Statistical Power Analysis with Missing Data: A Structural Equation Modeling Approach

by Davey; Adam

• ISBN13: 9780805863703
• ISBN10: 0805863702
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 2009-08-20
• Publisher: Routledge

Summary

Statistical power analysis has revolutionized the ways in which we conduct and evaluate research. Similar developments in the statistical analysis of incomplete (missing) data are gaining more widespread applications. This volume brings statistical power and incomplete data together under a common framework, in a way that is readily accessible to those with only an introductory familiarity with structural equation modeling. It answers many practical questions such as:how missing data affects the statistical power in a study how much power is likely with different amounts and types of missing data how to increase the power of a design in the presence of missing data, and how to identify the most powerful design in the presence of missing data.Points of Reflectio n encourage readers to stop and test their understanding of the material. Try Me sections test one's ability to apply the material. Troubleshooting Tips help to prevent commonly encountered problems. Exercises reinforce content and Additional Readings provide sources for delving more deeply into selected topics. Numerous examples demonstrate the book's application to a variety of disciplines. Each issue is accompanied by its potential strengths and shortcomings and examples using a variety of software packages (SAS, SPSS, Stata, LISREL, AMOS, and MPlus). Syntax is provided using a single software program to promote continuity but in each case, parallel syntax using the other packages is presented in appendixes. Routines, data sets, syntax files, and links to student versions of software packages are found at www.psypress.com/davey. The worked examples in Part 2 also provide results from a wider set of estimated models. These tables, and accompanying syntax, can be used to estimate statistical power or required sample size for similar problems under a wide range of conditions.Class-tested at Temple, Virginia Tech, and Miami University of Ohio, this brief text is an ideal supplement for graduate courses in applied statistics, statistics II, intermediate or advanced statistics, experimental design, structural equation modeling, power analysis, and research methods taught in departments of psychology, human development, education, sociology, nursing, social work, gerontology and other social and health sciences. The book's applied approach will also appeal to researchers in these areas. Sections covering Fundamentals, Applications , and Extensions are designed to take readers from first steps to mastery.

Table of Contents

Introduction	p. 1
Overview and Aims	p. 1
Statistical Power	p. 5
Testing Hypotheses	p. 6
Choosing an Alternative Hypothesis	p. 7
Central and Noncentral Distributions	p. 7
Factors Important for Power	p. 9
Effect Sizes	p. 10
Determining an Effect Size	p. 12
Point Estimates and Confidence Intervals	p. 14
Reasons to Estimate Statistical Power	p. 17
Conclusions	p. 17
Further Readings	p. 18
Fundamentals
The LISREL Model	p. 21
Matrices and the LISREL Model	p. 22
Latent and Manifest Variables	p. 24
Regression Coefficient Matrices	p. 25
Variance-Covariance Matrices	p. 25
Vectors of Means and Intercepts	p. 26
Model Parameters	p. 27
Models and Matrices	p. 30
Structure of a LISREL Program	p. 34
Reading and Interpreting LISREL Output	p. 38
Evaluating Model Fit	p. 41
Measures of Population Discrepancy	p. 42
Incremental Fit Indices	p. 42
Absolute Fit Indices	p. 43
Conclusions	p. 43
Further Readings	p. 43
Missing Data: An Overview	p. 47
Why Worry About Missing Data?	p. 47
Types of Missing Data	p. 48
Missing Completely at Random	p. 48
Missing at Random	p. 49
Missing Not at Random	p. 49
Strategies for Dealing With Missing Data	p. 51
Complete Case Methods	p. 51
List-Wise Deletion	p. 51
List-Wise Deletion With Weighting	p. 51
Available Case Methods	p. 52
Pair-Wise Deletion	p. 52
Expectation Maximization Algorithm	p. 52
Full Information Maximum Likelihood	p. 53
Imputation Methods	p. 54
Single Imputation	p. 54
Multiple Imputation	p. 55
Estimating Structural Equation Models with Incomplete Data	p. 56
Conclusions	p. 64
Further Readings	p. 65
Estimating Statistical Power with Complete Data	p. 67
Statistical Power in Structural Equation Modeling	p. 67
Power for Testing a Single Alternative Hypothesis	p. 68
Tests of Exact, Close, and Not Close Fit	p. 72
Tests of Exact, Close, and Not Close Fit Between Two Models	p. 75
An Alternative Approach to Estimate Statistical Power	p. 76
Estimating Required Sample Size for Given Power	p. 78
Conclusions	p. 80
Further Readings	p. 80
Applications
Effects of Selection on Means, Variances, and Covariances	p. 89
Defining the Population Model	p. 90
Defining the Selection Process	p. 92
An Example of the Effects of Selection	p. 93
Selecting Data Into More Than Two Groups	p. 99
Conclusions	p. 101
Further Readings	p. 102
Testing Covariances and Mean Differences With Missing Data	p. 103
Specifying the Population Model	p. 104
Specifying the Alternative Model	p. 105
Generate Data Structure Implied by the Population Model	p. 106
Decide on the Incomplete Data Model	p. 106
Apply the Incomplete Data Model to Population Data	p. 106
Estimate Population and Alternative Models With Missing Data	p. 109
Using the Results to Estimate Power or Required Sample Size	p. 110
Conclusions	p. 117
Further Readings	p. 117
Testing Group Differences in Longitudinal Change	p. 119
The Application	p. 119
The Steps	p. 122
Selecting a Population Model	p. 123
Selecting an Alternative Model	p. 124
Generating Data According to the Population Model	p. 125
Selecting a Missing Data Model	p. 126
Applying the Missing Data Model to Population Data	p. 127
Estimating Population and Alternative Models With Incomplete Data	p. 128
Using the Results to Calculate Power or Required Sample Size	p. 136
Conclusions	p. 140
Further Readings	p. 141
Effects of Following Up via Different Patterns When Data Are Randomly or Systematically Missing	p. 143
Background	p. 143
The Model	p. 145
Design	p. 146
Procedures	p. 148
Evaluating Missing Data Patterns	p. 152
Extensions to MAR Data	p. 158
Conclusions	p. 164
Further Readings	p. 164
Using Monte Carlo Simulation Approaches to Study Statistical Power With Missing Data	p. 165
Planning and Implementing a Monte Carlo Study	p. 165
Simulating Raw Data Under a Population Model	p. 170
Generating Normally Distributed Univariate Data	p. 171
Generating Nonnormally Distributed Univariate Data	p. 172
Generating Normally Distributed Multivariate Data	p. 174
Evaluating Convergence Rates for a Given Model	p. 178
Developing a Research Question	p. 180
Creating a Valid Model	p. 180
Selecting Experimental Conditions	p. 180
Selecting Values of Population Parameters	p. 181
Selecting an Appropriate Software Package	p. 182
Conducting the Simulations	p. 182
File Storage	p. 182
Troubleshooting and Verification	p. 183
Summarizing the Results	p. 184
Complex Missing Data Patterns	p. 186
Conclusions	p. 190
Further Readings	p. 191
Extensions
Additional Issues With Missing Data in Structural Equation Models	p. 207
Effects of Missing Data on Model Fit	p. 207
Using the NCP to Estimate Power for a Given Index	p. 211
Moderators of Loss of Statistical Power With Missing Data	p. 211
Reliability	p. 211
Auxiliary Variables	p. 215
Conclusions	p. 218
Further Readings	p. 219
Summary and Conclusions	p. 231
Wrapping Up	p. 231
Future Directions	p. 232
Conclusions	p. 233
Further Readings	p. 233
References	p. 235
Appendices	p. 243
Index	p. 359
Table of Contents provided by Ingram. All Rights Reserved.