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Sakesan Tongkhambanchong, Ph.D.(Applied Behavioral Science Research) Faculty of Education, Burapha University

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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)

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

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

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Probability Density High Variance Low Precision Reference value High Bias Low Accuracy Value Parameter Statistics

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Probability Density High Precision Low Variance Reference value High Bias Low Accuracy Value Parameter Statistics

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Probability Density Precision Reference value Accuracy Value Parameter Statistics

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AB SN PBC Intention Behavior Research Conceptual Framework Hypothesized Model: Causal Model (if X then Y) Statistical Design: Structural Equation Model (SEM) Time-1Time-2Time-3 Nature of Model: Longitudinal Design (3-points of time)

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

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

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

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

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

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Hypothesized Model & Number of Parameter Estimation

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Testing Hypothesized Model & Parameter Estimated

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Last Trimming Model & Parameter Estimated

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1 0 X X 10 01 00 100 010 001 000 d1d1 d2d2 d1d1 d2d2 d3d3 Observed variable (Nominal Scale) Observed variable (Interval Scale) 11 11 Latent variable Causal relationship Relationsh ip d1d1 11 11 Y Y

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Mean Mode Median (Y) Mean Mode Median (Y) Mean Mode Median (X1) Mean Mode Median (X1) Mean Mode Median (X2) Mean Mode Median (X2) Mean Mode Median (X3) Mean Mode Median (X3) Descriptive Statistics: How Importance? Central Tendency: Mean, Mode, Median Dispersion: Variance, Standard Deviation, Average Deviation 2 X1 2 X2 2 X3 2Y2Y

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2 X1 2 X2 2 X3 2Y2Y Cov (X1,Y) Cov (X1,X2) Cov (X1,X3) Cov (X2,X3) Cov (X2,Y) Cov (X3,Y)

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Bivariate Correlation Analysis (r xy ) Y Y X X rxyrxyrxyrxy Y Y X X ? Z Z ?? r * xy = (r xy )/sqrt(r xx * r yy ) Measurement error = 0, reliability = 1 r * xy = (0.90)/ (1.0 *1.0 ) = (0.90)/(1.0) = 0.90 0. 90 r * xy = (0.90)/ (0.60 *0.70 ) = (0.90)/(0.648) = 1.389 If r xx or r yy 1.00, Measurement error 0

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The Misconception: If Pearson’s product–moment correlation, r xy, 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

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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 is half 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

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The coefficient of determination, r 2, 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

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The Misconception: A single outlier cannot greatly influence the value of Pearson’s r, especially if N is large. Pearson’s r:

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

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1 0 X1X1X1X1 Y Y One-way ANOVA (Independent sample t- test) Y post Y pre One-way ANOVA with repeated measured (Dependent sample t-test) One Factor Within- subjects Design ? ? Different Change, Gain, Development One Factor Between- subjects Design Direct effects

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X1X1X1X1 Y Y 10 01 00 One-way ANOVA (F-test) Y T2 Y T1 One-way ANOVA with repeated measured Within-subjects Design Y T2 ? ? ? ? Between- subjects Design Direct effects

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1 0 X1X1 Y Y Two-way ANOVA (non-additive model) -- > Interaction effects X2X2 10 01 00 ? Main effect ? Interaction effect ? Between- subjects Design

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Y Y 1 0 1 0 10 01 00 Multi-way ANOVA (Non-additive model) (the interactive structure) X1X1 X2X2 X3X3 Between- subjects Design

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Y Y One-way Analysis of Covariance (ANCOVA) additive model X1X1 10 01 00 (Covari ate) X1 ? Between- subjects Design

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Bivariate Correlation Analysis (r xy ) Y Y X X rxyrxy Y Y X X Z Z Cov(x, y) rxyrxy ryzryz rxzrxz Cov(x, z) Cov(y, z) Cov(x, y)

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

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

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

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X1 X2 X3 Multiple Discriminant Analysis (Discriminant Structure with more than two population groups) 10 01 00 (Y)(Y)(Y)(Y) W W W Direct effects No Correlation (r = 0)

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Y1 1 0 1 0 10 01 00 Multivariate Analysis of Variance -- MANOVA (Interactive Structure two or several times) Y2 X1X1 X2X2 X3X3

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

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Canonical variates (Independe nt) Canonical variates (Dependent ) R C1, 1 Set of Independen t variables Set of Dependent variables Canonical Function-1 R C2, 2 Canonical Loading 2 Simple Correlation Canonical Correlation Analysis (CCA) Canonical weight Canonical Weight Canonical Function-2

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

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Concept & Construct Variables Indicator Item Conceptual Definition Theoretical Definition Real Definition Conceptual Definition Theoretical Definition Real Definition Operational Definition (How to measured?) Operational Definition (How to measured?) Generalized idea Communication Real world Hypothesis testing Time Space Context Time Space Context Test-1Test-2Test-n

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Y X y1 y2 x1 x2 x3 y3 Formative Indicator Model Reflective Indicator Model

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22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9 The Component Loading or the Structure/Pattern Coefficient Measured variables (Observed) / Indicators / Items Factor structure / Component / Dimensions / Unmeasured variables

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22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 The Factor Loading or the Structure/Pattern Coefficient Measured variables (Observed) / Indicators / Items Factor structure / Component / Dimensions / Unmeasured variables Errors or Uniqueness

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Measured variables (Observed) / Indicators / Items 22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9 The Factor Loading or the Structure/Pattern Coefficient Factor structure / Component / Dimensions / Unmeasured variables Errors or Uniqueness 2,1 3,1 3,2

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22 22 33 33 11 11 X1 X2 X3 X4 X5 X6 X7 X8 X9 The Factor Loading or the Structure/Pattern Coefficient 2,1 3,1 3,2 Some Errors are correlated 2,1 1,1 3,1 4,2 5,2 6,2 7,3 8,3 9,3 Measured variables (Observed) / Indicators / Items Factor structure / Component / Dimensions / Unmeasured variables Errors or Uniqueness

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11 22 33 44 55 66 77 88 99 10 1111 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 F-1 F-2 F-3 F-4 First-order Confirmatory Factor Analytic Model 2,1 3,2 4,3 3,1 4,2 4,1

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11 22 33 44 55 66 77 88 99 10 1111 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 F-1 F-2 F-3 F-4 F-A F-B Second-order Confirmatory Factor Analytic Model

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M-1 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20 x21 x22 x23 x24 x25 x26 x27 x28 x29 x30 x31 x32 x33 LV-1 LV-2 LV-3 LV-4 M-2

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Y Y X1 X2 X3 Causal Modeling I: Path Analysis with Observed Variables Y Y X1 X2 X5 X4 Total Effect = Direct + Indirect Effects X3

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22 1,1 2,1 3,1 2222 2222 Y 6, 2 Y 4, 2 Y 5, 2 1111 1111 X 3, 1 X 1, 1 X 2, 1 2222 2222 X 6, 2 X 4, 2 X 5, 2 1111 1111 Y 3, 1 Y 1, 1 Y 2, 1 Causal Modeling II: Path Analysis with Latent Variables Linear Structural Equation Modeling (SEM) 4,2 1,1 5,2 6,3 2,1 3,1 4,2 5,2 6,2 11 Total Effect = Direct + Indirect Effects SEM = [Path Analysis + Confirmatory Factor Analysis]

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YY X1X1 X2X2 X3X3 Independent variables Dependent variables No Correlation (r = 0) Direct effects y.x1 y.x2 y.x3 TI Regression Model DA NO=250 NI=4 MA=CM LA Y X1 X2 X3 KM 1.000 0.470 1.000 0.516 0.652 1.000 0.485 0.506 0.479 1.000 ME 6.638 6.338 6.420 6.634 SD 1.928 1.945 1.800 1.921 MO NY=1 NX=3 GA=FU PH=SY PS=SY PA GA 1 1 1 PA PH 1 0 1 0 0 1 PD OU SE TV RS MR EF SS SC MI ND=3 AD=OFF

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Y1Y1AA BB CC Independent variables Dependent variables No Correlation (r = 0) Direct effects y1.x 1 y.x2 y1.x 3 TI Testing MMR DA NI=6 NO=320 MA=CM LA Y1 Y2 A B C D KM SY 1.000 0.269 1.000 0.440 0.227 1.000 0.313 0.298 0.175 1.000 0.490 0.319 0.501 0.436 1.000 0.276 0.262 0.240 0.352 0.424 1.000 ME 93.94 87.57 24.47 86.12 110.45 96.27 SD 6.347 6.422 3.524 5.416 9.145 6.046 MO NX=4 NY=2 GA=FU PH=SY PS=SY PA GA 1 1 PA PH 1 0 1 0 0 1 0 0 0 1 PA PS 1 0 1 PD OU SE TV RS MR MI ND=3 AD=OFF DD y.1x4 Y2Y2 y2.x 1 y2.x2 y.2x3 y2.x4

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M1M1M1M1 M1M1M1M1 X1X1 X2X2 X3X3 Independent variables Dependent variables No Correlation (r = 0) Total effect = Direct effects + Indirect effect M2M2M2M2 M2M2M2M2 YY X4X4 X5X5

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TI Path analysis DA NI=8 NO=320 MA=KM LA M1 M2 Y X1 X2 X3 X4 X5 KM SY 1.00 0.40 1.00 0.70 0.60 1.00 0.40 0.10 0.20 1.00 0.60 0.10 0.20 0.20 1.00 -.40 0.10 0.20 -.20 0.20 1.00 0.10 0.50 0.20 0.10 0.10 0.10 1.00 0.10 0.50 0.20 0.10 0.10 0.10 0.20 1.00 MO NX=5 NY=3 GA=FU BE=SD PH=SY PS=SY PA GA 1 1 1 0 0 0 0 0 1 1 0 0 0 0 0 PA BE 0 0 0 1 0 0 1 1 0 PA PH 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1 PA PS 1 0 1 0 0 1 PD OU SE TV RS MR EF SC MI=OFF ND=2

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