Introduction To Latent GOLD [推广有奖]

Technical Guide for Latent GOLD 5.0.pdf (937.78 KB, 需要: 4 个论坛币)

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Contents

1 Introduction to Part I (BasicModels) . . . . . . . . . . . .. . . . . . . . 5

2 Components of a Latent GOLDModel  . . . . . . . . . . . . . . . . . 8

2.1 Probability Structure . . . . . . . . .. . . . . . . . . . . . . . 8

2.2 Conditional Distributions . . . . . . .. . . . . . . . . . . . . . 10

2.2.1 Nominal and ordinal dependentvariables . . . . . . . . 10

2.2.2 Continuous dependent variables . . .. . . . . . . . . . 11

2.2.3 Poisson counts . . . . . . . . . . .. . . . . . . . . . . 12

2.2.4 Binomial counts . . . . . . . . . . .. . . . . . . . . . . 13

2.3 Types of GLM-family Regression Models .. . . . . . . . . . . 15

2.4 Coding of Nominal Variables . . . . . .. . . . . . . . . . . . . 17

2.5 Known-Class Indicator . . . . . . . . .. . . . . . . . . . . . . 19

3 Latent Class Cluster Models. .. . . . . . . . . . . . . . . 20

3.1 Probability Structure and LinearPredictors . . . . . . . . . . 21

3.2 The Standard LC Model for CategoricalIndicators . . . . . . 23

3.3 Covariates . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 24

3.4 Local Dependencies . . . . . . . . . .. . . . . . . . . . . . . . 25

3.5 Finite Mixture Models for ContinuousResponse Variables . . 26

3.6 LC Cluster Models for Mixed Mode Data .. . . . . . . . . . . 28

3.7 Parameter Restrictions in Cluster Models. . . . . . . . . . . . 29

4 DFactor Models . . . . . . . .. . . . . . . . . . . . . . . . . . . . . .30

4.1 Probability Structure and LinearPredictors . . . . . . . . . . 31

4.2 A Two-DFactor Model for NominalIndicators . . . . . . . . . 32

4.3 Other Possibilities . . . . . . . . . .. . . . . . . . . . . . . . . 34

4.4 Parameter Restrictions in DFactorModels . . . . . . . . . . . 34

5 Latent Class Regression Models . . . . . . . . . . . . . . . . 35

5.1 Probability Structure and LinearPredictors . . . . . . . . . . 36

5.2 Some Special Cases . . . . . . . . . .. . . . . . . . . . . . . . 38

5.3 Restrictions for the Class-SpecificRegression Coefficients . . . 39

6 Step-Three Analysis andScoring  . . . . . . . . . . . . . . .44

6.1 Bias-Adjusted Step-Three Analysis . . .. . . . . . . . . . . . 44

6.2 Obtaining the Score Equation . . . . .. . . . . . . . . . . . . 47

6.3 Estimation of Step-Three Models and theScoring Equation . . 48

7 Estimation and Other TechnicalIssues . . . . . . . . . . . . . . . 49

7.1 Log-likelihood and Log-posteriorFunction . . . . . . . . . . . 49

7.2 Missing Data . . . . . . . . . . . . .. . . . . . . . . . . . . . 51

7.2.1 Indicators and dependent variable . .. . . . . . . . . . 51

7.2.2 Covariates and predictors . . . . . .. . . . . . . . . . 52

7.2.3 Summary of the Missing Value Settings. . . . . . . . . 53

7.3 Prior Distributions . . . . . . . . . .. . . . . . . . . . . . . . 54

7.4 Algorithms . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 56

7.5 Convergence . . . . . . . . . . . . . .. . . . . . . . . . . . . . 59

7.6 Parallel Processing . . . . . . . . . .. . . . . . . . . . . . . . 60

7.7 Start Values . . . . . . . . . . . . .. . . . . . . . . . . . . . . 60

7.8 Bootstrapping the P Value for Chi2Statistics or -2LL Difference 62

7.9 Identification Issues . . . . . . . . .. . . . . . . . . . . . . . . 63

7.10 Selecting and Holding out Cases orReplications . . . . . . . . 64

7.10.1 Selecting Cases or Replications . .. . . . . . . . . . . 64

7.10.2 Holding out Replications . . . . . .. . . . . . . . . . . 64

7.10.3 Holding out Cases . . . . . . . . .. . . . . . . . . . . 64

8 Latent GOLD’s Output . . . . .. . . . . . . . . . . . . .65

8.1 Model Summary . . . . . . . . . . . . .. . . . . . . . . . . . 65

8.1.1 Chi-squared statistics . . . . . . .. . . . . . . . . . . . 66

8.1.2 Log-likelihood statistics . . . . . .. . . . . . . . . . . 69

8.1.3 Classification statistics . . . . . .. . . . . . . . . . . . 69

8.1.4 Model classification statistics . . .. . . . . . . . . . . 73

8.1.5 Prediction statistics . . . . . . . .. . . . . . . . . . . . 73

8.2 Parameters . . . . . . . . . . . . . .. . . . . . . . . . . . . . 76

8.3 Profile . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 77

8.4 ProbMeans . . . . . . . . . . . . . . .. . . . . . . . . . . . . 80

8.5 Frequencies / Residuals . . . . . . . .. . . . . . . . . . . . . . 81

8.6 Bivariate Residuals . . . . . . . . . .. . . . . . . . . . . . . . 81

8.7 Estimated Values . . . . . . . . . . .. . . . . . . . . . . . . . 84

8.8 Classification . . . . . . . . . . . .. . . . . . . . . . . . . . . 84

8.9 Output-to-file Options . . . . . . . .. . . . . . . . . . . . . . 85

9 Introduction to Part II(Advanced Models) . . . . . . . . . . . . . . . 87

10 Latent Markov Models. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 89

10.1 The Simplest Latent Markov Model . . .. . . . . . . . . . . . 90

10.2 The General Mixture Latent Markov withCovariates . . . . . 90

10.3 Restrictions . . . . . . . . . . . . .. . . . . . . . . . . . . . . 92

10.4 Parameter Estimation . . . . . . . . .. . . . . . . . . . . . . 92

11 Continuous Factors . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .93

11.1 Model Components and Estimation Issues. . . . . . . . . . . 93

11.2 Application Types . . . . . . . . . .. . . . . . . . . . . . . . 96

11.2.1 Factor analysis . . . . . . . . . .. . . . . . . . . . . . 96

11.2.2 IRT models . . . . . . . . . . . . .. . . . . . . . . . . 98

11.2.3 Local dependence LC models . . . . .. . . . . . . . . 99

11.2.4 Random-effects models . . . . . . .. . . . . . . . . . . 100

11.2.5 Random-intercept model withcovariates . . . . . . . . 102

11.2.6 LC (FM) regression models withrandom effects . . . . 103

12 Multilevel LC Model. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . 104

12.1 Model Components and Estimation Issues. . . . . . . . . . . 104

12.2 Application Types . . . . . . . . . .. . . . . . . . . . . . . . 107

12.2.1 Two-level LC or FM model . . . . . .. . . . . . . . . 107

12.2.2 LC (FM) regression models forthree-level data . . . . 108

12.2.3 Three-level random-effects GLMs . .. . . . . . . . . . 109

12.2.4 LC growth models for multipleindicators or nested data110

12.2.5 Various IRT applications . . . . . .. . . . . . . . . . . 111

12.2.6 Non multilevel models . . . . . . .. . . . . . . . . . . 112

13 Complex Survey Sampling . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .112

13.1 Pseudo-ML Estimation and LinearizationEstimator . . . . . . 112

13.2 A Two-step Method . . . . . . . . . .. . . . . . . . . . . . . 115

14 Latent GOLD’s Advanced Output. . . . . . . . . . . . . . .115

14.1 Model Summary . . . . . . . . . . . .. . . . . . . . . . . . . 116

14.2 Parameters . . . . . . . . . . . . . .. . . . . . . . . . . . . . 117

14.3 Profile . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 118

14.4 GProfile . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 118

14.5 Profile-Longitudinal . . . . . . . . .. . . . . . . . . . . . . . . 119

14.6 ProbMeans . . . . . . . . . . . . . .. . . . . . . . . . . . . . 119

14.7 Bivariate Residuals . . . . . . . . .. . . . . . . . . . . . . . . 119

14.8 Frequencies . . . . . . . . . . . . .. . . . . . . . . . . . . . . 120

14.9 Estimated Values . . . . . . . . . . .. . . . . . . . . . . . . . 120

14.10Classification . . . . . . . . . . . .. . . . . . . . . . . . . . . 121

14.11Output-to-file Options . . . . . . . .. . . . . . . . . . . . . . 121

15 Introduction to Part III(Syntax Models) . . . . . . . . . . . . . . . . . .123

16 Various Modeling Optionswhich are Specific to Syntax . .. . . . . .126

16.1 Alternative Regression Models forDichotomous and Ordinal DependentVariables . . . . . . 126

16.2 Additional Regression Models forContinuous Dependent Variables. . . . . . . . 128

16.3 Log-linear Scale Factor Models forCategorical Dependent Variables . .. . . . 129

16.4 Regression Models with a Cell WeightVector (“wei” Option) 130

16.5 Continuous-Time Markov Models . . . .. . . . . . . . . . . . 131

17 Various Output Options whichare Specific to Syntax . . . . . . . . . . . . . . .133

17.1 Other Variance Estimators . . . . . .. . . . . . . . . . . . . . 133

17.1.1 Complex sampling standard errors . .. . . . . . . . . 133

17.1.2 Other standard errors . . . . . . .. . . . . . . . . . . 134

17.2 Power Computation for Wald Tests . . .. . . . . . . . . . . . 135

17.3 Score Tests and EPCs . . . . . . . . .. . . . . . . . . . . . . 135

17.4 Identification Checking . . . . . . .. . . . . . . . . . . . . . 136

17.5 Continuous-Factor and Random-EffectCovariances . . . . . . 137

18 Bibliography . . . . . . . .. . . . . . .139

19 Notation . . . . . . . . . .. . . . .158

19.1 Basic Models . . . . . . . . . . . . .. . . . . . . . . . . . . . 158

19.2 Advanced Models . . . . . . . . . . .. . . . . . . . . . . . . . 159

19.3 Syntax Models . . . . . . . . . . . .. . . . . . . . . . . . . . 159