Non-linear structural equation models: simulation studies of the Kenny-Judd model
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Stockholm
Almqvist & Wiksell Internat.
1997
|
| Series: | Uppsala Universitet: [Acta Universitatis Upsaliensis / Studia Statistica Upsaliensia]
4 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 160 S. |
| ISBN: | 9155439373 |
Staff View
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| adam_text | Contents
1 Models and Methods 1
1.1 The Kenny Judd Model 3
1.2 The Meaning of Interaction 3
1.3 Earlier Approaches 4
1.3.1 Product Term Regression Analysis 4
1.3.2 Subgroup Analysis 5
1.3.3 Two Step Techniques 5
1.3.4 Non linear Structural Equation Analysis 6
1.4 Assumptions 7
1.5 Identification 8
1.6 Estimation 11
1.6.1 Maximum Likelihood 12
1.6.2 Weighted Least Squares 13
1.6.3 WLS based on the Augmented Moment Matrix . . 14
1.7 More than One Product Variable 15
1.8 Rank Deficiency 16
1.9 Objectives 18
2 Simulation Study 19
2.1 Population 19
2.1.1 Parameter Values 20
2.1.2 Regression Equation 21
2.2 Design of Simulation Study 24
2.2.1 Models 24
2.2.2 Methods of Estimation 24
2.2.3 Sample Sizes 24
2.2.4 Number of Replicates 25
2.2.5 Generation of data 25
2.2.6 Non convergence 27
v
2.3 Treatment of Non Converged Samples 29
2.4 Outcome Variables 30
3 Maximum Likelihood Method 37
3.1 LISREL Implementation 37
3.1.1 Model 1: One Product Variable 37
3.1.2 Model 2: Four Product Variables 38
3.2 Admissibility 39
3.3 Bias 40
3.4 Mean Squared Error (MSE) 42
3.5 Empirical Standard Error 42
3.6 Distribution of Parameter Estimates 42
3.6.1 Skewness 43
3.6.2 Kurtosis 43
3.6.3 Multivariate Normality 43
3.6.4 Chi square Tests 43
3.7 Standard Errors 44
3.8 Confidence Intervals 45
3.9 Model Test 45
3.10 Conclusions for ML 46
4 Weighted Least Squares Method 63
4.1 LISREL Implementation 63
4.2 Admissibility 63
4.3 Bias 64
4.4 Mean Squared Error (MSE) 64
4.5 Empirical Standard Error 64
4.6 Distribution of Parameter Estimates 65
4.6.1 Skewness 65
4.6.2 Kurtosis 65
4.6.3 Multivariate Normality 66
4.7 Standard Errors 66
4.8 Confidence Intervals 67
4.9 Model Test 67
4.10 Conclusions for WLS 67
5 Weighted Least Squares Based on the Augmented Moment
Matrix 87
5.1 LISREL Implementation 87
5.1.1 Model 1: One Product Variable 87
vi
5.1.2 Model 2: Four Product Variables 88
5.2 Admissibility 90
5.3 Bias 91
5.4 Mean Squared Error (MSE) 91
5.5 Empirical Standard Error 91
5.6 Distribution of Parameter Estimates 92
5.6.1 Skewness 92
5.6.2 Kurtosis 92
5.6.3 Multivariate Normality 92
5.7 Standard Errors 93
5.8 Confidence Intervals 93
5.9 Model Test 94
5.10 Conclusions for WLSA 94
6 Comparisons of Models and Methods 109
6.1 Mean Squared Error (MSE) 109
6.2 Standard Errors 110
6.3 Asymptotic Standard Errors Ill
6.4 Model Test 114
6.5 Analysis of Variance 115
6.6 Discussion 118
6.6.1 Sample Size 118
6.6.2 Models 118
6.6.3 Methods 118
6.6.4 Asymptotic Normality 119
6.6.5 Limitations 120
7 An Application 131
7.1 Variables 131
7.2 Data and Model 133
7.3 Preliminary Analysis 137
7.3.1 Subgroup Analysis 137
7.3.2 Testing the Measurement Model 138
7.3.3 Factor Scores 139
7.4 Full Information Estimation 141
7.5 Results 144
7.6 Conclusion 146
References 149
vii
Appendix A: LISREL Input for Model 1, ML and WLS 153
Appendix B: LISREL Input for Model 2, ML and WLS 155
Appendix C: LISREL Input for Model 1, WLSA 157
Appendix D: LISREL Input for Model 2, WLSA 159
viii
List of Tables
2.1 Sample Sizes 24
2.2 Random Seeds Used to Generate Data 27
2.3 Percentage Converged Solutions Using LISREL Generated
Starting Values 29
2.4 Percentage Converged Solutions Using Population Starting
Values 30
2.5 Number of Matched Converged Samples 30
2.6 Frequency Distribution of Observed Variables 32
2.7 Frequency Distribution of Standardized Variables 34
3.1 Percentage of Non Admissible Parameters for Method 1 ML 47
3.2 Bias for Method 1 (ML) 48
3.3 Relative Bias in Percent for Method 1 (ML) 49
3.4 T Values for Testing Zero Bias for Method 1 (ML) 50
3.5 Test of Zero Bias for Method 1 (ML) 51
3.6 Test of Equal Mean Vectors Model 1 vs Model 2 for Method
1 (ML) 51
3.7 Mean Squared Error for Method 1 (ML) 52
3.8 Empirical Standard Errors for Method 1 (ML) 53
3.9 P Values for Test of Zero Skewness for Method 1 (ML) . . 54
3.10 P Values for Test of Zero Kurtosis for Method 1 (ML) ... 55
3.11 Z Scores for Test of Multivariate Normality for Method 1
(ML) 56
3.12 Frequency Distribution of Standardized 73 for 1 ML .... 57
3.13 Standard Error Ratios for Method 1 (ML) 58
3.14 Distribution of Standard Error Ratios of 73 for Method ML 59
3.15 Confidence Coverage for Method 1 (ML) 60
3.16 Distribution of x2 for Method 1 (ML) 61
be
4.1 Percentage of Non admissible Parameters for Mehtod 2 WLS
69
4.2 Relative Bias in Percent for Method 2 (WLS) 70
4.3 Relative Bias in Percent for Method 2 (WLS) 71
4.4 Mean Squared Error for Method 2 (WLS) 72
4.5 Mean Squared Error for Method 2 (WLS) 73
4.6 Empirical Standard Errors for Method 2 (WLS) 74
4.7 Empirical Standard Errors for Method 2 (WLS) 75
4.8 P Values for Test of Zero Skewness for Method 2 (WLS) . . 76
4.9 P Values for Test of Zero Skewness for Method 2 (WLS) . . 77
4.10 P Values for Test of Zero kurtosis for Method 2 (WLS) ... 78
4.11 P Values for Test of Zero Kurtosis for Method 2 (WLS) . . 79
4.12 Z Score for Test of Multivariate Normality for Method 2
(WLS) 79
4.13 Standard Error Ratios for Method 2 (WLS) 80
4.14 Standard Error Ratios for Method 2 (WLS) 81
4.15 Distribution of Standard Error Ratios of 73 for Method 2
WLS 82
4.16 Confidence Coverage for Method 2 (WLS) 83
4.17 Confidence Coverage for Method 2 (WLS) 84
4.18 Distribution of x2 for Method 2 (WLS) 85
5.1 Percentage of Non admissible Parameters for Method 3 WLS A 95
5.2 Bias for Method 3 (WLSA) 96
5.3 Relative Bias in Percent for Method 3 (WLSA) 97
5.4 T Values for Testing Zero Bias for Method 3 (WLSA) ... 98
5.5 Mean Squared Error for Method 3 (WLSA) 99
5.6 Empirical Standard Errors for Method 3 (WLSA) 100
5.7 P Values for Test of Zero Skewness for Method 3 (WLSA) . 101
5.8 P Values for Test of Zero Kurtosis for Method 3 (WLSA) . 102
5.9 Z Scores for Test of Multivariate Normality for Method 3
(WLSA) . 103
5.10 Standard Error Ratios for Method 3 (WLSA) 104
5.11 Distribution of Standard Error Ratios of 73 for Method 3
WLSA 105
5.12 Confidence Coverage for Method 3 (WLSA) 106
5.13 Mean and Standard Deviation of x2 for Method 3 (WLSA) 107
6.1 Mean Squared Error for Sample Size 400 122
6.2 Mean Squared Error for Sample Size 3200 123
x
6.3 Standard Error Ratios for Sample Size 400 124
6.4 Standard Error Ratios for Sample Size 3200 125
6.5 n5 Asymptotic Standard Errors 126
6.6 7i2 Empirical Standard Errors 127
6.7 Distribution of x2 128
6.8 Means and Standard Deviations of y^ 129
6.9 x2 Tests of ANOVA Hypotheses 129
6.10 Estimates of Effects 130
7.1 Means, Standard Deviations, and Correlations of Observed
Variables 136
7.2 Parameter Estimates for Measurement Model 139
7.3 Covariance Matrix of Factor Scores 140
7.4 Regression Estimates 141
7.5 Results for BEA Model with Two Product Variables .... 145
7.6 BEA Model with Four Product Variables 148
xi
List of Figures
2.1 Regression Surface 23
2.2 Histograms of y, x and x x $ 33
2.3 Histograms of Standardized y, x and x xj, 35
7.1 Path Diagram for BEA Model with Two Product Variables 135
7.2 Path Diagram for Subgroup Regression of At on VI .... 137
7.3 Path Diagram of Three Factor Model for BEA Data .... 138
xiii
|
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| spelling | Yang Jonsson, Fan Verfasser aut Non-linear structural equation models simulation studies of the Kenny-Judd model Fan Yang Jonsson Stockholm Almqvist & Wiksell Internat. 1997 XV, 160 S. txt rdacontent n rdamedia nc rdacarrier Uppsala Universitet: [Acta Universitatis Upsaliensis / Studia Statistica Upsaliensia] 4 Zugl.: Uppsala, Univ., Diss., 1997 Grootste aannemelijkheid gtt Kleinste-kwadratenmethode gtt Niet-lineaire vergelijkingen gtt Statistiek gtt Sozialwissenschaften Statistik Multivariate analysis Nonlinear theories Social sciences Statistical methods Strukturgleichungsmodell (DE-588)4252999-2 gnd rswk-swf Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd rswk-swf Simulation (DE-588)4055072-2 gnd rswk-swf Nichtlineare Gleichung (DE-588)4455337-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineare Gleichung (DE-588)4455337-7 s Simulation (DE-588)4055072-2 s DE-604 Strukturgleichungsmodell (DE-588)4252999-2 s Nichtlineares mathematisches Modell (DE-588)4127859-8 s Studia Statistica Upsaliensia] Uppsala Universitet: [Acta Universitatis Upsaliensis 4 (DE-604)BV008286146 4 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007604834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yang Jonsson, Fan Non-linear structural equation models simulation studies of the Kenny-Judd model Grootste aannemelijkheid gtt Kleinste-kwadratenmethode gtt Niet-lineaire vergelijkingen gtt Statistiek gtt Sozialwissenschaften Statistik Multivariate analysis Nonlinear theories Social sciences Statistical methods Strukturgleichungsmodell (DE-588)4252999-2 gnd Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd Simulation (DE-588)4055072-2 gnd Nichtlineare Gleichung (DE-588)4455337-7 gnd |
| subject_GND | (DE-588)4252999-2 (DE-588)4127859-8 (DE-588)4055072-2 (DE-588)4455337-7 (DE-588)4113937-9 |
| title | Non-linear structural equation models simulation studies of the Kenny-Judd model |
| title_auth | Non-linear structural equation models simulation studies of the Kenny-Judd model |
| title_exact_search | Non-linear structural equation models simulation studies of the Kenny-Judd model |
| title_full | Non-linear structural equation models simulation studies of the Kenny-Judd model Fan Yang Jonsson |
| title_fullStr | Non-linear structural equation models simulation studies of the Kenny-Judd model Fan Yang Jonsson |
| title_full_unstemmed | Non-linear structural equation models simulation studies of the Kenny-Judd model Fan Yang Jonsson |
| title_short | Non-linear structural equation models |
| title_sort | non linear structural equation models simulation studies of the kenny judd model |
| title_sub | simulation studies of the Kenny-Judd model |
| topic | Grootste aannemelijkheid gtt Kleinste-kwadratenmethode gtt Niet-lineaire vergelijkingen gtt Statistiek gtt Sozialwissenschaften Statistik Multivariate analysis Nonlinear theories Social sciences Statistical methods Strukturgleichungsmodell (DE-588)4252999-2 gnd Nichtlineares mathematisches Modell (DE-588)4127859-8 gnd Simulation (DE-588)4055072-2 gnd Nichtlineare Gleichung (DE-588)4455337-7 gnd |
| topic_facet | Grootste aannemelijkheid Kleinste-kwadratenmethode Niet-lineaire vergelijkingen Statistiek Sozialwissenschaften Statistik Multivariate analysis Nonlinear theories Social sciences Statistical methods Strukturgleichungsmodell Nichtlineares mathematisches Modell Simulation Nichtlineare Gleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007604834&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT yangjonssonfan nonlinearstructuralequationmodelssimulationstudiesofthekennyjuddmodel |