Introduction to psychometric theory:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Routledge
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 335 S. graph. Darst. |
| ISBN: | 9780415878227 0415878225 |
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| adam_text | IMAGE 1
CONTENTS
PREFACE XI
1. MEASUREMENT, MEASURING INSTRUMENTS, AND PSYCHOMETRIC THEORY 1 1.1
CONSTRUCTS AND THEIR IMPORTANCE IN THE BEHAVIORAL AND SOCIAL SCIENCES 1
1.2 HOW TO MEASURE A CONSTRUCT 4
1.3 WHY MEASURE CONSTRUCTS? 6
1.4 MAIN CHALLENGES WHEN MEASURING CONSTRUCTS 7
1.5 PSYCHOMETRIC THEORY AS A SCIENTIFIC DISCIPLINE 8
1.6 INITIAL STEPS IN INSTRUMENT CONSTRUCTION 10
1.7 MEASURING INSTRUMENT SCORES AS COMPOSITES 11
2. BASIC STATISTICAL CONCEPTS AND RELATIONSHIPS 13
2.1 BEHAVIORAL CHARACTERISTICS AS RANDOM VARIABLES 13
2.2 VARIABLE DISTRIBUTIONS AND PARAMETERS 15
2.2.1 MEAN AND ITEM DIFFICULTY 15
2.2.2 VARIANCE AND STANDARD DEVIATION 16
2.2.3 Z-SCORES 17
2.3 THE NORMAL DISTRIBUTION 18
2.4 VARIABLE RELATIONSHIP INDEXES 18
2.5 VARIANCES AND COVARIANCES OF LINEAR COMBINATIONS OF RANDOM VARIABLES
20 2.6 A SHORT INTRODUCTION TO MATRIX ALGEBRA 21
2.6.1 TYPES OF MATRICES 21
2.6.2 MATRIX OPERATIONS 22
2.7 PREDICTION OF INDIVIDUAL PERFORMANCE 27
2.8 A BRIEF INTRODUCTION TO THE STATISTICAL ANALYSIS SOFTWARE R 28
3. AN INTRODUCTION TO FACTOR ANALYSIS 37
3.1 WHAT IS FACTOR ANALYSIS? 37
3.2 A SIMPLIFIED START-UP EXAMPLE 38
3.3 THE TRADITIONAL FACTOR ANALYSIS MODEL 39
3.3.1 MODEL PARAMETERS 40
3.3.2 FACTOR ANALYSIS AND PRINCIPAL COMPONENT ANALYSIS 42
3.3.3 FACTOR ANALYSIS AND CONDITIONAL INDEPENDENCE 42
3.4 FACTOR LOADINGS AND OBSERVED MEASURE INTERRELATIONSHIPS 43
3.5 FACTOR ROTATION 44
3.5.1 THE IDEA OF ROTATION 45
3.5.2 TYPES OF ROTATION 46
3.5.3 SIMPLE STRUCTURE AND HOW ROTATION PROCEEDS 46
3.5.4 OBLIQUE ROTATION AS A MATTER OF ROUTINE IN BEHAVIORAL RESEARCH?
47 3.6 A USEFUL DIAGRAMMATIC NOTATION 48
3.7 COMMUNALITY AND UNIQUENESS 49
IMAGE 2
VI CONTENTS
3.8 EXPLORING THE NUMBER OF FACTORS 51
3.9 AN ILLUSTRATION OF FACTOR ANALYSIS 52
3.10 FACTOR ANALYSIS AS A MEANS OF DATA EXPLORATION 58
4. INTRODUCTION TO LATENT VARIABLE MODELING AND CONFIRMATORY FACTOR
ANALYSIS 61 4.1 A LATENT VARIABLE MODELING FRAMEWORK 61
4.2 AN INTRODUCTION TO MPLUS, AND TRADITIONAL FACTOR ANALYSIS WITH THIS
SOFTWARE 63
4.3 EXPLORATORY VERSUS CONFIRMATORY FACTOR ANALYSIS 79
4.4 CONFIRMATORY FACTOR ANALYSIS USING MPLUS 81
4.5 APPLICATION OF CONFIRMATORY FACTOR ANALYSIS IN TEST CONSTRUCTION: AN
INTRODUCTION 87
4.5.1 CONTINUOUS INSTRUMENT COMPONENTS 87
4.5.2 DISCRETE COMPONENTS 91
4.6 POINT AND INTERVAL ESTIMATION OF CLASSICAL ITEM ANALYSIS INDEXES
USING LATENT VARIABLE MODELING 98
4.6.1 ESTIMATION OF ITEM DIFFICULTY 99
4.6.1.1 USING MPLUS FOR INTERVAL ESTIMATION OF ITEM DIFFICULTY 101
4.6.1.2 EMPLOYING R FOR INTERVAL ESTIMATION OF ITEM DIFFICULTY 105 4.6.2
ESTIMATION OF INTER-ITEM AND ITEM-TOTAL INTERRELATIONSHIP INDEXES 107
4.6.2.1 USING MPLUS FOR ESTIMATION OF INTER-ITEM AND ITEM-TOTAL
CORRELATIONS 108
4.6.2.2 EMPLOYING R FOR INTERVAL ESTIMATION OF POLYCHORIC CORRELATIONS
112
APPENDIX: INITIAL ACTIVITIES FACILITATING USE OF MPLUS 113
5. CLASSICAL TEST THEORY 115
5.1 THE NATURE OF MEASUREMENT ERROR 115
5.1.1 SYSTEMATIC ERROR 115
5.1.2 RANDOM ERROR OF MEASUREMENT 116
5.2 FOUNDATIONS OF CLASSICAL TEST THEORY 117
5.2.1 THE CLASSICAL TEST THEORY EQUATION 117
5.2.2 A DEFINITION OF TRUE SCORE AND ERROR SCORE 118
5.2.3 INTERPRETATION OF THE TRUE SCORE 119
5.2.4 MISCONCEPTIONS ABOUT CLASSICAL TEST THEORY 121
5.2.5 RELATIONSHIPS BETWEEN TRUE SCORE AND ERROR SCORE 122
5.3 MODELS BASED ON CLASSICAL TEST THEORY 123
5.3.1 MODEL OF PARALLEL TESTS 124
5.3.2 MODEL OF TRUE SCORE EQUIVALENT TESTS (TAU-EQUIVALENT TESTS) 125
5.3.3 MODEL OF CONGENERIC TESTS 126
5.4 RELATIONSHIP BETWEEN FACTOR ANALYSIS AND CTT-BASED MODELS 128 5.5
TESTING AND EVALUATION OF CTT-BASED MODELS 130
5.6 EMPIRICAL ILLUSTRATION OF MODEL TESTING AND EVALUATION 132
5.6.1 SEARCHING FOR THE MOST RESTRICTIVE, TENABLE MODEL 132
5.6.2 MODEL TESTING THROUGH RESTRICTION TESTING 134
5.6.3 TESTING ERROR VARIANCE EQUALITY 135
IMAGE 3
CONTENTS VII
6. RELIABILITY 137
6.1 RELIABILITY INDEX AND RELIABILITY COEFFICIENT 137
6.1.1 DEFINITIONS AND IMPLICATIONS 137
6.1.2 RELIABILITY AND RELATIONSHIPS BETWEEN PARALLEL TESTS 139 6.2
RELIABILITY OF A COMPOSITE 140
6.2.1 THE SPEARMAN-BROWN FORMULA 140
6.2.2 COEFFICIENT ALPHA 142
6.3 RELATIONSHIPS OF COEFFICIENT ALPHA TO COMPOSITE RELIABILITY 143
6.3.1 UNCORRELATED ERRORS 143
6.3.2 CORRELATED ERRORS 144
6.4 THE STANDARD ERROR OF MEASUREMENT 144
7. PROCEDURES FOR ESTIMATING RELIABILITY 147
7.1 TRADITIONAL METHODS FOR RELIABILITY ESTIMATION 147
7.1.1 PROCEDURES WITH TWO TEST ADMINISTRATIONS 147
7.1.1.1 ALTERNATE FORM METHOD 147
7.1.1.2 TEST-RETEST METHOD 148
7.1.1.3 TEST-RETEST WITH ALTERNATE FORMS 149
7.1.2 PROCEDURES REQUIRING A SINGLE TEST ADMINISTRATION 150 7.1.2.1
SPLIT-HALF METHOD 150
7.1.2.2 METHODS BASED ON ITEM COVARIANCES 152
7.2 WHAT COEFFICIENT ALPHA IS, AND WHAT IT IS NOT 154
7.3 FACTORS AFFECTING RELIABILITY COEFFICIENTS AND THEIR ESTIMATES 156
7.3.1 GROUP HOMOGENEITY 156
7.3.2 TIME LIMIT 157
7.3.3 TEST LENGTH 158
7.4 ESTIMATING TRUE SCORES 158
7.5 FACTOR-ANALYSIS-BASED ESTIMATION OF MEASURING INSTRUMENT RELIABILITY
160 7.5.1 POINT ESTIMATION 160
7.5.2 INTERVAL ESTIMATION 161
7.6 INSTRUMENT REVISION AND DEVELOPMENT SATISFYING RELIABILITY
REQUIREMENTS 169
7.6.1 POINT AND INTERVAL ESTIMATION OF RELIABILITY FOLLOWING REVISION
169 7.6.2 LIMITATIONS OF APPROACH 175
7.7 RELIABILITY EVALUATION WITH CATEGORICAL ITEMS 176
7.8 RELIABILITY ESTIMATION FOR MEASURING INSTRUMENTS WITH GENERAL
STRUCTURE 179
7.9 OUTLOOK 181
8. VALIDITY 183
8.1 INTRODUCTION 183
8.2 TYPES OF VALIDITY 185
8.3 CONTENT VALIDITY 186
8.4 CRITERION VALIDITY 187
8.5 CONSTRUCT VALIDITY 190
8.6 CORRECTION FOR ATTENUATION 191
8.7 THE RELATIONSHIP BETWEEN RELIABILITY AND VALIDITY 192
IMAGE 4
VIII CONTENTS
8.8 ESTIMATION OF CRITERION VALIDITY AND REVISION EFFECT ON IT 194
8.8.1 ESTIMATION WITH LARGE SAMPLES 194
8.8.1.1 THE CASE OF NORMAL DATA 194
8.8.1.2 THE CASE OF NONNORMAL DATA 198
8.8.2 ESTIMATION WITH SMALL SAMPLES 198
8.8.3 ESTIMATION OF CHANGE IN CRITERION VALIDITY DUE TO INSTRUMENT
REVISION 201
8.9 EXAMINING CONSTRUCT VALIDITY USING CONFIRMATORY FACTOR ANALYSIS 206
8.9.1 EVALUATION OF CONSTRUCT CORRELATIONS 206
8.9.2 THE MULTITRAIT-MULTIMETHOD MATRIX APPROACH 212
9. GENERALIZABILITY THEORY 223
9.1 THE NATURE OF MEASUREMENT ERROR 223
9.2 A ONE-FACET CROSSED DESIGN 226
9.3 TYPES OF ERROR VARIANCES 228
9.4 GENERALIZABILITY COEFFICIENTS 229
9.5 G STUDIES AND D STUDIES 231
9.6 SOFTWARE FOR GENERALIZABILITY ANALYSIS 232
9.7 EXAMPLE OF ONE-FACET DESIGN ANALYSIS 233
9.8 TWO-FACET AND HIGHER-ORDER CROSSED DESIGNS 237
9.9 EXAMPLE TWO-FACET ANALYSIS 238
9.10 EXTENSIONS TO MULTIVARIATE MEASUREMENT DESIGNS 240
9.11 ALTERNATIVE MODELING APPROACHES TO GENERALIZABILITY THEORY ANALYSES
242 9.12 STRUCTURAL EQUATION MODELING APPLICATIONS 243
9.13 CONCLUSION 245
NOTE 246
10. INTRODUCTION TO ITEM RESPONSE THEORY 247
10.1 WHAT IS ITEM RESPONSE THEORY? 247
10.2 BASIC STATISTICAL RELATIONSHIPS FOR ITEM RESPONSE THEORY 248
10.2.1 EXPECTATION AND PROBABILITY OF CORRECT RESPONSE 248
10.2.2 WHAT IS BEING MODELED IN CONVENTIONAL REGRESSION ANALYSIS? 249
10.3 THE GENERALIZED LINEAR MODEL 250
10.3.1 RELATIONSHIP TO THE GENERAL LINEAR MODEL 250
10.3.2 THE ELEMENTS OF A GENERALIZED LINEAR MODEL 252
10.4 THE RELEVANCE OF THE GENERALIZED LINEAR MODEL FOR BEHAVIORAL AND
SOCIAL MEASUREMENT 253
10.4.1 THE LOGIT AND LOGISTIC FUNCTIONS 253
10.4.2 THE NORMAL OGIVE 256
10.4.3 EXPRESSING EVENT PROBABILITY IN TWO DISTINCT WAYS 257 10.4.4 HOW
IS THE GENERALIZED LINEAR MODEL FRAMEWORK RELEVANT IN BEHAVIORAL
MEASUREMENT AND TESTING SETTINGS? 258
10.4.5 OTHER GENERALIZED LINEAR MODELS AND WHAT UNDERLIES THE PROCESS OF
MODEL FITTING 259
10.4.6 FITTING A GENERALIZED LINEAR MODEL USING POPULAR STATISTICAL
SOFTWARE 259
10.5 THE GENERAL FACTOR ANALYSIS MODEL AND ITS RELATION TO ITEM RESPONSE
MODELS 263
10.5.1 A GENERAL FACTOR ANALYSIS MODEL 263
IMAGE 5
CONTENTS IX
10.5.2 NONLINEAR FACTOR ANALYSIS MODELS 265
10.5.2.1 A NONLINEAR FACTOR ANALYSIS MODEL BASED ON THE LOGIT LINK 265
10.5.2.2 A NONLINEAR FACTOR ANALYSIS MODEL BASED ON THE PROBIT LINK 266
10.5.3 NONLINEAR FACTOR ANALYSIS MODELS AS GENERALIZED LINEAR MODELS AND
THE GENERALIZED LATENT LINEAR MIXED MODEL 266
11. FUNDAMENTALS AND MODELS OF ITEM RESPONSE THEORY 269
11.1 LATENT TRAITS AND ITEM CHARACTERISTIC CURVES 269
11.1.1 WHAT DOES AN ITEM CHARACTERISTIC CURVE REPRESENT? 269 11.1.2 WHAT
DOES THE PROBABILITY OF CORRECT RESPONSE ACTUALLY MEAN? 271 11.1.3 WHAT
CHANGES ACROSS ITEM CHARACTERISTIC CURVES IN A GIVEN MEASURING
SITUATION? 271
11.1.4 HOW COULD AN ITEM CHARACTERISTIC CURVE BE THOUGHT TO
HAVE EMERGED ? 272
11.2 UNIDIMENSIONALITY AND LOCAL INDEPENDENCE 273
11.2.1 INDEPENDENCE OF DISCRETE RANDOM VARIABLES 273
11.2.2 WHAT DOES UNIDIMENSIONALITY MEAN IN AN IRT CONTEXT? 274 11.2.3
ANOTHER LOOK AT LOCAL INDEPENDENCE 275
11.3 THE NORMAL OGIVE AND LOGISTIC FUNCTIONS REVISITED 276
11.4 TWO POPULAR NORMAL OGIVE MODELS 277
11.4.1 THE TWO-PARAMETER NORMAL OGIVE MODEL (2PN-MODEL) 278 11.4.2 THE
SCALE OF MEASUREMENT ISSUE 280
11.4.3 THE TWO-PARAMETER NORMAL OGIVE MODEL AS A GENERALIZED LINEAR
MODEL 281
11.4.4 THE ONE-PARAMETER NORMAL OGIVE MODEL (LPN-MODEL) 281 11.4.5
TESTING ONE- AND TWO-PARAMETER NORMAL OGIVE MODELS 282 11.4.5.1 TESTING
THE TWO-PARAMETER NORMAL OGIVE MODEL 282 11.4.5.2 TESTING THE
ONE-PARAMETER NORMAL OGIVE MODEL 288
11.5 LOGISTIC MODELS 293
11.5.1 THE TWO-PARAMETER LOGISTIC MODEL (2PL-MODEL) 293 11.5.2 THE
ONE-PARAMETER AND THREE-PARAMETER LOGISTIC MODELS (1PL-AND 3PL-MODELS)
294
11.5.3 FITTING ONE- AND TWO-PARAMETER LOGISTIC MODELS 296 11.6
RELATIONSHIPS BETWEEN ITEM RESPONSE THEORY AND CLASSICAL TEST THEORY 301
NOTES 304
APPENDIX: A BRIEF INTRODUCTION TO SOME GRAPHICS APPLICATIONS OF R IN
ITEM RESPONSE MODELING 305
EPILOGUE 317
REFERENCES 319
NAME INDEX 329
SUBJECT INDEX 333
|
| any_adam_object | 1 |
| author | Raykov, Tenko Marcoulides, George A. 1955- |
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| indexdate | 2024-07-09T22:46:35Z |
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| isbn | 9780415878227 0415878225 |
| language | English |
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| spelling | Raykov, Tenko Verfasser aut Introduction to psychometric theory Tenko Raykov ; George A. Marcoulides New York [u.a.] Routledge 2011 XII, 335 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Psychometrie (DE-588)4176236-8 gnd rswk-swf Psychometrics Psychometrie (DE-588)4176236-8 s DE-604 Marcoulides, George A. 1955- Verfasser (DE-588)171190467 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020639193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Raykov, Tenko Marcoulides, George A. 1955- Introduction to psychometric theory Psychometrie (DE-588)4176236-8 gnd |
| subject_GND | (DE-588)4176236-8 |
| title | Introduction to psychometric theory |
| title_auth | Introduction to psychometric theory |
| title_exact_search | Introduction to psychometric theory |
| title_full | Introduction to psychometric theory Tenko Raykov ; George A. Marcoulides |
| title_fullStr | Introduction to psychometric theory Tenko Raykov ; George A. Marcoulides |
| title_full_unstemmed | Introduction to psychometric theory Tenko Raykov ; George A. Marcoulides |
| title_short | Introduction to psychometric theory |
| title_sort | introduction to psychometric theory |
| topic | Psychometrie (DE-588)4176236-8 gnd |
| topic_facet | Psychometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020639193&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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