRAWAL IN LONGITUDINAL CLINICAL TRIALS Mike Kenward London School of Hygiene and Tropical Medicine Acknowledgements to James Carpenter (LSHTM) Geert Molenberghs (Universities of

### Missing data in randomized controlled trials (RCTs) can

EVALUATION TECHNICAL ASSISTANCE BRIEF for OAH & ACYF Teenage Pregnancy Prevention Grantees May 2013 Brief 3 Coping with Missing Data in Randomized Controlled Trials Missing data in randomized controlled

### Statistical Analysis with Missing Data

Statistical Analysis with Missing Data Second Edition RODERICK J. A. LITTLE DONALD B. RUBIN WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION Contents Preface PARTI OVERVIEW AND BASIC APPROACHES

### Imputing Attendance Data in a Longitudinal Multilevel Panel Data Set

Imputing Attendance Data in a Longitudinal Multilevel Panel Data Set April 2015 SHORT REPORT Baby FACES 2009 This page is left blank for double-sided printing. Imputing Attendance Data in a Longitudinal

### WHAT DO WE DO WITH MISSING DATA?SOME OPTIONS FOR ANALYSIS OF INCOMPLETE DATA

Annu. Rev. Public Health 2004. 25:99 117 doi: 10.1146/annurev.publhealth.25.102802.124410 Copyright c 2004 by Annual Reviews. All rights reserved WHAT DO WE DO WITH MISSING DATA?SOME OPTIONS FOR ANALYSIS

### PATTERN MIXTURE MODELS FOR MISSING DATA. Mike Kenward. London School of Hygiene and Tropical Medicine. Talk at the University of Turku,

PATTERN MIXTURE MODELS FOR MISSING DATA Mike Kenward London School of Hygiene and Tropical Medicine Talk at the University of Turku, April 10th 2012 1 / 90 CONTENTS 1 Examples 2 Modelling Incomplete Data

### A Review of Methods for Missing Data

Educational Research and Evaluation 1380-3611/01/0704-353\$16.00 2001, Vol. 7, No. 4, pp. 353±383 # Swets & Zeitlinger A Review of Methods for Missing Data Therese D. Pigott Loyola University Chicago, Wilmette,

### Bayesian Approaches to Handling Missing Data

Bayesian Approaches to Handling Missing Data Nicky Best and Alexina Mason BIAS Short Course, Jan 30, 2012 Lecture 1. Introduction to Missing Data Bayesian Missing Data Course (Lecture 1) Introduction to

### 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

### APPLIED MISSING DATA ANALYSIS

APPLIED MISSING DATA ANALYSIS Craig K. Enders Series Editor's Note by Todd D. little THE GUILFORD PRESS New York London Contents 1 An Introduction to Missing Data 1 1.1 Introduction 1 1.2 Chapter Overview

### 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

### ANALYSIS WITH MISSING DATA IN PREVENTION RESEARCH

10 ANALYSIS WITH MISSING DATA IN PREVENTION RESEARCH JOHN W. GRAHAM, SCOTT M. HOFER, STEWART I. DONALDSON, DAVID P. MAcKINNON, AND JOSEPH L. SCHAFER Missing data are pervasive in alcohol and drug abuse

### ARTICLE Methods for Handling Missing Data in the Behavioral Neurosciences: Don t Throw the Baby Rat out with the Bath Water

ARTICLE Methods for Handling Missing Data in the Behavioral Neurosciences: Don t Throw the Baby Rat out with the Bath Water Leah H. Rubin, 1,2 Katie Witkiewitz, 1 Justin St. Andre, 1 and Steve Reilly 1

### Missing Data in Educational Research: A Review of Reporting Practices and Suggestions for Improvement

Review of Educational Research Winter 2004, Vol. 74, No. 4, pp. 525-556 Missing Data in Educational Research: A Review of Reporting Practices and Suggestions for Improvement James L. Peugh University of

### NCEE 2009-0049. What to Do When Data Are Missing in Group Randomized Controlled Trials

NCEE 2009-0049 What to Do When Data Are Missing in Group Randomized Controlled Trials What to Do When Data Are Missing in Group Randomized Controlled Trials October 2009 Michael J. Puma Chesapeake Research

### ZHIYONG ZHANG AND LIJUAN WANG

PSYCHOMETRIKA VOL. 78, NO. 1, 154 184 JANUARY 2013 DOI: 10.1007/S11336-012-9301-5 METHODS FOR MEDIATION ANALYSIS WITH MISSING DATA ZHIYONG ZHANG AND LIJUAN WANG UNIVERSITY OF NOTRE DAME Despite wide applications

### AMELIA II: A Program for Missing Data

AMELIA II: A Program for Missing Data James Honaker, Gary King, and Matthew Blackwell Version 1.7.4 December 5, 2015 Contents 1 Introduction 3 2 What Amelia Does 3 2.1 Assumptions................................

### Longitudinal Studies, The Institute of Education, University of London. Square, London, EC1 OHB, U.K. Email: R.D.Wiggins@city.ac.

A comparative evaluation of currently available software remedies to handle missing data in the context of longitudinal design and analysis. Wiggins, R.D 1., Ely, M 2. & Lynch, K. 3 1 Department of Sociology,

### An extension of the factoring likelihood approach for non-monotone missing data

An extension of the factoring likelihood approach for non-monotone missing data Jae Kwang Kim Dong Wan Shin January 14, 2010 ABSTRACT We address the problem of parameter estimation in multivariate distributions

### In part 1 of this series, we provide a conceptual overview

Advanced Statistics: Missing Data in Clinical Research Part 2: Multiple Imputation Craig D. Newgard, MD, MPH, Jason S. Haukoos, MD, MS Abstract In part 1 of this series, the authors describe the importance

### An Analysis of Four Missing Data Treatment Methods for Supervised Learning

An Analysis of Four Missing Data Treatment Methods for Supervised Learning Gustavo E. A. P. A. Batista and Maria Carolina Monard University of São Paulo - USP Institute of Mathematics and Computer Science

### Comparison of Imputation Methods in the Survey of Income and Program Participation

Comparison of Imputation Methods in the Survey of Income and Program Participation Sarah McMillan U.S. Census Bureau, 4600 Silver Hill Rd, Washington, DC 20233 Any views expressed are those of the author

### MISSING DATA IN NON-PARAMETRIC TESTS OF CORRELATED DATA

MISSING DATA IN NON-PARAMETRIC TESTS OF CORRELATED DATA Annie Green Howard A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements

### Bayesian Multiple Imputation of Zero Inflated Count Data

Bayesian Multiple Imputation of Zero Inflated Count Data Chin-Fang Weng chin.fang.weng@census.gov U.S. Census Bureau, 4600 Silver Hill Road, Washington, D.C. 20233-1912 Abstract In government survey applications,

### Analysis of Various Techniques to Handling Missing Value in Dataset Rajnik L. Vaishnav a, Dr. K. M. Patel b a

Available online at www.ijiere.com International Journal of Innovative and Emerging Research in Engineering e-issn: 2394-3343 e-issn: 2394-5494 Analysis of Various Techniques to Handling Missing Value

### Software Cost Estimation with Incomplete Data

890 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING, VOL. 27, NO. 10, OCTOBER 2001 Software Cost Estimation with Incomplete Data Kevin Strike, Khaled El Emam, and Nazim Madhavji AbstractÐThe construction of

### Bayesian Statistics in One Hour. Patrick Lam

Bayesian Statistics in One Hour Patrick Lam Outline Introduction Bayesian Models Applications Missing Data Hierarchical Models Outline Introduction Bayesian Models Applications Missing Data Hierarchical

### arxiv:1301.2490v1 [stat.ap] 11 Jan 2013

The Annals of Applied Statistics 2012, Vol. 6, No. 4, 1814 1837 DOI: 10.1214/12-AOAS555 c Institute of Mathematical Statistics, 2012 arxiv:1301.2490v1 [stat.ap] 11 Jan 2013 ADDRESSING MISSING DATA MECHANISM

### (Howell, D.C. (2008) The analysis of missing data. In Outhwaite, W. & Turner, S. Handbook of Social Science Methodology. London: Sage.

The Treatment of Missing Data David C. Howell (Howell, D.C. (2008) The analysis of missing data. In Outhwaite, W. & Turner, S. Handbook of Social Science Methodology. London: Sage.) The treatment of missing

### Published online: 25 Sep 2014.

This article was downloaded by: [Cornell University Library] On: 23 February 2015, At: 11:23 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office:

### Missing Data in Survival Analysis and Results from the MESS Trial

Missing Data in Survival Analysis and Results from the MESS Trial J. K. Rogers J. L. Hutton K. Hemming Department of Statistics University of Warwick Research Students Conference, 2008 Outline Background

### IBM SPSS Missing Values 20

IBM SPSS Missing Values 20 Note: Before using this information and the product it supports, read the general information under Notices on p. 87. This edition applies to IBM SPSS Statistics 20 and to all

### Electronic Theses and Dissertations UC Riverside

Electronic Theses and Dissertations UC Riverside Peer Reviewed Title: Bayesian and Non-parametric Approaches to Missing Data Analysis Author: Yu, Yao Acceptance Date: 01 Series: UC Riverside Electronic

### Improved approximations for multilevel models with binary responses

Improved approximations for multilevel models with binary responses (Goldstein, H. and Rasbash, J. (1996). Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical

### Design-Based Estimators for Snowball Sampling

Design-Based Estimators for Snowball Sampling Termeh Shafie Department of Statistics, Stockholm University SE-106 91 Stockholm, Sweden Abstract Snowball sampling, where existing study subjects recruit

### Parametric fractional imputation for missing data analysis

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 Biometrika (????,??,?, pp. 1 14 C???? Biometrika Trust Printed in

### Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model

Overview of Violations of the Basic Assumptions in the Classical Normal Linear Regression Model 1 September 004 A. Introduction and assumptions The classical normal linear regression model can be written

### Call Centre Forecasting. A comprehensive analysis of missing data, extreme values, holiday influences and different forecasting methods

A comprehensive analysis of missing data, extreme values, holiday influences and different forecasting methods Master Thesis Econometrics and Operations Research Master Operations Research and Management

### HCUP Methods Series Missing Data Methods for the NIS and the SID Report # 2015-01

HCUP Methods Series Contact Information: Healthcare Cost and Utilization Project (HCUP) Agency for Healthcare Research and Quality 540 Gaither Road Rockville, MD 20850 http://www.hcup-us.ahrq.gov For Technical

### An Analysis of Missing Data Treatment Methods and Their Application to Health Care Dataset

P P P Health An Analysis of Missing Data Treatment Methods and Their Application to Health Care Dataset Peng Liu 1, Elia El-Darzi 2, Lei Lei 1, Christos Vasilakis 2, Panagiotis Chountas 2, and Wei Huang

### Analysis of Incomplete Survey Data Multiple Imputation via Bayesian Bootstrap Predictive Mean Matching

Analysis of Incomplete Survey Data Multiple Imputation via Bayesian Bootstrap Predictive Mean Matching Dissertation zur Erlangung des akademischen Grades eines Doktors der Sozial- und Wirtschaftswissenschaften

### in press, Communication Methods and Measures Effective Tool for Handling Missing Data Teresa A. Myers George Mason University

HOTDECK: An SPSS Tool for Handling Missing Data 1 in press, Communication Methods and Measures Goodbye, Listwise Deletion: Presenting Hot Deck Imputation as an Easy and Effective Tool for Handling Missing

### Sensitivity Analysis in Multiple Imputation for Missing Data

Paper SAS270-2014 Sensitivity Analysis in Multiple Imputation for Missing Data Yang Yuan, SAS Institute Inc. ABSTRACT Multiple imputation, a popular strategy for dealing with missing values, usually assumes

### Copyright 2010 The Guilford Press. Series Editor s Note

This is a chapter excerpt from Guilford Publications. Applied Missing Data Analysis, by Craig K. Enders. Copyright 2010. Series Editor s Note Missing data are a real bane to researchers across all social

### Missing Data: Our View of the State of the Art

Psychological Methods Copyright 2002 by the American Psychological Association, Inc. 2002, Vol. 7, No. 2, 147 177 1082-989X/02/\$5.00 DOI: 10.1037//1082-989X.7.2.147 Missing Data: Our View of the State

### From the help desk: Bootstrapped standard errors

The Stata Journal (2003) 3, Number 1, pp. 71 80 From the help desk: Bootstrapped standard errors Weihua Guan Stata Corporation Abstract. Bootstrapping is a nonparametric approach for evaluating the distribution

### How to choose an analysis to handle missing data in longitudinal observational studies

How to choose an analysis to handle missing data in longitudinal observational studies ICH, 25 th February 2015 Ian White MRC Biostatistics Unit, Cambridge, UK Plan Why are missing data a problem? Methods:

### Multiple Imputation of Missing Data with Genetic Algorithm based Techniques

Multiple Imputation of Missing Data with Genetic Algorithm based Techniques Dipak V. Patil Department of Computer Engineering Sandip Institute of Technology and Research Centre, Nashik, M.S., India. R.