Compiled by: Assoc. Prof. Dr Bahaman Abu Samah Department of Professional Developmentand Continuing Education Faculty of Educational Studies

Transcription

1 Compiled by: Assoc. Prof. Dr Bahaman Abu Samah Department of Professional Developmentand Continuing Education Faculty of Educational Studies Universiti Putra Malaysia Serdang

2 Structural Equation Modeling is an extension of the General Linear Model (GLM) SEM is used more as a confirmatory technique rather than exploratory technique i.e. SEM is used to confirm model rather than to discover a new model A multivariate techniques combining Confirmatory Factor Analysis, Multiple Regression and Path Analysis

3 SEM is also known as: Linear Causal Analysis Latent Variable Analysis Dependent Analysis Analysis of Covariance Structure Linear Structural Relations (LISREL) Simultaneous Equation Modeling Covariance Structural Modeling Linear Structural Relationships

4 Model interdependencies between several outcome (DV s) and their causal factors (IV s) SEM provide overall tests of model fit and individual parameter estimate tests simultaneously Regression coefficients, means, and variances may be compared simultaneously, even across multiple between-subjects groups It improves statistical estimation by incorporate measurement errors It enables use of latent (unobserved) variables in dependence relationships

5 AMOS LISREL CALIS of SAS/STAT EQS LISCOMP SEPATH Mx (

6 Stands for Analysis of MOment Structures Moment structures refer to: :: Mean :: Variance :: Covariance A computer application under SPSS Utilizes graphical interface

7 Exogenous = Independent variable Endogenous = Dependent or mediating variables Manifest = observed variable Latent = unobserved variable Correlations and covariances are represented by bidirectional arrows Causal effects are represented by single-headed arrows Number 1 refers to the paths coefficients have fixed values of 1.00 e1 1 1 F1 e2 1 e3 1 F2 e4 1 1

8 Theory Model Construction Instrument Construction Data Collection Model Testing Results Interpretation The researcher first specifies a model based on theory, then determines how to measure constructs, collects data, and then inputs the data into the SEM software package. The package fits the data to the specified model and produces the results, which include overall model fit statistics and parameter estimates.

9 Kline (2010) has suggested 3 framework for testing SEM1: 1. Strictly confirmatory Test a single model theory: reject or fail to reject 2 Alternative model Test several alternative or competing model which are supported by theories. Choose the best fit 3. Model generating Test a single model theory. However may modify and re-estimate the model This is most commonly used framework

10 Two types of SEM model: 1. Measurement model Assess the measures/instrument Involve Confirmatory Factor Analysis (CFA) 2. Structural model Test relationship between variables Involve regression and path analysis

11 A SEM that: Specifies the indicators for each construct Use in Confirmatory Factor Analysis (CFA) Enables an assessment of construct validity (convergent and discriminant validity)

12 Convergent validity refers to a set of variables that presume to measure a construct (Kline, 2005) It can be tested using: Average Variance Extracted (AVE) A high AVE (>.5) indicates a high convergent validity (Fornell & Larcker, 1981) Factor loadings High factor loadings (.5) on a factor indicate high convergent validity (Hair, et al, 2006)

13 Convergent validity refers to a set of variables that presume to measure different constructs (Kline, 2005) It can be tested by examining the AVE for each construct against squared correlations (shared variance) between the construct and all other constructs in the model A construct will have sufficient dicriminant validity If the AVE exceeds the squared correlation among the constructs (Fornell and Larcker, 1981; Hair et al, 2006)

14 Structural model represents set of one or more dependence relationship linking the hypothesized model s construct This model is most useful in representing the interrelationships between exogenous and endogenous Variables Use to test direct and indirect effects

15 Generally requires large sample size Klien (2005) suggests: < 100 Small sample size 100 to 200 Medium sample size > 200 Large sample size Critical sample size = 200 (Hoe, 2008) Minimum ration of 10:1 (Ho, 2006) A general rule for sample size of 15 cases per predictor

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17 Cont. Tool Box Use mouse and click the appropriate icons to draw a figure of the proposed model

18 Draw manifest variables Select all objects Draw latent variables Draw a latent variable and add an indicator to it Draw causal path Draw covariance/correlation Add a unique variable to an existing variable Figure captions Deselect all objects Duplicate objects Move objects Rotate the indicators of a latent variable Select data file(s) Analysis properties List variables in the model Calculate estimates List variables in the data set Object properties Select one object at a time Resize diagram to fit page

19 1. Draw figure 2. Click to select data 3. Click to display variable list 4. Drag variable into the observed variable box and label the unobserved/latent variables 5. Type the following commands in the text box 6. Click Analysis Properties 7. Click to Calculate Estimates 8. Click to view the detailed text output

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24 Chi-Square=\cmin DF=\df p=\p GFI=\gfi AGFI=\agfi CFI=\cfi NFI=\nfi TLI=\tli RMSEA=\rmsea

25 :: For CFA may want to select - Normality and Outliers :: For Structural Model, select Indirect

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29 1. Test assumption for normality and presence of outliers 2. Look for Offending Estimate (value>1) 3. Examine the Fit indexes 4 Identify values of path coefficients 5 Report the proportion of variance explained 6 Competing models 7 Multicolinearity

30 Use skewness and kurtosis to test on normality Data is considered to be normal if: :: Skewness is between -3 to +3 :: Kurtosis is between -7 to +7 (Byren, 2010)

31 By default, SEM uses maximum likelihood as the estimation technique Otherwise you may use other techniques

32 Test for outliers Remove cases if both p1 and p2 for the Mahalanobis d-squared are.000 and.000

33 Offending estimate exists when standardized regression weight > 1 We need to remove the highest std. regression estimate

34 A number of fit indices can be used to test for model fit Generally we need to present at least four (4) fit indices or 3 (Garson) The recommended indices include: :: GFI :: CFI :: IFI :: RMSEA

35 Fit Indices Authors Recommended Current value Fit Indices CMIN/DF Marsh & Hocevar, 1985 < 5.0 Bentler, 1990 < 5.0 Reported if n > 200 GFI Chau, 1997 >.90 Segars & Grover, 1993 >.90 CFI Bentler, 1990 >.90 Hatcher, 1994 >.90 RMSEA Byrne, 2001 <.08 Hu & Bentler, 1999 <.05 NFI Bentler & Bonett, 1980 >.90 CMIN Tabachnik & Fidell, 1996 Reported if n between

36 The path coefficients must be significant and the std. value >.20 Look for: _ SE (Standard Error) _ CR (Coefficient Ratio) _ CR is equivalent to t value in Regression _ p (sig-value)

37 R 2 refers to the proportion of variance explained Must be at least.10 In the example, the three variables (JRV,OV and MPV) explained 71% of variance in TM Error = 1 R 2 =.29

38 Compare the different models Choose the best fit model

39 If there is no mention of Model is NOT admissible