ESTIMATING INTRACLUSTER HOMOGENEITY IN MULTISTAGE SAMPLES by Anne Fakler ...

155 Pages·2008·3 MB·English

ESTIMATING INTRACLUSTER HOMOGENEITY IN
MULTISTAGE SAMPLES
by
Anne Fakler Clemmer
Department of Biostatistics
University of North Carolina at Chapel Hill
Institute of Statistics Mimeo Series No. 1482lr
February 1985
Estimating Intracluster Homogeneity In
Multistage Samples
by
Anne Fakler Clemmer
ADissertation submitted to the faculty of the
University of North Carolina at Chapel Hill in
partial fulfillment of the requirements for
the degree of Doctor of Public Health in the
Department of Biostatistics
Chapel Hill
1985
Approved by:
ABSTRACT
CLEMMER, ANNE FAKLER, Estimating Intracluster Homogeneity In
Multistage Samples. (Under the direction of WILLIAM D. KALSBEEK.)
Multistage cluster samples are often used in social science because
clusters of households are cost effective. However, sampling elements
within the clusters are homogeneous, thus negating independence assump-
tions and increasing the variance compared to simple random sampling.
This research quantifies when each of two formulas is appropriate to
estimate rate of homogeneity (roh). Roh is a measure of how much
sampling elements are alike within clusters. It is speculated that one
formula performs better when several different domain categories are
present within each sampling cluster (cross-class domains) and the other
better when only one domain category is present per cluster (segregated
domains). As a secondary issue, this research investigates how the
relationship between the domain and analysis variables may determine the
appropriate formula for roh.
To investigate the primary issue, two-stage cluster samples were
selected from the National Medical Care Expenditure Survey (NMCES)
household file; sample values for roh were calculated using each formula
and compared with the population value from the entire file. The secon-
dary issue was explored in two steps. First, the average domain ratio
(ADR) or ratio of average rate of homogeneity across all categories in a
particular domain to roh for the population total was calculated for
each sample. The ADR was calculated using each of the two estimation
procedures and compared with the true population value. Secondly, the
~
domain degree of segregation or cross-classness in each sample was
modeled and the fit evaluated separately for each estimation procedure.
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TABLE OF CONTENTS
ACKNm~LEDGMENTS
LIST OF TABLES
LIST OF FIGURES
CHAPTER 1 - STATEMENT OF THE PROBLEM
1.1 What Is Intracluster Homogeneity And Why Is It
Important • • • • • • • • • • • • • • • • • 1
1.2 Usefulness Of Intracluster Homogeneity 3
1.2.1 Population Measures For Cluster Homogeneity:
Clusters Of Equal Sizes •••••••••• 3
1.2.2 Sample Estimate For Cluster Homogeneity:
Clusters of Equal Sizes •••••••••• 5
1.2.3 Population Measures For Cluster Homogeneity:
Clusters Of Unequal Sizes •••••••• 6
1.2.4 Sample Estimate For Cluster Homogeneity:
Clusters Of Unequal Sizes ••••••••• 11
1.2.5 Current Uses For Intracluster Homogeneity • 12
1.2.6 Range Of Values For Intracluster Homogeneity 20
1.3 Recapitulation and Specification of Objectives Of This
Research ••••.•••••...•••••.•••. 29
1.3.1 Primary Objective ••• • • • • • • • • 30
1.3.2 Secondary Objective ••• • • • • • • • • 31
1.3.3 Orientation Of Analysis Toward Veterans •••• 31
CHAPTER 2 - PLAN OF RESEARCH
2.1 Sample Selection ••••••••••••••••• 34
2.1.1 Subsample From Total To Limited Population. 35
2.1.2 Select Ten Independent Samples From Limited
Population. • • • • • • • • • • • • • • • • 38
2.2 Selection Of Domain And Analysis Variables 44
2.2.1 Determination Of Analysis Variables 45
2.2.2 Determination Of Domain Variables 46
2.3 Primary Purpose: To Determine Under What Circumstances
The Design Effect and Proportion Variation Estimation
Method Are Appropriate To Calculate The Rate Of
Homogeneity •••••••••••••••••••••• 48
2.3.1 Estimation Of Roh Using Design Effect Method •• 48
2.3.2 Estimation Of Roh Using Proportion Variation
Method • • • • • • • • • • • • • • • • 50
2.3.3 Comparison Of Methods ••••••••••••• 50
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TABLE OF CONTENTS (continued)
2.4 Secondary Purpose: To Investigate How The Relationship
Between The Analysis Variable And The Nature Of The
Domain May Determine The Appropriate Formula ••••• 54
2.4.1 Evaluate How Average Domain Ratio May Determine
Appropriate Formula For Roh •••••••••• 54
2.4.2 Investigate How The Proportion Of The Domain
Contained In AParticular Category May Affect
The Appropriate Formula •••••••••••• 57
2.5 Analyses Of Interest To Veterans . 65
CHAPTER 3 - FINDINGS
3.1 Results from Primary Objective •••••• 70
3.2 Secondary Objective Findings •••••• 87
3.2.1 Determination of Average Domain Ratio 89
3.2.2 Model Proportion of Domain Contained In a
Particular Category. • • • ••• 93
3.3 Findings of Interest to Veterans •• 96
3.4 Discussion of Results ••••• 107
CHAPTER 4 - SUMMARY OF RESULTS AND SUGGESTIONS FOR FUTURE RESEARCH
4.1 Summary of Results ••••••••• 113
4.2 Suggestions For Further Research 115
BIBLIOGRAPHY
APPENDIX A- Flowchart And Computer Software To Calculate Rate
Of Homogeneity
APPENDIX B - Show Algebraically That p* For Unequal Clusters
Reduces To For Equal Clusters
p
APPENDIX C - Summary Of Checks To Insure Computer Software To
Calculate Roh Is Accurate
APPENDIX D- Derivation Of Another Estimator For Roh, Designed
Specifically For Proportions And Assuming
Approximately Equal Samp1 ing C1 usters
APPENDIX E - Proof That Mean of Difference In Absolute Values Of
Relative Deviations Minus Its Expected Value And Divided
By Its Standard Error Follows Student's t Distribution
APPENDIX F - Proof That Proportion Variation Estimator Provides A
Consistent Estimate For Roh According To The Definition
Of Consistency In Hansen, Hurwitz, and Madow
iv
ACKNOWLEDGMENTS
I am especially indebted to my advisor, Dr. William D. Kalsbeek, for
his patient guidance, strong encouragement, and helpful suggestions at
each step of this research effort. The valuable comments and support of
the other members of my committee, Dr. Shirley A. A. Beresford, Dr.
James R. Chromy, Dr. Dennis B. Gillings, Dr. Barbara S. Hulka, and Dr.
Gary G. Koch are also gratefully acknowledged.
Many thanks are additionally due to the Veterans Administration
Medical Center in Durham, North Carolina for providing financial support
for this research project.
I also am grateful to Ruth Drum for her skillful and conscientious
typing of this manuscript.
Finally, very special thanks are due to my husband, Tom, my
children, Hew and Nikki Dalhouse, and my parents, Mr. and Mrs. Paul C.
Fakler, whose unwavering support, patience, and understanding, I have
constantly relied on.
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LIST OF TABLES
TABLE PAGE
1.1 Analysis of variance of the mean into the components
of the total variance. • • • • • • • 7
2.1 Comparison of stratum representation in total and . . .
limited population •••••••••••• 37
2.2 Comparison of response frequencies for total and
limited population •••••••••••• 39
2.3 Description of one independent replicate from limited
population •••••••••••••••••• 41
2.4 Some summary measures of intracluster homogeneity
for analysis variables in limited population •••• 45
. . . . . . .
2.5 Selected analysis variables •• 46
2.6 Four interesting average domain sample sizes 46
2.7 Selected domain variables ••• 47
2.8 Recommended domain and analysis variables to calculate
rates of homogeneity •• • • • • • • • • • • • • •• 67
2.9 Suggested domain and analysis variables to compare
differences in domain proportions. • • • • • • • 67
3.1 Comparison of sample rates of homogeneity by estimation
method and analysis variable •••••••••••• 72
3.2 Sample rates of homogeneity by estimation method and
domain variable for categorical analysis variables.. 74
3.3 Sample rates of homogeneity by estimation method and
domain variable for continuous analysis variables.. 75
3.4 Comparison of relative deviations by estimation method
and analysis variable. • • • • • • • • • • • • • • 78
3.5 Comparison of differences in absolute values of
relative deviations by domain category and analysis
variable •• • •• • • • • • • • • • • • • • •• 80
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LIST OF TABLES (continued)
3.6 Comparison of estimation methods for categorical
analysis variables •••••••••••••• 83
3.7 Comparison of estimation methods for continuous
analysis variables ••••••••••••• 85
3.8 Comparison of true average domain ratios (ADR)
for study population ••••••••••••• 88
3.9 Comparison of average domain ratios by estimation
method and analysis variable •••• • • • • • • 92
3.10 Estimates of study population degree of segregation
and model fit for Verma et al model • • • • • 93
3.11 Estimated rates of homogeneity by design effect and
proportion variation methods for urban and rural
veteran users of medical services from entire
NMCES sample •••••••••••••••• 99
3.12 Estimated rates of homogeneity by design effect and
proportion variation methods for veteran users
of medical services by region from entire NMCES
sample ••••••.•••• • • • • • • • • 101
3.13 Comparisons between veterans and nonveterans in the
total NMCES sample ••••••• 104
3.14 Comparisons between veteran users of medical services
and other veterans in the total NMCES sample •••• 106
3.15 Comparisons between urban and rural veteran users of
medical services in the total NMCES sample • •• 108
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LIST OF FIGURES
FIGURE PAGE
1.1 Indirect Imputation of Deft and S.ta.nd.ar.d.E.rro.r.V.ia. .
Roh • • • • • • • • 14
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