Latent trait and latent class models:
Saved in:
| Other Authors: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Plenum Press
1988
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000808447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 311 S. |
| ISBN: | 0306427273 |
Staff View
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| 245 | 1 | 0 | |a Latent trait and latent class models |c ed. by Rolf Langeheine ... |
| 264 | 1 | |a New York u.a. |b Plenum Press |c 1988 | |
| 300 | |a XV, 311 S. | ||
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Record in the Search Index
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| adam_text | Contents
Introduction and Overview...................................... 1
Rolf Langeheine and Jürgen Rost
1. Introduction................................................... 1
2. Common Concepts of Latent Trait and Latent Class Models . . 2
3. The Search for the Most General Model.......................... 3
4. Ordered Classes and Discrete Traits............................ 3
5. The Use of Restrictions for Extending Applicability............ 5
6. Extensions of the Basic Models................................. 6
7. Testing and Comparing the Fit of Models........................ 6
8. References..................................................... 7
PART I LATENT TRAIT THEORY
Chapter 1
Measurement Models for Ordered Response Categories.......... 11
Geofferey Norman Masters
1. Introduction............................................... 11
2. Objective Comparison....................................... 13
3. Ordered Categories......................................... 17
4. Interpreting Parameters.................................... 20
5. Related Models............................................. 23
5.1. Rating Scales.......................................... 24
5.2. Binomial Trials........................................ 25
5.3. Poisson Counts......................................... 26
5.4. Other Constraints...................................... 27
6. References............................................... 28
ix
X CONTENTS
Chapter 2
Testing a Latent Trait Model................................. 31
Arnold van den Wollenberg
1. Introduction................................................ 31
2. The Model.................................................. 32
3. Tests for Sample Independence............................... 34
3.1. The Conditional Maximum Likelihood Ratio Test......... 34
3.2. The Martin-Lof Test................................... 35
3.3. The van den Wollenberg Statistic Qx................... 35
3.4. The Fischer-Scheiblechner Statistic S................. 36
3.5. The Wright-Panchapakesan Statistic Y.................. 37
3.6. Comparison of Tests for Sample Independence............. 39
3.7. Other Procedures for Testing Sample Independence .... 40
4. Tests for Dimensionality and Local Independence............. 41
4.1. The Martin-Lof Procedure................................ 41
4.2. The Q2 Statistic........................................ 42
4.3. The Splitter Item Technique............................. 43
5. Descriptive Goodness of Fit................................. 44
5.1. The Redundancy Index.................................... 44
5.2. Graphic Representation.................................. 45
5.3. The Correlation between Parameters...................... 46
5.4. Probability Plots and Parameter Plots................... 47
5.5. Component Analysis of Standardized Q2 Residuals......... 48
6. Conclusion.................................................. 48
7. References.................................................. 49
Chapter 3
Latent Trait Models with Indicators of Mixed Measurement Level . 51
Gerhard Arminger and Ulrich Küsters
1. Introduction................................................ 51
2. Model Formulation........................................... 52
2.1. The Structural Equation System.......................... 52
2.2. Measurement Relations for Equations with Single Indicators. 52
2.3. Factor Analytic Structure and Measurement Relations for
Equations with Multiple Indicators ..................... 53
2.4. The Joint Density of Each Observation ................ 56
3. Identification Problems................................... 57
3.1. Full System Identification.............................. 57
3.2. Reduced Form Identification for Each Equation......... 57
CONTENTS xi
3.3. Identification in the Simultaneous Equation System .... 60
4. Marginal Likelihood Estimation for Each Equation.............. 60
4.1. Single Indicator Estimation............................... 60
4.2. Multiple Indicator Estimation............................. 60
5. Latent Trait Score Estimation ................................ 66
5.1. Score Estimation from Single Indicators................... 67
5.2. Score Estimation from Multiple Indicators................. 67
6. Estimation of Structural Parameters from the Reduced Form
Parameters..................................................... 68
7. Extensions.................................................... 71
8. References.................................................... 72
PART II LATENT CLASS THEORY
Chapter 4
New Developments in Latent Class Theory.................... 77
Rolf Langeheine
1. Introduction.............................................. 77
2. Unconstrained LCA......................................... 80
3. Constrained LCA........................................... 81
3.1. Goodman-Type Constraints............................ 81
3.2. LCA with Linear Constraints on the Parameters ...... 92
4. Linear Logistic LCA....................................... 93
5. Haberman’s General LCM.................................. 96
6. Analysis of Sequential Categorical Data................... 99
7. References................................................105
Chapter 5
Log-Linear Modeling, Latent Class Analysis, or Correspondence
Analysis: Which Method Should Be Used for the Analysis of
Categorical Data?............................................109
B. S. Everitt and G. Dunn
1. Introduction.................................................109
2. Methods for Analysis of Multidimensional Categorical Data . . HO
2.1. Log-Linear Modeling.......................................HO
2.2. Latent Class Analysis....................................113
xii
CONTENTS
2.3. Correspondence Analysis.................................115
3. Illustrative Comparisons of the Three Approaches ...........118
3.1. Example 1: Voting Patterns..............................118
3.2. Example 2: Suicide Data.................................121
4. Discussion..................................................124
5. References..................................................127
Chapter 6
A Latent Class Covariate Model with Applications to
Criterion-Referenced Testing...............................129
C. Mitchell Dayton and George B. Macready
1. Introduction................................................129
2. A General Concomitant-Variable Latent Class Model...........130
2.1. Notation and Model......................................130
2.2. Submodels...............................................133
2.3. Classes of Hypotheses...................................134
3. The Binomial-Mixture Covariate Model........................136
3.1. The Constrained Model...................................136
3.2. Numerical Example.......................................137
3.3. Estimation Procedures...................................138
4. Application of the Binomial-Mixture Covariate Model.........139
5. References..................................................142
PART III COMPARATIVE VIEWS OF LATENT TRAITS AND
LATENT CLASSES
Chapter 7
Test Theory with Qualitative and Quantitative Latent Variables . . 147
Jürgen Rost
1. Introduction.............................................147
2. Traits versus Classes....................................148
3. The Threshold Approach in LCA............................155
4. Three Restricted LC Models for Ordered Categories ..... 158
5. Comparing the Fit of LT and LC Models for Ordered Categories 165
6. Conclusion...............................................169
7. References...............................................170
CONTENTS
xiii
Chapter 8
Latent Class Models for Measuring ............................173
Clifford C. Clogg
1. Introduction...............................................173
2. Local Independence.........................................175
3. Unrestricted Latent Class Models...........................180
3.1. Data....................................................180
3.2. Two-Class and Three-Class Models........................181
3.3. The Two-Class Latent Structure and the Common
Factor Model............................................182
3.4. Scores Based on the Two-Class Latent Structure .......184
4. The General Response-Error Model...........................186
4.1. Scaling Models Have Ordered Latent Classes..............186
4.2. Results Obtained from Some Response-Error Models . . . 187
4.3. Scores for X and for Response Patterns ...............188
4.4. Remarks.................................................189
5. Latent-Association Models..................................190
5.1. Motivation..............................................190
5.2. The General Model—Dichotomous Items ....................191
5.3. Results.................................................192
5.4. Some Generalizations....................................194
6. Scaled Latent Class Models.................................195
6.1. Rasch’s Model—Dichotomous Items......................195
6.2. The Rasch Model Applied to the Data in Table 1........197
6.3. Some Models Related to Rasch’s Model....................198
6.4. Modified Rasch Models and Measurement...................199
6.5. Another Modification of Rasch’s Model: A Discrete
Latent Trait Model......................................199
6.6. Results.................................................200
7. Conclusion.................................................202
8. References.................................................203
Chapter 9
Comparison of Latent Structure Models.........................207
Erling B. Andersen
1. Introduction...............................................207
2. Models.....................................................208
3. Checking the Model.........................................216
4. Examples...................................................216
XIV
CONTENTS
4.1. Example 1..........................................216
4.2. Example 2..........................................223
5. References.............................................228
PART IV APPLICATION STUDIES
Chapter 10
Latent Variable Techniques for Measuring Development..........233
John R. Bergan
1. Introduction...............................................233
2. Measurement in Head Start: A Path-Referenced Approach . . 234
2.1. Overview of the Head Start Measures Program............234
2.2. Rationale for a Path-Referenced Approach...............234
2.3. Path-Referenced Assessment and Latent Variable Models . 236
3. Latent Class Models........................................236
3.1. The General Model......................................236
3.2. Model Variations.......................................237
3.3. Model Fitting..........................................237
3.4. Testing Developmental Hypotheses with Latent Class
Models.................................................238
3.5. Summary for Latent Class Models........................249
4. Latent Trait Models........................................249
4.1. Theoretical Framework..................................251
4.2. Methods of Estimation..................................253
4.3. Model Testing..........................................253
4.4. Models for Testing Developmental Hypotheses............253
4.5. Summary and Conclusions for Latent Trait Models .... 256
5. Conclusion.................................................258
6. References.................................................259
Chapter 11
Item Bias and Test Multidimensionality........................263
Frank Kok
1. Introduction...............................................263
2. Test Multidimensionality and Relevant Abilities ...........266
3. Model.................................................... 267
CONTENTS
XV
4. Discussion of the Model......................................269
5. Applications.................................................272
6. Conclusions..................................................274
7. References...................................................274
Chapter 12
On a Rasch-Model-Based Test for Noncomputerized Adaptive
Testing......................................................277
Klaus D. Kubinger
1. Introduction................................................277
2. The Adaptive Intelligence Diagnosticum (AID)................278
3. The Aimed-for Branched Testing Design.......................278
4. Item Calibration............................................279
5. The Evaluation of “SEE”.....................................284
6. The Problem of Learning.....................................286
7. The Other Subtests of AID...................................286
8. The Handling of AID.........................................288
9. Conclusions.................................................289
10. References..................................................289
Chapter 13
Systematizing the Item Content in Test Design ................ 291
Fons J. R. van de Vijver
1. Introduction.................................................291
2. Method.......................................................293
2.1. Subjects.................................................293
2.2. Tests....................................................293
3. Results and Discussion.......................................299
3.1. General..................................................299
3.2. Rasch Model..............................................299
3.3. Linear Logistic Test Model...............................301
3.4. Test of the Facet Hypotheses.............................304
4. Conclusion...................................................306
5. References...................................................307
Index.
309
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| genre | (DE-588)1071861417 Konferenzschrift 1985 Kiel gnd-content |
| genre_facet | Konferenzschrift 1985 Kiel |
| id | DE-604.BV001336995 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T07:34:36Z |
| institution | BVB |
| isbn | 0306427273 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000808447 |
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| physical | XV, 311 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Plenum Press |
| record_format | marc |
| spellingShingle | Latent trait and latent class models Analyse de structure latente Statistische methoden gtt Latent structure analysis Latent trait (DE-588)4166855-8 gnd Latent-Class-Analyse (DE-588)4166857-1 gnd |
| subject_GND | (DE-588)4166855-8 (DE-588)4166857-1 (DE-588)1071861417 |
| title | Latent trait and latent class models |
| title_auth | Latent trait and latent class models |
| title_exact_search | Latent trait and latent class models |
| title_full | Latent trait and latent class models ed. by Rolf Langeheine ... |
| title_fullStr | Latent trait and latent class models ed. by Rolf Langeheine ... |
| title_full_unstemmed | Latent trait and latent class models ed. by Rolf Langeheine ... |
| title_short | Latent trait and latent class models |
| title_sort | latent trait and latent class models |
| topic | Analyse de structure latente Statistische methoden gtt Latent structure analysis Latent trait (DE-588)4166855-8 gnd Latent-Class-Analyse (DE-588)4166857-1 gnd |
| topic_facet | Analyse de structure latente Statistische methoden Latent structure analysis Latent trait Latent-Class-Analyse Konferenzschrift 1985 Kiel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000808447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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