New developments in structural equation modeling

Transcription

1 New developments in structural equation modeling Rex B Kline Concordia University Montréal Set A: SCM A1 UNL Methodology Workshop

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5 Topics o Graph theory o Mediation: Design Conditional Causal A5

6 Topics o Graph theory: Pearl s SCM Causal reasoning Causal estimation A6

7 Topics o Mediation: Design requirements Conditional process modeling Cause mediator (SCM) A7

8 Graph theory o Pearl, J. (2009a). Causal inference in statistics: An overview. Statistics Surveys, 3, o Pearl, J. (2009b). Causality: Models, reasoning, and inference (2nd ed.). New York: Cambridge University Press. o Pearl, J. (2012). The causal foundations of structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp ). New York: Guilford Press. A8

9 Graph theory o Bollen, K. A., & Pearl, J. (2013). Eight myths about causality and structural equation models. In S.L. Morgan (Ed.), Handbook of causal analysis for social research (pp ). New York: Springer. o Cole, S. R., Platt, R. W., Schisterman, E. F., Chu, H., Westreich, D., Richardson, D., & Poole, C. (2010). Illustrating bias due to conditioning on a collider. International Journal of Epidemiology, 39, o Elwert, F. (2013). Graphical causal models. In S. L. Morgan (Ed.), Handbook of causal analysis for social research (pp ). New York, NY: Springer. A9

10 Graph theory o Elwert, F. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, o Glymour, M. M. (2006). Using causal diagrams to understand common problems in social epidemiology. In M. Oakes & J. Kaufman (Eds), Methods in social epidemiology (pp ). San o Francisco: Jossey-Bass. Hayduk, L., Cummings, G., Stratkotter, R., Nimmo, M., Grygoryev, K., Dosman, D., Boadu, K. (2003). Pearl s d-separation: One more step into causal thinking. Structural Equation Modeling, 10, A10

11 Graph theory o Kenny, D. A. (2014). Mediation. Retrieved from o Shipley, B. (2000). A new inferential test for path models based on directed acyclic graphs. Structural Equation Modeling, 7, o Spector, P. E., & Brannick, M. T. (2011). Methodological urban legends: The misuse of statistical control variables. Organizational Research Methods, 14, A11

12 Graph theory o Knüppel, S., & Stang, A. (2010). DAG Program: Identifying minimal sufficient adjustment sets. Epidemiology, 21, o Porter, K., Poole, D., Kisynski, J., Sueda, S., & Knoll, B., Mackworth, A., Hoos, H., Gorniak, P., & Conati, C. ( ). Belief and Decision Network Tool (Version ) (computer software). o Textor, J., Hardt, J., & Knüppel, S. (2011). DAGitty: A graphical tool for analyzing causal diagrams. Epidemiology, 5, A12

13 Mediation o Design: Cheung, J., & MacKinnon, D. P. (2012). Mediational/indirect effects in structural equation modeling. In R. H. Hoyle (Ed.), Handbook of structural equation modeling (pp ). New York: Guilford Press. Little, T. D. (2013). Longitudinal structural equation modeling. New York, NY: Guilford. MacKinnon, D. P. (2011). Integrating mediators and moderators in research design. Research on Social Work Practice, 21, A13

14 Mediation o Design: Maxwell, S. E., & Cole, D. A. (2007). Bias in cross-sectional analyses of longitudinal mediation. Psychological Methods, 12, Selig, J. P., & Preacher, K. J. (2009). Mediation models for longitudinal data in developmental research. Research in Human Development, 6, Wu, A. D., & Zumbo, B. D. (2008). Understanding and using mediators and moderators. Social Indicators Research, 87, A14

15 Mediation o Conditional: Edwards, J. R., & Lambert, L. S. (2007). Methods for integrating moderation and mediation: A general analytical framework using moderated path analysis. Psychological Methods, 12, Hayes, A. F. (2013). Introduction to mediation, moderation, and process control analysis: A regression-based approach. New York: Guilford Press. A15

16 Mediation o Conditional: Hayes, A. F., & Preacher, K. J. (2013). Conditional process modeling: Using structural equation modeling to examine contingent causal processes, In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp ). Charlotte: IAP. Preacher, K. J., Rucker, D. D., & Hayes, A. F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, A16

17 Mediation o Causal: Bullock, J. G., Green, D. P., & Ha, S. E. (2010). Yes, but what s the mechanism? (Don t expect an easy answer). Journal of Personality and Social Psychology, 98, Imai, K., Keele, L., & Yamamoto, T. (2010) Identification, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25, A17

18 Mediation o Causal: Lange, T., Vansteelandt, S., & Bekaert, M. 2012). A simple unified approach for estimating natural direct and indirect effects. American Journal of Epidemiology, 176, Pearl, J. (2014). Interpretation and identification of causal mediation. Psychological Methods. Advance online publication. A18

19 Mediation o Causal: Petersen, M. L., Sinisi, S. E., & van der Laan, M. J. (2006). Estimation of direct causal effects. Epidemiology, 17, Valeri, L., & VanderWeele, T. J. (2013). Mediation analysis allowing for exposure mediator interactions and causal Interpretation: Theoretical assumptions and implementation with SAS and SPSS macros. Psychological Methods, 18, A19

20 Mediation o Hicks, R., & Tingley, D. H. (2012). MEDIATION: Stata module for causal mediation analysis and sensitivity analysis [computer software]. o Muthén, B. O. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. o Tingley, D., Yamamoto, T., Hirose, K., Keele, L., & Imai, K. (2014). Package mediation [computer software]. A20

21 Intro to SCM o Unifies: Parametric & nonparametric SEM and potential outcomes Data, graphical analysis A21

22 Intro to SCM o Alternative to path analysis o SEM program not needed o But not latent variable models A22

23 Intro to SCM o Hayduk, L. A. & Littvay, L. (2012). Should researchers use single indicators, best indicators, or multiple indicators in structural equation models? BMC Medical Research Methodology, 12(159). A23

24 Intro to SCM o Multiple indicators o Some weak o Best indicator is better A24

25 (a) Single endogenous indicator 1 EX 1 1 EX 2 1 EY 3 1 EY 4 X1 X2 Y3 Y4 1 1 A Y1 C 1 DY 1 1 DC (b) ryy =.70 for Y1.30 s 2 Y 1 1 EX 1 1 EX 2 1 EY 1 1 EY 3 1 EY 4 X1 X2 Y1 Y3 Y A B 1 C 1 A25 DB DC

26 (1 r 11 ) 2 s 1 (1 r YY ) 2 s Y 1 E1 1 EY X1 Y 1 1 A C (1 r 22 ) 2 s E2 DY X2 1 B A26

27 Intro to SCM o Bayesian networks o Graph structure o Dependence relations A27

28 Intro to SCM o Hypotheses as graphs o Directly analyze graph (no data) o Computer tools A28

29 Intro to SCM o Nonparametric causal models o Ideas (no operationalization) o Study planning A29

30 Intro to SCM o Directed acyclic graph (DAG) o Directed cyclic graph (DCG) o Recursive, nonrecursive A30

31 Intro to SCM o Causal effects identified? o If no, what should be measured? o If yes, how many estimates? A31

32 Intro to SCM o Identified model not required o Estimate what you can o Acknowledge info. gap for rest A32

33 Intro to SCM o Regression analysis o Causal model o Covariate selection A33

34 Intro to SCM o Bring on the data o Model predictions o Conditional independences A34

35 Intro to SCM o All testable hypotheses o Vanishing partial correlations o Vanishing tetrads A35

36 SCM vocabulary o Nodes, vertices (variables) o Arcs, edges, links (paths) o Adjacent ( ), nonadjacent A36

37 SCM vocabulary o Parents, ancestors o Children, descendants o Path is any sequence of edges A37

38 SCM vocabulary o Directed path (causal) o Undirected path (noncausal) A38

39 SCM vocabulary o Open (unblocked) path o Closed (blocked) path A39

40 SCM vocabulary o Front-door path (causal) o Back-door path (biasing) A40

41 SCM vocabulary o Estimate causal effect o Block all open biasing paths o Do not open any blocked path A41

42 SCM vocabulary o Ways to block or open paths: Covariates Sampling A42

43 Basic graphs o Chain: X W Y A43

44 Basic graphs o Conditional independence: X W Y X Y W A44

45 Basic graphs o Fork: X W Y A45

46 Basic graphs o Conditional independence: X W Y X Y W A46

47 Basic graphs o Inverted fork (collider): X W Y X Y A47

48 Basic graphs o Special role of colliders: Controlling for a collider (or descendant) opens a blocked path A48

49 Basic graphs o Special role of colliders: Controlling for a common outcome induces a spurious association between unrelated causes A49

50 Basic graphs o Special role of colliders: Controlling for a common outcome adds a spurious component to related causes A50

51 Basic graphs o Inverted fork (collider): X W Y X Y X Y W A51

52 Basic graphs o Control for a collider (statistical): rxy = 0 ryw =.40 rxw =.30 rxy W =.14 A52

53 Basic graphs o Control for a collider (sampling): Speed Fatalities Alcohol A53

54 Basic graphs o Descendant of a collider: X W Y A X Y A A54

55 Covariates o Achen, C. H. (2005). Let s put garbage-can regressions and garbage-can probits where they belong. Conflict Management and Peace Science, 22, A55

56 Covariates o Regression assumes: No causal effects between predictors Single equation A56

57 Basic graphs o Overcontrol bias: X W Y X Y W Y on (X, W), BX = 0 A57

58 Basic graphs o Endogenous selection bias: X W Y X Y Y on (X, W), BX 0 A58

59 d-separation o Conditional independences o Testable implications o Basis for identification A59

60 d-separation o Z d-separates X, Y if 1. Z closes all open paths 2. Z opens no blocked path A60

61 X A B Y X B A A61

62 X A B Y A Y B A62

63 X A B Y X Y A X Y B X Y (A, B) A63

64 A64

65 X A B Y X B X B A A65

66 X A B Y A Y B A66

67 X A B Y X Y X Y B X Y A A67

68 X B A A68

69 A69

70 Identification o Graphical criteria o Sufficient (deconfounding) set o Removes all noncausal aspects A70

71 Identification o Back-door criterion (total effects) o Closes biasing (back-door) paths o Leaves only causal A71

72 D Causal A X E Y X E Y C A72

73 D Back-door A X C Y X E Y X A D Y C X A D E Y A73

74 D X C Y A X E Y C A74

75 D X A D Y A X E Y C A75

76 D X A D E Y A X E Y C A76

77 Back-door X C Y X A D Y X A D E Y Y on (X, A, C) A77

78 Back-door X C Y X A D Y X A D E Y Y on (X, C, D) A78

79 D Y on (X, A, C) A Y on (X, C, D) X E Y C A79

80 A80

81 Identification o Single-door criterion (direct) o Recursive, linear, continuous o Multiple estimates A81

82 Identification o Single-door criterion (D Y) o Delete o Sufficient set d-separates A82

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84 U2 X B X B Y U1 Y A C A C A84

85 A85

86 d-separation X A B Y (X, B) (X, Y) (A, Y) 3. Z closes all open paths A86

87 Identification o Merchant, A. T, & Pitiphat, W. (2002). Directed acyclic graphs (DAGs): An aid to assess confounding in dental research. Community Dentistry and Oral Epidemiology, 30: o Fleischer, N. L., & Diez Roux, A. V. (2008). Using directed acyclic graphs to guide analyses of neighbourhood health effects: An introduction. Journal of Epidemiology & Community Health, 62, A87

88 Analysis o Roth, D. L., Wiebe, D. J., Fillingim, R. B., & Shay, K. A. (1989). Life events, fitness, hardiness, and health: A simultaneous analysis of proposed stress-resistance effects. Journal of Personality and Social Psychology, 57, A88

89 1 DFi Fitness Exercise 1 DIl Illness Hardiness Stress 1 DSt Figure 8.5. A recursive path model of health factors. A89

90 Variable Exercise 2. Hardiness Fitness Stress Illness M SD Note. These data (correlations, means, and variances) are from D. Roth et al. (1989); N = 373. A90

91 Independence Conditioning set Partial correlation Exercise Stress Hardiness.058 Exercise Illness Fitness, Stress.039 Hardiness Fitness Exercise.089 Hardiness Illness Fitness, Stress.081 Fitness Stress Exercise, Hardiness.103 A91

92 Minimally sufficient set Direct effect Exercise Hardiness Stress Fitness Exercise Fitness.108 (.013).390 Hardiness Stress.203 (.045).230 Fitness Illness (.183) (.168) (.162).250 Stress Illness.628 (.091) (.093) (.089).307 Note. Estimates are reported as unstandardized (standard error) standardized;, empty set. Values in boldface control for the all parents of each outcome. A92

93 Extensions o Locate instruments o Models counterfactuals o Potential outcomes (PO) A93

94 Strengths o Unifying model (SEM, PO) o Supports reasoning, planning o Local fit, not global A94

95 Limitations o Classical measurement o No global fit o Few software tools A95

96 A96