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Structural Equation Modeling (SEM) using AMOS

Prepared by

Anuar Mohd Mokhtar, Ng Wen Jin, Fatin Athirah, Nur Ifzan, Narozieta & Dr. Amir Hamzah Sharaai

Faculty of Environmental Studies, Universiti Putra Malaysia

Introduction

1. 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.

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Two main functions of SEM

a) Alternative to multiple regression analysis, path analysis, factor analysis,

time series analysis, ANCOVA, MANOVA to determine relationships

between variables.

b) Identifying tools

i. 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, baseline

comparison, RMSEA and others.

c) Model Development tools

i. Combined identifying and exploring functions.

ii. SEM will suggest new relationships if the model is not compatible with

research data.

Procedures in performing SEM

Designing hypothesis model based on theory

Designing research tools

Data collection

Hypothesis model testing

Reporting analysis result

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Characteristics of variables in SEM

Variable Characteristics

Indicator Variable Variable measured by research tools.

A.K.A. observed variable. In SEM, it is represented by a

square with 2 arrows pointed to it.

Unobserved Variable Variable is not measured by the research tools. It represented

by 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. Pointed

by a one-way arrow.

Latent Variable It is not measured directly from the research. It is represented

by its indicator variables.

Variable EXAMPLE

Indicator

Variable

EMOSI 1, EMOSI 2, EMOSI

3, MOTIVASI 1, MOTIVASI

2, MOTIVASI 3.

Unobserved

Variable

EMOSI, MOTIVASI, e1, e2,

e3, e4, e5, e6, z1

Exogenous

Variable

EMOSI, e1, e2, e3, e4, e5, e6,

z1

Endogenous

Variable

MOTIVASI, EMOSI 1,

EMOSI 2, EMOSI 3,

MOTIVASI 1, MOTIVASI 2,

MOTIVASI 3.

Latent Variable EMOSI, MOTIVASI

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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 one

indicator variable.

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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 Hypothesis

Null Hypothesis (HO):

There is no relationships between family size, energy consumption, and

transportation with their carbon emission.

Research Hypothesis (Ha):

There is a relationships between family size, energy consumption, and

transportation with their carbon emission.

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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 as“Tutorial 1”.

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Step 2: Open up AMOS Graphics from your computer

Step 3: Click “File”, then choose “Data Files”

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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”.

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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”.

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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)…

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….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.

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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.

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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”.

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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.

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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”.

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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…

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… 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.

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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. Click“Save” button at the left panel.

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Save it as “Tutorial 1”.

Step 13: Then, click on “View” and select “Analysis Properties” to choose the output of the analysis.

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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

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Step 15: Tick the “Maximization history”, “ Standardized estimates”,“Squared multiple correlations”, and “Modification indices”. Change the“Threshold for modification indices” into 10. Then, close the “AnalysisProperties” window.

Step 16: Now, click on “Analyze” and choose “Calculate Estimates” to analyze the model.

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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 “View”and choose “Text Output”.

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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.

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Results

Estimate S.E. P Label

CO2 <---Household 1.083 .966 .262

CO2 <--- Electricity .987 .018 ***

CO2 <--- Transport 1.000 .001 ***

Regression Weights: (Group number 1 - Default model)

Transport - lowest S.E. value, 0.001 which means it has the strongest ability to predict the household carbon emission; number of household - highest value of S.E., 0.966 which has the weakest ability to predict the carbon emission. Electricity: C.R. = 55.385, p < 0.05; Transportation: C.R. = 690.840, p < 0.05

C.R. value is out of ±1.96 range - significant variable to household carbon emission.

Estimate

CO2 <--- Household .002

CO2 <--- Electricity .098

CO2 <--- Transport 1.023

Standardized Regression Weights: (Group number 1 - Default model)

•Positive correlations•Transportation has the highest correlation.•Most significant contributor.

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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

Estimate

Household <--> Electricity .566

Household <--> Transport .161

Electricity <--> Transport -.283

Correlations: (Group number 1 - Default model)

Correlation between Numbers of Household and electricity consumption is the highest

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Estimate S.E. P Label

Household 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)

Estimate

CO2 1.000

Squared Multiple Correlations: (Group number 1 - Default model)

It shows 100% variance in CO2 emission can be predicted by all the variables.

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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,

electricity consumption, and transportation fuels are significant predictor variables for

carbon emission variable (Household:β = .002, C.R. = 1.121, p < 0.05. Electricity β =

.098, C.R. = 55.385, p < 0.05, and Transportation:β = 1.023, C.R. = 690.840, p < 0.05).

b) Overall, SEM analysis result has shown that the variance value in endogenous variable

(CO2 emission) that been predicted by the three exogenous variables is 1.00. It shows

that 100.0% variance in CO2 emission is predicted by the numbers of household,

electricity consumption, and transportation fuel.