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Structural Equation Modeling (SEM) using AMOS
Prepared byAnuar Mohd Mokhtar, Ng Wen Jin, Fatin Athirah, Nur Ifzan, Narozieta & Dr. Amir Hamzah Sharaai
Faculty of Environmental Studies, Universiti Putra Malaysia
Introduction1. SEM specifically designed to analysis quantitative data.2. Parametric test for normal distribution data.3. Use model testing method to examine the cause-effect relationships
between a group of variables in a research.4. Hypothesis model is tested to determine its compatibility with the
research data collected from the respondents.5. SEM analysis is a combination of path analysis and factor analysis.6. SEM can be analyze using AMOS, LISREL, and EQS.7. AMOS is the newest software by IBM and provide attractive graphic.
Two main functions of SEMa) Alternative to multiple regression analysis, path analysis, factor analysis,
time series analysis, ANCOVA, MANOVA to determine relationshipsbetween variables.
b) Identifying toolsi. Identify whether the relationships between variables proposed in the model
is correct among the research respondents.ii. Identify whether the pattern of variance and covariance in research data are
matched with hypothesis model using Chi-Square Goodness-of-fit, baselinecomparison, RMSEA and others.
c) Model Development toolsi. Combined identifying and exploring functions.ii. SEM will suggest new relationships if the model is not compatible with
Procedures in performing SEMDesigning hypothesis model based on theory
Designing research tools
Hypothesis model testing
Reporting analysis result
Characteristics of variables in SEMVariable Characteristics
Indicator Variable Variable measured by research tools.A.K.A. observed variable. In SEM, it is represented by asquare with 2 arrows pointed to it.
Unobserved Variable Variable is not measured by the research tools. It representedby an oval/circle in SEM.
Exogenous Variable Independent Variable in the regression model of SEM. One-way arrow pointed out of it.
Endogenous Variable Dependent Variable in the regression model of SEM. Pointedby a one-way arrow.
Latent Variable It is not measured directly from the research. It is representedby its indicator variables.
EMOSI 1, EMOSI 2, EMOSI3, MOTIVASI 1, MOTIVASI2, MOTIVASI 3.
EMOSI, MOTIVASI, e1, e2,e3, e4, e5, e6, z1
EMOSI, e1, e2, e3, e4, e5, e6,z1
MOTIVASI, EMOSI 1,EMOSI 2, EMOSI 3,MOTIVASI 1, MOTIVASI 2,MOTIVASI 3.
Latent Variable EMOSI, MOTIVASI
Conditions that need to be fulfill for SEM
1. Normality multivariate: Every indicator variables should be normally distributed.
2. Type of data: Interval and ratio (known as scale in SPSS).
3. Sample size:Depends on the numbers of parameters. 1 parameter = 10 respondents
4. Numbers of variables in regression model: Most suitable = 3 - 5 latent variables. 1 latent variable = 3 5 indicator variables.
5. Linearity: Relationships between endogenous and exogenous variables should
be linear relationships (to avoid bias).6. Random sampling:
Samples must be choose randomly from the population.7. Free indicators variables:
Items in the questionnaire should not represents more than oneindicator variable.
Tutorial Some researchers are trying to determine the factors that contributed to
the household carbon emission at a residential area in Penang. 52 out 60 residents were chosen using Krejcie and Morgan formula and
they were chosen by using simple random methods. To determine the relationships, they used SEM to analyze the data.
Research HypothesisNull Hypothesis (HO):There is no relationships between family size, energy consumption, andtransportation with their carbon emission.
Research Hypothesis (Ha):There is a relationships between family size, energy consumption, andtransportation with their carbon emission.
Regression Model Hypothesis model for our study: Household Carbon emission = b1(household) + b2
(electricity) + b3 (transportation) + other factors.
Data preparation Step 1: Type in your data in SPSS and save them asTutorial 1.
Step 2: Open up AMOS Graphics from your computer
Step 3: Click File, then choose Data Files
Step 4: Then, click File Name to select the data set,
and choose the SPSS file Tutorial 1 that you have saved before, then click Open.
As you can see, the numbers of sample is displayed (N = 30/30)Then, click OK
Step 5: Next, click on View and choose Variables in Dataset.
A pop up will come up and it lists all the variables available in your Tutorial 1 (SPSS file).
Step 6: Click on one of the variables (continue pressing your left cursor)
.and drag it into the AMOS window (release your cursor). Now, the variable Household is inserted into the model.
Continue Step 6 until all the variables are placed into the model.
Step 7: To rearrange the placement of the variables, click Moveobjects button at the left panel.
Arrange them according to the regression model that you have suggested.
Step 8: Now, start to draw the path that represents the Step 8: Now, start to draw the path that represents the relationship between the variables by clicking Draw paths button at the left panel.
Click on Household as the first point and drag the arrow until it reaches CO2.
Now, you already have the first path. Continue to draw the paths for other exogenous variables ( Electricity and Transport).
Once you have finish, the model will looks like this.
Step 9: Then, you can start to draw the relationships between the exogenous variables. Click Draw covariances at the left panel.
Start by drawing the covariance from Transport to Electricity.
Continue to draw the covariances between all the exogenous variables.
Step 10: Now, click on Add a unique variable at the left panel to add an unobserved variable
and click on CO2 until you fit it in the right position.
Step 11: Double click at the circle (unobserved variable) to name the variable.
The Object Properties window will comes up. Name the variable as Residue and type in its label as e1.
Step 12: Now, all the variables are named and the model is completed.Then, you need to save the model before you can analyze it. ClickSave button at the left panel.
Save it as Tutorial 1.
Step 13: Then, click on View and select Analysis Properties to choose the output of the analysis.
Step 14: In the Estimation tab, make sure that Maximum likelihood and Fit the saturated and independence models are selected.
Then, switch to Output tab (at the right of Estimation tab
Step 15: Tick the Maximization history, Standardized estimates,Squared multiple correlations, and Modification indices. Change theThreshold for modification indices into 10. Then, close the AnalysisProperties window.
Step 16: Now, click on Analyze and choose Calculate Estimates to analyze the model.
Step 17: Once the analysis is complete, you see the output in the modelitself, by clicking View the output path diagram at the left panel.
Step 18: You can also look at the full result by clicking Viewand choose Text Output.
Step 19: The Amos Output window will come up and choosethe Estimates option on the left list.
Finally, You can see the result of the analysis from this window.
Estimate S.E. P Label
Estimate S.E. C.R. P Label
Household Electricity 83.137 31.341 .008
Household Transport 242.999 284.014 .856 .392
Electricity Transport -23818.259 16259.741 -1.465 .143
Covariances: (Group number 1 - Default model)
Significant correlations between these variables. These variables are affecting each others
EstimateHousehold Electricity .566Household Transport .161Electricity Transport -.283
Correlations: (Group number 1 - Default model)
Correlation between Numbers of Household and electricity consumption is the highest
Estimate S.E. P LabelHousehold 2.632 .691 ***Electricity 8195.731 2152.304 ***Transport 866266.473 227492.721 ***Residue 40.439 10.620 ***
Variances: (Group number 1 - Default model)
Since C.R. Value is more than 1.96, so it shows exogenous variables are significantly able to forecast any changes in endogenous variable (CO2 emission)
Squared Multiple Correlations: (Group number 1 - Default model)
It shows 100% variance in CO2 emission can be predicted by all the variables.
Reporting the results.a) The result of SEM Analysis has shown that the regression model designed by the
researcher is suitable, as three of the variables which are numbers of household,electrici