Sakesan Tongkhambanchong, Ph.D.(Applied Behavioral Science Research)

1. Statistical Analysis by SEM: From Theoretical Model to Hypothetical Model and Statistical Analysis Sakesan Tongkhambanchong, Ph.D.(Applied Behavioral Science Research) Faculty of Education, Burapha University

2. Agenda • Introduction to SEM • Research Process & Designs • Statistical Designs & Models • Variance & Covariance Matrix (CM) & Correlation Matrix (KM) • LISREL’s Matrix • MRA: Multiple Regression Analysis by LISREL • MMRA: Multivariate Multiple Regression Analysis by LISREL • Confirmatory Factor Analysis (CFA) • First-order CFA • Second-order CFA • Structural Equation Modeling (SEM)

3. What Research is? Conceptualization ความรู้-ความเข้าใจ (Cognitive Process) ระดับหลักการ แนวคิด Operationalization ระดับปฏิบัติการ การประยุกต์ระเบียบวิธีวิจัยสู่การปฏิบัติ, การดำเนินการอย่างมีระบบ Empirical Evidence รายงานผลการวิจัย เป็นการแสดงหลักฐาน และสื่อสารไปยังประชาคมวิจัย

4. Knowledge Inquiry and Validation How we know, what we know andHow we know, we know Bouma Gary D. & G.B.J.Atkinson. (1995) A Handbook of Social Science Research. (p.3)

5. What Research is? • Research is… “…the systematic process of collecting and analyzinginformation (data) in order to increase our understanding of the phenomenon about which we are concerned or interested.”

6. Idea Interest Theory ? A B C D E F G H I ? Y X Y ? Y ? A B Choice of Research Method Conceptualization Population & Sampling Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Observation Collecting data for analysis and interpretation Analysis Application Analyzing data and drawing conclusions Data Processing Reporting results and assessing their implications. Transforming the data collected into a form appropriate to manipulation and analysis Research Process 1 2 5 3 4 6 8 9 7

7. Idea Interest Theory ? A B C D E F G H I ? Y X Y ? Y ? A B Choice of Research Method Conceptualization Population & Sampling Experimental Research Survey Research Field Research Content Analysis Existing Data Research Comparative Research Evaluation Research Mixed Design Whom do we want to be able to draw conclusions about? Who will be observed for the purpose? Specify the meaning of the concepts and variables to be studied. Operationalization How will we actually measure the variables under study? Observation Collecting data for analysis and interpretation Analysis Application Analyzing data and drawing conclusions Data Processing Reporting results and assessing their implications. Transforming the data collected into a form appropriate to manipulation and analysis Research Process <------> Research Design 1 Problem Formulating Design Measurement Design Sampling Design Research Design 2 5 3 4 6 Data Collection Design 8 9 7 Statistical Design

8. Validity • & • Reliability • of • Research

9. Low Validity and Low Reliability Reference value Statistics Probability Density High Bias Low Accuracy Value Parameter High Variance Low Precision Low Validity = Low Accuracy = High Bias Low Reliability = Low Precision = High Variance

10. Low Validity and High Reliability Reference value Statistics Probability Density High Bias Low Accuracy Value Parameter High Precision Low Variance Low Validity = Low Accuracy = High Bias High Reliability = High Precision = Low Variance

11. Validity and Reliability of Research Finding Reference value Statistics Probability Density Accuracy Value Precision Parameter Validity = Accuracy = Low Bias Reliability = Precision = Low Variance

12. Discrepancy between Conceptual Model & Data Collection Research Conceptual Framework Hypothesized Model: Causal Model (if X then Y) Statistical Design: Structural Equation Model (SEM) AB Data Collection: Cross-sectional Design All variables were collected at the same 1-point of time (1-point of time) Intention Behavior SN PBC Time-1 Time-2 Time-3 Nature of Model: Longitudinal Design (3-points of time)

13. Examples of Causal Model Testing

14. Endogenous Variable Exogenous Variable Resilience Emotional Capital psychological well-being Affect Balance Ultimate Dependent Variable Mediator Variable Independent Variable

15. Endogenous Variable Exogenous Variable Resilience Emotional Capital psychological well-being Affect Balance Mindfulness Ultimate Dependent Variable Mediator Variable Independent Variable

16. Endogenous Variable Exogenous Variable Mindfulness Moderator Variable Resilience Emotional Capital psychological well-being Affect Balance Ultimate Dependent Variable Mediator Variable Independent Variable

17. Endogenous Variable Exogenous Variable Resilience Emotional Capital psychological well-being Mindfulness Affect Balance Ultimate Dependent Variable Mediator Variable Independent Variable

18. Research Conceptual Framework Theory of Planned Behavior :TPB (Ajzen, 1991)

19. Hypothesized Model & Number of Parameter Estimation

20. Testing Hypothesized Model & Parameter Estimated

21. Last Trimming Model & Parameter Estimated

22. Hypothetical Model & Statistical Models

23. Statistical Model: Symbols d1 d1 d1 d2 d2 d3 Observed variable (Nominal Scale) Observed variable (Interval Scale) Causal relationship X Y 1 1 Relationship Latent variable

24. Statistical Analysis: Descriptive Statistics Mean Mode Median (X1) Mean Mode Median (X2) Mean Mode Median (X3) Mean Mode Median (Y) 2X1 2X2 2X3 2Y Descriptive Statistics: How Importance? Central Tendency: Mean, Mode, Median Dispersion: Variance, Standard Deviation, Average Deviation

25. Statistical Analysis: Mean, Mode, Median, AD, SD, SD2

26. Statistical Analysis: Mean, Mode, Median, AD, SD, SD2

27. Statistical Analysis: Mean, Mode, Median, AD, SD, SD2

28. Bivariate relationship (Correlation)

29. Bivariate: Variables, Variance & Covariance Cov (X1,Y) Cov (X1,X3) Cov (X2,Y) Cov (X1,X2) Cov (X2,X3) Cov (X3,Y) 2X1 2X2 2X3 2Y

30. Bivariate Correlation (r > 1) Bivariate Correlation Analysis (rxy) ? rxy ? ? X Y X Y Z 0.90 r*xy = (rxy)/sqrt(rxx*ryy) Measurement error = 0, reliability = 1 r*xy = (0.90)/(1.0*1.0) = (0.90)/(1.0) = 0.90 r*xy = (0.90)/(0.60*0.70) = (0.90)/(0.648) = 1.389 If rxx or ryy 1.00 , Measurement error  0

31. Statistical Model: The Meaning of r = 0 The Misconception: If Pearson’s product–moment correlation, rxy, turns out equal to 0.00, this indicates that there is no relationship between the X and Y scores used to compute that correlation coefficient. Pearson’s r works well only if the relationship between X and Y is linear. If the relationship between the two variables is curvilinear, the value for r will underestimate the strength of the existing relationship

32. Statistical Model: The Strange of r

33. Statistical Model: The Meaning of r = 0

34. Statistical Model: Relationship Strength and r The Misconception: If the data on two variables having similar distributional shapes are correlated using Pearson’s r, the resulting correlation coefficient can land anywhere on a continuum that extends from 0.00 to ±1.00; therefore, an r of +.50 (or –.50) indicates that the measured relationship ishalf as strong as it possibly could be. Pearson’s r:  1.0 = Perfect correlation  0.8 = Strong correlation  0.5 = Moderate correlation  0.2 = Weak correlation 0.00 = No correlation

35. Statistical Model: The Meaning of r & r2 The coefficient of determination, r2, is a better measure of relationship strength than the correlation coefficient, r. This is because the square of r indicates the proportion of variability in one of the two variables that is explained by variability in the other variable

36. Statistical Model: The Meaning of r (why r> 0.30)

37. Statistical Model: The Effect of a Single Outlier on r The Misconception: A single outlier cannot greatly influence the value of Pearson’s r, especially if N is large. Pearson’s r:

38. Statistical Model: The Effect of a Single Outlier on r

39. Statistical Model

40. Analysis Using dependent Techniques SakesanTongkhambanchong, Ph.D(Applied Behavioral Science Research)

41. One-way ANOVA (Independent sample t-test) ? Y X1 One Factor Between-subjects Design Different Direct effects One-way ANOVA with repeated measured (Dependent sample t-test) ? Ypre Ypost One Factor Within-subjects Design Different Change, Gain, Development Direct effects

42. One-way ANOVA (F-test) ? Y X1 Between-subjects Design Direct effects One-way ANOVA with repeated measured ? ? YT2 YT1 YT2 Within-subjects Design ?

43. Two-way ANOVA (non-additive model) -- > Interaction effects Main effect X1 ? Y ? Interaction effect Between-subjects Design ? Main effect X2

44. Multi-way ANOVA (Non-additive model) (the interactive structure) X1 Y X2 Between-subjects Design X3

45. One-way Analysis of Covariance (ANCOVA) additive model ? Y Between-subjects Design X1 X1 (Covariate)

46. Bivariate Correlation Analysis (rxy) Standardized Score rxz rxy rxy ryz X Y X Y Z Cov(x,y) Cov(y,z) Cov(x,y) Cov(x,z) Raw Score

47. Simple Regression Analysis (SRA) Multiple Regression Analysis (MRA) (Convergent Causal structure) rxy X Y X1 y.x1  y.x2 X2 Y No Correlation (r = 0) y.x X Y  y.x3 X3 Direct effects

48. Multivariate Multiple Regression Analysis (MMR) (Convergent Causal structure two or several times) X1  Y1   X2 No Correlation (r = 0)   Y2  X3 Direct effects

49. Two-groups Discriminant Analysis (Discriminant structure) Binary Logistic Regression Analysis X1 W W X2 (Y) No Correlation (r = 0) W X3 Direct effects

50. Multiple Discriminant Analysis (Discriminant Structure with more than two population groups) X1 W X2 W (Y) No Correlation (r = 0) W X3 Direct effects