Rasch models for measurement:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Newbury Park [u.a.]
Sage Publ.
1988
|
| Edition: | 1. print. |
| Series: | Sage university papers
Ser. 7 ; 68 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 95 S. graph. Darst. |
| ISBN: | 080392741X |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Titel: Rasch models for measurement
Autor: Andrich, David
Jahr: 1988
CONTENTS
Editor s Introduction 7
1. Magnitudes and Quantities: Differences
in Degree 9
Unidimensionality 9
The Observation Framework and the Frame
of Reference 10
Discrete Observations 11
Mathematical Models 11
Deterministic Models 11
Statistical Models 11
Replications 12
Statistical Independence 12
Mean Value Estimates (MVE) 12
Maximum Likelihood (ML) Estimation 13
Example 1.1 13
Latent Variables 14
Measurement Models 15
Conclusion: Constructing a Variable 16
2. Fundamental Measurement 16
Concatenation 17
The Two-Way Frame of Reference 17
Simultaneous Conjoint Measurement 19
Invariant Comparisons 20
Example 2.1 22
Cumulative Data and Models 23
Conclusion 24
3. The Simple Logistic Model 24
The Parametric Structure 25
The Probability Function 25
The Odds Formulation 26
Estimation: Constructing Replications on a
Pair of Items 26
Statistical Independence 26
Estimation Through Odds 27
Estimation Through Probabilities 28
A Constraint on the Item Parameters 30
Maximum Likelihood Estimation 31
Check on the Model: Invariance of
the Comparison 32
Example 3.1 32
Conclusion 34
4. The General Form of the SLM and the
Guttman and Thurstone Principles for Scaling 34
The General Form of the SLM 34
The Total Score and Sufficiency 35
Relationships to Guttman Scaling 39
Relationships to Thurstone Scaling 41
Specifically Objective Comparisons 43
Conclusion 44
5. Estimation 44
Symmetry in the SLM—Asymmetry in
the Data 45
Conditional Estimation 45
Solution Algorithms and Standard Errors 47
Example Continued 48
Interpreting the Continuum 48
Joint Estimation 48
Person Parameters 51
Standard Errors 52
Example Continued 52
Pair-wise Estimation 53
Example Continued 57
Linking 57
Conclusion 61
6. Tests of Fit: Accord Between the Model
and the Data 61
Checking the Data 62
Fit Tests with Respect to the
Total Score: Check on the ICCs 63
Comparing Observed and Model Proportions
and Frequencies 63
Graphical Representation: The ICC 65
Graphical Representation: Simultaneous
Linearization 67
Likelihood Ratio Tests 67
Reproduction of the Guttman Pattern 69
Invariance of Parameter Estimates
Across Designated Classes 69
Male and Female Scale Values 70
A Comparison of a Pair of Items
Across Sexes 72
A Systematic Scale Effect Across Sexes 75
Effects of Sample Size 76
Person Fit (Profiles) 76
Studying Response Patterns 77
Response Patterns and Large Item Sets 78
Relationships to Traditional Test Theory 83
Conclusion 86
Appendices 87
Notes 89
References 91
About the Author 95
|
| adam_txt |
Titel: Rasch models for measurement
Autor: Andrich, David
Jahr: 1988
CONTENTS
Editor's Introduction 7
1. Magnitudes and Quantities: Differences
in Degree 9
Unidimensionality 9
The Observation Framework and the Frame
of Reference 10
Discrete Observations 11
Mathematical Models 11
Deterministic Models 11
Statistical Models 11
Replications 12
Statistical Independence 12
Mean Value Estimates (MVE) 12
Maximum Likelihood (ML) Estimation 13
Example 1.1 13
Latent Variables 14
Measurement Models 15
Conclusion: Constructing a Variable 16
2. Fundamental Measurement 16
Concatenation 17
The Two-Way Frame of Reference 17
Simultaneous Conjoint Measurement 19
Invariant Comparisons 20
Example 2.1 22
Cumulative Data and Models 23
Conclusion 24
3. The Simple Logistic Model 24
The Parametric Structure 25
The Probability Function 25
The Odds Formulation 26
Estimation: Constructing Replications on a
Pair of Items 26
Statistical Independence 26
Estimation Through Odds 27
Estimation Through Probabilities 28
A Constraint on the Item Parameters 30
Maximum Likelihood Estimation 31
Check on the Model: Invariance of
the Comparison 32
Example 3.1 32
Conclusion 34
4. The General Form of the SLM and the
Guttman and Thurstone Principles for Scaling 34
The General Form of the SLM 34
The Total Score and Sufficiency 35
Relationships to Guttman Scaling 39
Relationships to Thurstone Scaling 41
Specifically Objective Comparisons 43
Conclusion 44
5. Estimation 44
Symmetry in the SLM—Asymmetry in
the Data 45
Conditional Estimation 45
Solution Algorithms and Standard Errors 47
Example Continued 48
Interpreting the Continuum 48
Joint Estimation 48
Person Parameters 51
Standard Errors 52
Example Continued 52
Pair-wise Estimation 53
Example Continued 57
Linking 57
Conclusion 61
6. Tests of Fit: Accord Between the Model
and the Data 61
Checking the Data 62
Fit Tests with Respect to the
Total Score: Check on the ICCs 63
Comparing Observed and Model Proportions
and Frequencies 63
Graphical Representation: The ICC 65
Graphical Representation: Simultaneous
Linearization 67
Likelihood Ratio Tests 67
Reproduction of the Guttman Pattern 69
Invariance of Parameter Estimates
Across Designated Classes 69
Male and Female Scale Values 70
A Comparison of a Pair of Items
Across Sexes 72
A Systematic Scale Effect Across Sexes 75
Effects of Sample Size 76
Person Fit (Profiles) 76
Studying Response Patterns 77
Response Patterns and Large Item Sets 78
Relationships to Traditional Test Theory 83
Conclusion 86
Appendices 87
Notes 89
References 91
About the Author 95 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Andrich, David ca. 20. Jh |
| author_GND | (DE-588)119303418 |
| author_facet | Andrich, David ca. 20. Jh |
| author_role | aut |
| author_sort | Andrich, David ca. 20. Jh |
| author_variant | d a da |
| building | Verbundindex |
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| discipline | Soziologie Psychologie Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Wirtschaftswissenschaften |
| edition | 1. print. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T16:13:46Z |
| indexdate | 2024-07-09T20:50:07Z |
| institution | BVB |
| isbn | 080392741X |
| language | English |
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| physical | 95 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Sage Publ. |
| record_format | marc |
| series | Sage university papers |
| series2 | Sage university papers : Ser. 7 |
| spelling | Andrich, David ca. 20. Jh. Verfasser (DE-588)119303418 aut Rasch models for measurement 1. print. Newbury Park [u.a.] Sage Publ. 1988 95 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Sage university papers : Ser. 7 68 Rasch-Modell (DE-588)4176964-8 gnd rswk-swf Psychometrie (DE-588)4176236-8 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 s DE-604 Rasch-Modell (DE-588)4176964-8 s Psychometrie (DE-588)4176236-8 s 1\p DE-604 Sage university papers Ser. 7 ; 68 (DE-604)BV000005102 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015282055&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Andrich, David ca. 20. Jh Rasch models for measurement Sage university papers Rasch-Modell (DE-588)4176964-8 gnd Psychometrie (DE-588)4176236-8 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| subject_GND | (DE-588)4176964-8 (DE-588)4176236-8 (DE-588)4057633-4 |
| title | Rasch models for measurement |
| title_auth | Rasch models for measurement |
| title_exact_search | Rasch models for measurement |
| title_exact_search_txtP | Rasch models for measurement |
| title_full | Rasch models for measurement |
| title_fullStr | Rasch models for measurement |
| title_full_unstemmed | Rasch models for measurement |
| title_short | Rasch models for measurement |
| title_sort | rasch models for measurement |
| topic | Rasch-Modell (DE-588)4176964-8 gnd Psychometrie (DE-588)4176236-8 gnd Stochastisches Modell (DE-588)4057633-4 gnd |
| topic_facet | Rasch-Modell Psychometrie Stochastisches Modell |
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