amos – analysis of moment structuresutlc.uum.edu.my/images/penerbitan/slide/intro part...

19-12-2012 1

Bidin Yatim, PhD Assoc. Prof. School of Quantitative Sciences College of Arts & Sciences [email protected] 019-3394959

PhD Applied Statistics (Exeter, UK) MSc Industrial Mathematics (Aston, UK) BSc Mathematics and Statistics (Nottingham, UK)

INTRODUCTORY STRUCTURAL

EQUATION MODELING WITH AMOS

WORKSHOP

mailto:[email protected]

Structural Equation Modelling with AMOS. Basic

Concepts, Applications and Programming Barbara M. Bryne

Part Three Modeling and Computing II

Implementing SEM Using AMOS

Modeling and Computing II

Implementing SEM Using AMOS 1.How to draw a model using AMOS.

2.How to run the AMOS model and evaluate several key components of the AMOS graphics and text output, including overall model fit and test statistics for individual path coefficients.

3.How to modify and re-specify a non-fitting model.

• Exogenous variables=independent

• Endogenous variables =dependent

• Observed variables =measured

• Latent variables=unobserved

Structural Equation Modeling

Model Identification

P is # of measured variables

[P*(P+1)]/2

Df=[P*(P+1)]/2-(# of estimated parameters)

If DF>0 model is over identified

If DF=0 model is just identified

If DF<0 model is under identified

Structural Equation Modeling

Missing data in SEM

Handling Missing data in SEM

• Listwise

• Pairwise

• Mean substitution

• Regression methods

• Expectation Maximization (EM) approach

• Full Information Maximum Likelihood

(FIML)**

• Multiple imputation(MI)**

The two best methods: FIML and MI

SEM Software

• Several different packages exist – EQS, LISREL, MPLUS, AMOS, SAS, ...

• Provide simultaneously overall tests of – model fit

– individual parameter estimate tests

• May compare simultaneously – Regression coefficients

– Means

– Variances

even across multiple between-subjects groups

Introduction to

AMOS

AMOS Advantages

• Easy to use for visual SEM ( Structural Equation Modeling).

• Easy to modify, view the model

• Publication –quality graphics

AMOS Components

• AMOS Graphics

– draw SEM graphs

– runs SEM models using graphs

• AMOS Basic

– runs SEM models using syntax

Starting AMOS Graphics

Start Programs Amos 21 Amos Graphics

Reading Data into AMOS

• File Data Files

• The following dialog appears:


Click on File Name to specify the name of the data file

Currently AMOS reads the following data file formats:

Access

dBase 3 – 5

Microsft Excel 3, 4, 5, and 97

FoxPro 2.0, 2.5 and 2.6

Lotus wk1, wk3, and wk4

SPSS *.sav files, versions 7.0.2 through 13.0 (both raw data and matrix formats)


• Example USED for this workshop:

– Condom use and what predictors

affect it

• DATASET: AMOS_data_valid_condom.sav

Drawing in AMOS

• In Amos Graphics, a model can be specified by drawing a diagram on the screen

1. To draw an observed variable, click "Diagram" on the top menu, and click "Draw Observed." Move the cursor to the place where you want to place an observed variable and click your mouse. Drag the box in order to adjust the size of the box. You can also use in the tool box to draw observed variables.

2. Unobserved variables can be drawn similarly. Click "Diagram" and "Draw Unobserved." Unobserved variables are shown as circles. You may also use in the toolbox to draw unobserved variables.

Drawing in AMOS

• To draw a path, Click “Diagram” on the top menu and click “Draw Path”.

• Instead of using the top menu, you may use the Tool Box buttons to draw arrows ( and ).

Drawing in AMOS

• To draw Error Term to the observed and unobserved variables.

• Use “Residual Variable” button in the Tool Box. Click and then click a box or a circle to which you want to add errors or a unique variables.(When you use "Unique Variable" button, the path coefficient will be automatically constrained to 1.)

1

1 1

Drawing in AMOS

• Let us draw:

Naming the variables in AMOS

• double click on the objects in the path diagram. The Object Properties dialog box appears.

• OR

Click on the Text tab and enter the name of the variable in the Variable name field:

Naming the variables in AMOS

• Example: Name the variables

ISSUEB1

SXPYRC1

eSXPYRC1

1

SEX1

eiss

FRBEHB1

efr1

1 1

IDM

Constraining a parameter in

AMOS • The scale of the latent variable or variance of

the latent variable has to be fixed to 1.

Double click on the arrow between EXPYA2 and SXPYRA2.

The Object Properties dialog appears.

Click on the Parameters tab and enter the value “1” in the Regression weight field:

Improving the appearance of the path

diagram

• You can change the appearance of your path diagram by moving objects around

• To move an object, click on the Move icon on the toolbar. You will notice that the picture of a little moving truck appears below your mouse pointer when you move into the drawing area. This lets you know the Move function is active.

• Then click and hold down your left mouse button on the object you wish to move. With the mouse button still depressed, move the object to where you want it, and let go of your mouse button. Amos Graphics will automatically redraw all connecting arrows.

Improving the appearance of the path

diagram

• To change the size and shape of an object, first press the Change the shape of objects icon on the toolbar.

• You will notice that the word “shape” appears under the mouse pointer to let you know the Shape function is active.

• Click and hold down your left mouse button on the object you wish to re-shape. Change the shape of the object to your liking and release the mouse button.

• Change the shape of objects also works on two-headed arrows. Follow the same procedure to change the direction or arc of any double-headed arrow.

Improving the appearance of

the path diagram • If you make a mistake, there are

always three icons on the toolbar to quickly bail you out: the Erase and Undo functions.

• To erase an object, simply click on the Erase icon and then click on the object you wish to erase.

• To undo your last drawing activity, click on the Undo icon and your last activity disappears.

• Each time you click Undo, your previous activity will be removed.

• If you change your mind, click on Redo to restore a change.

Selected Drawing Tools in AMOS

Graphics

Performing the

analysis in AMOS

• View/Set Analysis Properties and click on the Output tab.

• There is also an Analysis Properties icon you can click on the toolbar. Either way, the Output tab gives you the following options:

Performing the analysis

in AMOS

• For our example, check the Minimization history, Standardized estimates, and Squared multiple correlations boxes. (We are doing this because these are so commonly used in analysis).

• To run AMOS, click on the Calculate estimates icon on the toolbar. – AMOS will want to save this problem to a file.

– if you have given it no filename, the Save As dialog box will appear. Give the problem a file name; let us say, tutorial1:

Results

• When AMOS has completed the calculations, you have two options for viewing the output:

– text output,

– graphics output.

• For text output, click the View Text ( or F10) icon on the toolbar.

• Here is a portion of the text output for this problem:

Viewing the graphics output

in AMOS

• To view the graphics output, click the View output icon next to the drawing area.

• Chose to view either unstandardized or (if you selected this option) standardized estimates by click one or the other in the Parameter Formats panel next to your drawing area:

MODELING AND COMPUTING II

Implementing SEM Using AMOS 1.How to draw a model using AMOS.

2.How to run the AMOS model and evaluate several key components of the AMOS graphics and text output, including overall model fit and test statistics for individual path coefficients.

3.How to modify and re-specify a non-fitting model.

AMOS DIAGRAM -

SATISFACTION

6 JULY 2011

Residuals

Indicators for

“Appreciation”

Errors for

“Skill”

Latent

Variable

(Exogenous)

Endogenous

AMOS DIAGRAM –

SATISFACTION

RESULT FROM DIAGRAM

6 JULY 2011

AMOS DIAGRAM – RESULT

FROM TEXT Regression Weights: (Group number 1 - Default model)

Estimate S.E. C.R. P Label

Skill <--- Satisfaction 1

Appreciation <--- Satisfaction 1

cq3 <--- Appreciation 1

cq8 <--- Appreciation 1.086 0.055 19.672 ***

cq9 <--- Appreciation 1.143 0.062 18.403 ***

cq10 <--- Appreciation 1.224 0.062 19.712 ***

cq11 <--- Appreciation 1.205 0.061 19.825 ***

cq12 <--- Appreciation 1.212 0.061 19.955 ***

cq14 <--- Appreciation 1.155 0.06 19.283 ***

cq15 <--- Appreciation 1.324 0.066 19.936 ***

cq4 <--- Skill 1

cq6 <--- Skill 1

cq13 <--- Skill 1

6 JULY 2011

CMIN

Model NPA

R CMIN DF P CMIN/D

F

Default model 32 1142.935 45 0 25.399

Saturated model 77 0 0

Independence model 22 7594.645 55 0 138.084

Baseline Comparisons

Model

NFI RFI IFI TLI

CFI Delta1 rho1 Delta2 rho2

Default model 0.85 0.816 0.855 0.822 0.854


Independence model 0 0 0 0 0

AMOS DIAGRAM – RESULT

FROM TEXT

6 JULY 2011

RMSEA

Model RMSEA LO 90 HI 90 PCLOSE

Default model 0.104 0.098 0.109 0

Independence model 0.246 0.241 0.25 0

NCP

Model NCP LO 90 HI 90

Default model 1097.935 991.479 1211.79


Independence model 7539.645 7256.631 7828.95

FMIN

Model FMIN F0 LO 90 HI 90

Default model 0.503 0.483 0.437 0.534

Saturated model 0 0 0 0

Independence model 3.344 3.32 3.195 3.447

Requirements for Fit of Model Output Values of fit indices indicate only the average or overall fit of a

model:

CMIN - the minimum value of the discrepancy function between the

sample covariance matrix and the estimated covariance matrix

DF - the number of degrees of freedom

CMIN/DF - the ratio of the minimum discrepancy to degrees of

freedom

Normed Fit Index (NFI) - compares the improvement in the

minimum discrepancy for the specified (default) model to the

discrepancy for the Independence model

Comparative Fit Index (CFI) - the ratio between the discrepancy of

this target model to the discrepancy of the independence model.

Tucker-Lewis Coefficient (TLI) - known as the Bentler-Bonett non-

normed fit index (NNFI). The Tucker-Lewis index does have such a

penalty of Bentler Bonett

Root Mean Square Error of Approximation (RMSEA) - This

measure is based on the non-centrality parameter

Specification for Testing Fit

Variance and correlation -> must always be positive

Estimation of Critical Ratio, C.R > 1.96

P-value (Chi Square) > 0.05

CMIN / DF < 5

CFI > 0.9

NFI > 0.8

Tucker-Lewis (TLI) > 0.95

RMSEA < 0.06

Check on Modification Indices (MI)

INITIAL DIAGRAM -

SATISFACTION

Endogenous

Endogenous

Latent Variable

(Exogenous)

FINAL DIAGRAM - SATISFACTION

Model fit

AMOS RESULT FROM DIAGRAM


Appreciation <--- Satisfaction 1

Skills <--- Satisfaction 1

cq15 <--- Appreciation 1

cq14 <--- Appreciation 0.956 0.056 17.065 ***

cq11 <--- Appreciation 0.958 0.055 17.583 ***

cq9 <--- Appreciation 0.926 0.06 15.509 ***

cq7 <--- Appreciation 0.584 0.044 13.322 ***

cq4 <--- Skills 1

cq1 <--- Skills 1.619 0.262 6.181 ***

cq3 <--- Skills 2.051 0.206 9.937 ***

CMIN

Model NPAR CMIN DF P CMIN/DF

Default model 17 202.09 19 0 10.636


Independence model 8 1734.496 28 0 61.946

RMR, GFI

Model RMR GFI AGFI PGFI

Default model 0.042 0.955 0.916 0.504

Saturated model 0 1


RMSEA


Default model 0.092 0.081 0.104 0


NFI RFI IFI TLI

Delta1 rho1 Delta2 rho2

Default model 0.883 0.828 0.893 0.842 0.893


Independence model 0 0 0 0 0

Model CFI

MODIFICATION INDICES (GROUP

NUMBER 1 - DEFAULT MODEL)

M.I. Par Change

e5 <--> e8 5.211 -0.041

e5 <--> e6 14.563 0.05

e4 <--> e6 11.238 -0.055

e3 <--> Satisfaction 5.42 0.021

e3 <--> e10 11.197 0.027

e3 <--> e8 28.279 0.098

e3 <--> e4 46.509 0.122

e2 <--> e10 5.438 -0.02

e2 <--> e8 13.861 -0.073

e2 <--> e5 4.353 0.032

e2 <--> e4 8.602 -0.056

e2 <--> e3 31.879 -0.087

e1 <--> e5 12.284 -0.053

e1 <--> e4 10.796 -0.063

e1 <--> e3 8.087 -0.044

e1 <--> e2 71.277 0.139

M.I. Par Change

cq3 <--- cq11 12.825 0.108

cq3 <--- cq14 6.57 -0.074

cq4 <--- cq7 9.018 0.076

cq4 <--- cq9 8.36 -0.055

cq7 <--- cq4 11.142 0.099

cq7 <--- cq15 5.655 -0.053

cq9 <--- cq4 9.585 -0.116

cq9 <--- cq11 20.879 0.135

cq9 <--- cq14 4.275 -0.059

cq9 <--- cq15 5.023 -0.063

cq11 <--- Satisfaction 5.42 0.15

cq11 <--- cq3 18.537 0.09

cq11 <--- cq9 28.734 0.113

cq11 <--- cq14 16.175 -0.093

cq14 <--- cq3 9.048 -0.067

cq14 <--- cq9 5.289 -0.052

cq14 <--- cq11 14.541 -0.098

cq14 <--- cq15 33.664 0.141

cq15 <--- cq7 9.007 -0.089

cq15 <--- cq9 6.658 -0.058

cq15 <--- cq14 36.065 0.148

AMOS DIAGRAM

(SATISFACTION)

Before After

AMOS DIAGRAM (OC)

Before After

AMOS DIAGRAM (OVERALL)

Before After

The hypothesized model generated to examine the significant

relationships between the organizational culture and job satisfaction

in Politeknik Kementerian Pengajian Tinggi Malaysia. The model

contains two factors composed of organisational culture and job

satisfaction.

SatisfactionOrg

Culture

cq3 e1

1

1

cq4 e21

cq6 e31

cq8 e41

cq9 e51

cq10 e61

cq11 e71

cq12 e81

cq13 e91

cq14 e101

cq15 e111

bq76e12

1

1bq75e13

1bq73e14

1bq72e15

1bq67e16

1bq66e17

1bq65e18

1bq62e19

1bq55e20

1bq53e21

1bq50e22

1bq48e23

1bq47e24

1bq44e25

1bq41e26

1bq39e27

1bq36e28

1bq34e29

1bq32e30

1bq29e31

1bq27e32

1bq26e33

1bq24e34

1bq23e35

1bq22e36

1bq20e37

1bq15e38

1bq14e39

1bq13e40

1bq12e41

1bq8e42

1bq6e43

1bq5e44

1bq4e45

1bq2e46

1bq1e47

1ORGANISATION CULTURE AND JOB SATISFACTION

e48

1

Figure : 1.0

Satisfaction

.32

Org

Culture

cq3

.72

e1

1.00

1

cq4

.34

e2

.54

1

cq6

.45

e3

.38

1

cq8

.36

e4

1.08

1

cq9

.72

e51.081

cq10

.45

e61.15 1

cq11

.47

e7

1.161

cq12

.42

e8

1.14

1

cq13

.34

e9

.83

1

cq14

.51

e10

1.21

1

cq15

.50

e11

1.32

1

bq76

.42

e12

1.00

1bq75

.98

e13

1.17

1bq73

.46

e14

1.01

1bq72

.50

e15

1.03

1bq67

.64

e16

.50

1bq66

1.17

e17

.60

1bq65

.64

e18

.62

1bq62

.47

e19

1.18

1bq55

.44

e20

.96

1bq53

.40

e211

bq50

1.36

e22

1.04

1bq48

1.30

e23

1.16

1bq47

.44

e24

1.23

1bq44

1.62

e25

.79

1bq41

.41

e26

1.27

1bq39

.36

e27

1.23

1bq36

.32

e28

.841

bq34

.99

e29

1.001bq32

.39

e30.791

bq29

.57

e31 1.221

bq27

.35

e32.85

1bq26

.40

e33

1.20

1bq24

.34

e34

1.18

1bq23

.40

e35

1.19

1bq22

.37

e36

1.17

1bq20

.43

e37

1.02

1bq15

.42

e38

1.30

1bq14

1.10

e39

1.35

1bq13

.43

e40

1.18

1bq12

.42

e41

.89

1bq8

.39

e42

.78

1bq6

.55

e43

1.00

1bq5

.54

e44

.88

1bq4

.35

e45

.70

1bq2

.50

e46

.80

1bq1

.43

e47

.76

1

.86

ORGANISATION CULTURE AND JOB SATISFACTION

.27

.27

e48

1

Figure : 1.1

Number of variables in your model: 97

Number of observed variables: 47

Number of unobserved variables: 50

Number of exogenous variables: 49

Number of endogenous variables: 48

Parameter summary (Group number 1)

Weights Covariances Variances Means Intercepts Total

Fixed 50 0 0 0 0 50

Labeled 0 0 0 0 0 0

Unlabeled 46 0 49 0 0 95 Total 96 0 49 0 0 145

Table : 2.1 Parameter summary (Group number 1)

Table : 2.0 Variable and Parameter Summary

Computation of degrees of freedom (Default Model)

Number of distinct sample moments: 1128

Number of distinct parameters to be estimated: 95

Degrees of freedom (1128 - 95): 1033

Result (Default model)

Minimum was achieved

Chi-square = 15110.956

Degrees of freedom = 1033

Probability level = .000

Table : 2.3 Computation of degrees of freedom

Table : 2.4 Result

Regression Weights: (Group number 1 - Default

model)


Satisfaction <--- Org_Culture 0.266 0.021 12.545 ***

cq3 <--- Satisfaction 1

cq4 <--- Satisfaction 0.542 0.028 19.657 ***

cq6 <--- Satisfaction 0.385 0.028 13.903 ***

cq8 <--- Satisfaction 1.08 0.041 26.243 ***

cq9 <--- Satisfaction 1.077 0.047 23.086 ***

cq10 <--- Satisfaction 1.148 0.044 25.894 ***

cq11 <--- Satisfaction 1.156 0.045 25.769 ***

cq12 <--- Satisfaction 1.135 0.044 26.063 ***

cq13 <--- Satisfaction 0.832 0.034 24.294 ***

cq14 <--- Satisfaction 1.212 0.047 25.779 ***

cq15 <--- Satisfaction 1.316 0.05 26.502 ***

Table : 2.5 Regression Weights: (Group number 1 - Default model)

Variances: (Group number 1 - Default model) Estimate S.E. C.R. P Label

Org_Culture 0.318 0.016 19.567 ***

e48 0.266 0.018 14.532 *** e1 0.724 0.02 35.849 ***

e2 0.335 0.009 36.623 *** e3 0.448 0.012 37.457 ***

e4 0.362 0.011 33.019 *** e5 0.721 0.02 35.501 *** e6 0.447 0.013 33.445 ***

e7 0.468 0.014 33.584 *** e8 0.419 0.013 33.246 ***

e9 0.338 0.01 34.828 ***

e10 0.513 0.015 33.573 ***

e11 0.501 0.015 32.661 ***

Table : 2.6 Variances: (Group number 1 - Default model)

CMIN

Model NPAR

CMI

N DF P CMIN/DF

Default model 95

1511

1 1033 0 14.628


Independence

model 47

6647

2 1081 0 61.491

RMR, GFI Model RMR GFI AGFI PGFI

Default model 0.047 0.751 0.729 0.688

Saturated model 0 1


Baseline Comparisons

Model

NFI RFI IFI TLI

CFI

Delta

1 rho1 Delta2 rho2

Default model 0.773 0.762 0.785 0.775 0.785


Independence

model 0 0 0 0 0

Table: 2.9 Baseline Comparisons

Table: 2.8 RMR,GFI

Table: 2.7 CMIN

Parsimony-Adjusted Measures

Model PRATIO PNFI PCFI Default model 0.956 0.738 0.75


Independence model 1 0 0

NCP

Model NCP LO 90 HI 90

Default model 14077.956 13683.756

14478.58

4


Independence

model 65390.532 64548.991

66238.38

3

Table : 2.10 Parsimony-Adjusted Measures

Table : 2.11 NCP

RMSEA


Default model 0.069 0.068 0.07 0


FMIN

Model FMIN F0 LO 90 HI 90

Default model 5.243 4.885 4.748 5.024

Saturated model 0 0 0 0


Table : 2.12 RMSEA

Table : 2.13 FMIN

AIC

Model AIC BCC BIC CAIC

Default model

15300.95

6

15304.1

7

15867.7

81

15962.7

81

Saturated model 2256 2294.21 8986.31

10114.3

1

Independence model

66565.53

2

66567.1

2

66845.9

61

66892.9

61

ECVI

Model ECVI LO 90 HI 90 MECVI

Default model 5.309 5.172 5.448 5.31

Saturated model 0.783 0.783 0.783 0.796


HOELTER

Model

HOELTER HOELTER

0.05 0.01

Default model 212 218

Independence model 51 52

Table : 2.14 AIC

Table : 2.16 HOELTER

Table : 2.15 ECVI

Minimization History (Default model)

Iteration Negative

Condition # Smallest

Diameter F NTries Ratio eigenvalues eigenvalue 0 e 4 -1.69 9999 57799.655 0 9999 1 e 4 -0.041 6.409 25791.197 19 0.103 2 e 3 -0.05 1.71 20643.606 5 0.743 3 e 1 -0.054 1.599 17560.115 5 0.983 4 e 1 -0.019 1.231 16350.729 5 0.594 5 e 0 44.915 0.613 15495.335 4 0.953 6 e 0 90.79 0.868 15200.275 1 1.077 7 e 0 155.385 0.454 15117.706 1 1.119 8 e 0 237.588 0.251 15111.137 1 1.082 9 e 0 254.141 0.042 15110.956 1 1.023

10 e 0 240.957 0.002 15110.956 1 1.001 11 e 0 240.982 0 15110.956 1 1.002

Table : 2.17 Minimization History (Default model)

Goodness of fit is the decision to measure whether model has a good fit with the

data based on assessment criteria such as CMIN/ df ratio (<5), p-value (>0.05),

Goodness of Fit Index (GFI) (>0.95), CFI (>0.9), Tucjer –Lewis (TLI) (>0.95), Normed

Fit Index (NFI) (>0.8) and root mean square error of approximation (RMSEA) of

values (<0.06) as suggested by (Hair et al., 2010). Based on the goodness of fit of

hypothesized model shows, GFI is 0.751; CMIN/DF ratio is 14.63, NFI is 0.773,

RMSEA is 0.069, TLI is 0.775 and P- Value shows a result of 0.

The textual output of the above model indicates a χ2 value of 15110.96, degrees

of freedom value of 1033 and a probability of less than .0001 (p < .0001). Thus

the fit of the data to the above hypothesized model is not adequate. According to

Joreskog & Sorbom, (1993) in Structural Equation Modeling with AMOS, if the

results indicate a large χ2 compare to degrees of freedom, the model need to be

modify until fit the data.

Therefore, the data for the above model on job satisfaction and organisational

culture represent an unlikely event and should be rejected and need to be

modified for better fit.

Baiyin Yang. Factor Analysis Methods. Berrett –Koehler publishers.

Barbara M. Byrne. Structural Equation Modeling with AMOS. Basic Concept,

Application and Programming. Second Edition, Multivariate Applications Series.

Hair, J.F. Jr; Black, W.C.; Babin, B.J.; Anderson, R.E; Tatham, R.L. (2010).

Multivariate Data Analysis, seventh edition, Prentice Hall.

Jamie DeCoster (1998). Overview of Factor Analysis,Department of Psychology

University of Alabama, http://www.stat-help.com

Lawrence S. Meyers, Glenn Gamst, A.J. Guarino. Applied Multivariate Research,

Design and Interpretation. Sage Publication.

http://www.stat-help.com/









19-12-2012

63

THE END

THANK YOU

amos – analysis of moment structuresutlc.uum.edu.my/images/penerbitan/slide/intro part...

Documents