Introduction to IBM AMOS SPSS

AMOS is statistical software and it stands for analysis of a moment structures. AMOS is an added SPSS module, and is specially used for Structural Equation Modeling, path analysis, and confirmatory factor analysis.  It is also known as analysis of covariance or causal modeling software. AMOS is a visual program for structural equation modeling (SEM). In AMOS, we can draw models graphically using simple drawing tools. AMOS quickly performs the computations for SEM and displays the results.

In the calculation of SEM coefficients, AMOS uses the following methods:

• Maximum likelihood
• Unweighted least squares
• Generalized least squares
• Browne’s asymptotically distribution-free criterion
• Scale-free least squares

Amos is a powerful structural equation modeling (SEM) software helping support your research and theories by extending standard multivariate analysis methods, including regression, factor analysis, correlation and analysis of variance. Build attitudinal and behavioral models reflecting complex relationships more accurately than with standard multivariate statistics techniques using either an intuitive graphical or programmatic user interface. Amos is included in the Premium edition of SPSS Statistics (except in Campus Edition, where it is sold separately). You can also buy Amos as part of the Base, Standard and Professional editions of SPSS Statistics, or separately as a stand-alone application.

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Basic Concepts of Structural Equation Modeling

1. Latent versus Observed Variables In the behavioral sciences, researchers are often interested in studying theoretical constructs that cannot be observed directly. These abstract phe­nomena

What Is Structural Equation Modeling?

Structural equation modeling (SEM) is a statistical methodology that takes a confirmatory (i.e., hypothesis-testing) approach to the analysis of a structural theory bearing on some

Introduction to IBM AMOS SPSS

AMOS is statistical software and it stands for analysis of a moment structures. AMOS is an added SPSS module, and is specially used for Structural Equation Modeling, path analysis, and confirmatory factor

Application 1: Testing the Factorial Validity of a Theoretical Construct (First-Order CFA Model) with AMO

1. Key Concepts Hypothesized models conceptualized within a matrix format Error/uniqueness parameters Congeneric measures Working with model-refining tools in Amos Graphics Specification of data in

Using the Amos Program

1. Key Concepts Building SEM models using Amos Graphics Building SEM models using Amos Tables View Corollary associated with single variable estimation Concept of model

The General Structural Equation Model

1. Symbol Notation Structural equation models are schematically portrayed using particular configurations of four geometric symbols—a circle (or ellipse), a square (or rectangle), a single-headed

Application 7: Testing Invariance of a Causal Structure (Full Structural Equation Model) with AMOS

1. Key Concepts Importance of cross-validation in SEM Approaches to cross-validation in SEM Testing invariance for a programmed set of measurement and struc­tural parameters based

Application 6: Testing Invariance of Latent Mean Structures (First-Order CFA Model) with AMOS

1. Key Concepts Distinguishing between observed and latent means Distinguishing between covariance and mean structures The moment matrix Critically important constraints regarding model identification and

Application 5: Testing Factorial Invariance of Scales from a Measurement Scale (First-Order CFA Model) with AMOS

1. Key Concepts Conceptual notion of factorial invariance (i.e., equivalence) Analysis of covariance (COVS) versus means and covariance (MaCs) structures Evidence of partial measurement invariance

Application 4: Testing the Validity of a Causal Structure with AMOS

1. Key Concepts The full structural equation model Issue of item parceling Addressing evidence of multicollinearity Parameter change statistic Issue of model parsimony and nonsignificant

Application 3: Testing the Factorial Validity of Scores from a Measurement Scale (Second-Order CFA Model) with AMOS

1. Key Concepts Model identification issue in higher-order models Determination of critical ratio differences Specification of equality constraints Likert scale scores analyzed as continuous versus

Application 2: Testing the Factorial Validity of Scores from a Measurement Scale (First-Order CFA Model) with AMOS

1. Key Concepts Assumption of multivariate normality The issue of multivariate outliers The issue of multivariate kurtosis Statistical strategies in addressing nonnormality SEM robust statistics

What Is Structural Equation Modeling?

Structural equation modeling, or SEM, is a statistical method that examines the relation- ships among numerous variables in a simultaneous way. SEM is not considered

Procedural Steps in Structural Equation Modelling

Structural equation modelling includes six key steps. In addition to data collection, the steps are model specification, identification, estimation, evaluation and modification (Fig. 3.1). Model

Application 11: Addressing the Issues of Missing Data with AMOS

1. Key Concepts Unstructured versus structured missing data Basic patterns of missing data Ad hoc versus theory-based strategies for dealing with missing data Amos approach

Application 10: Use of Bootstrapping in Addressing Nonnormal Data with AMOS

1. Key Concepts SEM assumption of multivariate normality Concept of bootstrapping Benefits, limitations, and caveats related to bootstrapping Nonparametric (simple, naive) bootstrap Sample ML estimates

Application 9: Testing Change Over Time with AMOS: The Latent Growth Curve Model

1. Key Concepts Measuring change over three or more time points Intraindividual versus interindividual differences in change Factor intercept and slope as growth parameters Importance

Application 8: Testing Evidence of Construct Validity with AMOS: The Multitrait-Multimethod Model

1. Key Concepts The dual focus of construct validation procedures Convergent validity, discriminant validity, and method effects Reorientation of Amos Graphics models to fit page

Assumptions of SEM

With any statistical technique, assumptions are made. Here are a few of the assumptions with SEM that you need to be aware of going forward:

Theory Should Lead Conceptualization for SEM Model

A problem you will see with many SEM studies is when a model is conceptualized apart from any theory. A theory should be a guide

A Confirmatory Approach to SEM

Testing a SEM model is said to take a confirmatory approach. Put another way, a conceptual model is determined a priori and then data is

Is SEM Causal Modeling?

You will often hear SEM referred to as a causal modeling approach. SEM does not determine causation between two variables. This is a misnomer that

Correlations Between Constructs in SEM Model

While directionality is calculated with a covariance analysis, the strength of the relationships is determined through a correlation analysis. A correlation between two concepts is

Basics of SEM Input: The Covariance Matrix

For the purposes of this book, I will strictly use a covariance-based approach to structural equation modeling.This method is the most robust for theory testing

Screening for Impermissible Values in the Data

There are times when respondents simply key in a value wrong or list an invalid response to an inquiry.To test if an answer is outside

Data Screening for SEM Model

The first step before analyzing your SEM model is to examine your data to make sure there are no errors, outliers, or respondent misconduct. We

Greek Notation and SEM

Many SEM programs produce their results using Greek notations. They use Greek letters to represent different constructs and relationships. AMOS does not produce output using

How to Measure an Unobserved Construct in SEM Model

With an unobservable construct, we are trying to use indicators to measure the concept.With any unobservable analysis, you will rarely be able to say you

Independent vs. Dependent Latent Variables in SEM Model

Independent variables (also called exogenous variables) are the constructs that influence another variable. Dependent variables (called endogenous variables) are constructs influenced by independent variables. Figure

Understanding Diagram Symbols in SEM Model

SEM uses diagrams to denote relationships to be tested. It is important that you understand what these diagram symbols mean because AMOS is going to

What Do I Do if My SEM Model Is Under-Identified?

If your model is under-identified, you have two primary solutions to fix this problem. First, you can reduce the number of proposed parameter estimates. This

How Do I Calculate the Degrees of Freedom of SEM Model?

As stated earlier, AMOS will calculate your degrees of freedom, but if you have a problem or want to verify another researcher’s work, you need

Identification With SEM Models

Identification in regards to a SEM model deals with whether there is enough information to identify a solution (or in this instance, estimate a parameter).

Assessing Reliability for SEM Model

After you have screened your data on both the respondent and variable levels, the next step is to assess the reliability of your indicators to

How Do I Address Missing Data?

Before we address what to do with missing data, we need to understand why data goes miss- ing. Missing data is typically classified in three

How Do I Assess If I Have Missing Data?

We have already addressed how to find respondent abandonment, but finding missing data that takes place in a random manner can be more challenging. To

Quick Reference to AMOS Functions

Shortcut Keys for AMOS Functions: F1 = Search Content Directory F2 = “Select one object at a time” button F3 = “Draw Observed Variable” button

Tips to Using AMOS More Efficiently

Tip 1: Change the AMOS graphics page from portrait to landscape. In the AMOS graphic win- dow, the program will default with the page in

AMOS Functions Listed as Icons in Pinned Ribbon

This function allows you to draw an observable variable.You can drag the square in the graph- ics window to the size of the box you

Overview of the AMOS Graphics Window

When you open the AMOS graphics program, the software will display a window that looks like it has a white page in the middle of

Understanding the Validity of Measures for SEM Model

After screening your data and assessing if the measures are reliable, you need to examine the validity of your constructs and indicators. There are numerous

Sample Size: How Much Is Enough?

With covariance-based SEM, one of the major assumptions is that this technique requires a larger sample size than other statistical techniques. SEM relies on tests

Modification Indices in SEM Model

Modification indices are part of the analysis that suggest model alterations to achieve a better fit to the data. Making changes via modification indices should

Model Fit and Fit Statistics of SEM Model

One of the advantages of SEM is that you can assess if your model is “fitting” the data or, specifically, the observed covariance matrix.The term

Setting the Metric in SEM Model

In SEM, each unobserved variable must be assigned a metric, which is a measurement range. This is done by constraining one of the factor loadings

Interpretation of Factor Loadings in CFA

The factor loadings in a CFA estimate the direct effects of unobservable constructs on their indica- tors.If an unstandardized factor loading is 2.0 for the

How Is a CFA Different From an EFA?

An exploratory factor analysis (EFA) is useful in data reduction of a large number of indicators and can be quite helpful in seeing if indicators

Introduction to Confirmatory Factor Analysis for SEM Model

Confirmatory factor analysis (CFA) is a statistical technique that analyzes how well your indi- cators measure your unobserved constructs and if your unobserved constructs are

How Do I Report My CFA Results of SEM Model?

One of the challenges in performing research is analyzing the data, but an equally challenging task is how to report my findings when I am

What If I Have a Standardized Factor Loading Greater Than 1 in SEM Model?

A standardized factor loading greater than 1 is stating that you are explaining more than 100% of the variance in an indicator. In this instance,

How to Calculate Composite Reliability for SEM Model

I have discussed earlier that reliability of indicators can be explored by calculating Cronbach’s alpha, but this test has had its detractors. Yang and Green

If I Have a Weak Factor Loading in SEM Model, Should I Drop It?

If you have a factor loading that is near or below the .70 threshold, it does not mean you need to drop the indicator from

Assessing Convergent and Discriminant Validity of Your Measures in SEM Model

After initially establishing that each indicator is loading on its respective construct and the model has an acceptable fit to the data, we now need

CFA Example in AMOS

Let’s say I want to test a simple model that has three unobserved variables. The first vari- able is a concept called “Adaptive Behavior”, which

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