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 factor identification Illustrated use of the automated multigroup procedure in testing invariance Link between multigroup dialog box and automated labeling of Amos graphical models In the years since the

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 on the Amos multiple-group automated approach Interpreting statistical versus practical evidence of tests for invari­ance based on the Amos multiple-group automated approach In Chapter 4, I highlighted several problematic

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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 size Comparison of the correlated traits-correlated methods (CT-CM) and correlated traits-correlated uniquenesses (CT-CU) multitrait- multimethod models Warning messages regarding inadmissible solutions and negative variances Construct validity embraces two modes

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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 of the Amos plug-in menu Incorporating a time-invariant predictor of change Use of Amos Graphics interface properties option Behavioral scientists have long been intrigued with the investigation of change.

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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 versus bootstrap Ml estimates Bollen-Stine bootstrap option Two critically important assumptions associated with structural equation modeling (SEM) in the analysis of covariance and mean structures are that the data

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 to dealing with missing data Missing (i.e., incomplete) data, an almost inevitable occurrence in social science research, may be viewed either as a curse or as a gold mine

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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 Specification: The first step in SEM analysis is the model specification. It is performed prior to data collection and data modelling. This involves the devel- opment of a theoretical

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 a single procedure but rather a family of related statistical techniques. This family of analysis tech- niques examines the measurement properties of a variable along with the interrelationships between

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 and assessing the “struc- ture” of a specified model along with its relationships. Before we move forward, a discussion is warranted on concepts such as variance, covariance, and correlation

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 essentially derived from the covariance. With a covariance analysis, the calculated values do not have a definable range or limit. If you have two variables that are measured on

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 is used quite often with SEM. As stated earlier, SEM uses a covariance matrix as its input, so you are essentially looking at cor- relations between variables to determine

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 collected to test how well the model fits the data, thus trying to “confirm” the researcher’s hypotheses about how constructs influence one another. Joreskog (1993) outlines how SEM testing

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 to understanding a phenomenon of interest and ulti- mately help to explain why two variables are influencing each other. Sadly, it seems like many SEM models are conceptualized first

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: Multivariate Normal Distribution of the Indicators—there is an assumption that the data has a normal distribution. Dependent variables need to be continuous in SEM—while the independent variables do not

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 make you draw out your concep- tual model. One of the frustrating aspects of SEM is that there are often multiple terms that mean the exact same thing.You can

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 1.6 Source: Thakkar, J.J. (2020). “Procedural Steps in Structural Equation Modelling”. In: Structural Equation Modelling. Studies in Systems, Decision and Control, vol 285. Springer,

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 are capturing the “true” or actual score without some degree of error. Thus, an indicator is a function of the “true” score plus error: Construct Indicator =True or Actual

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 Greek notations, but you need to be familiar with them so you can understand the results from other SEM programs. What Do All These Greek Symbols Mean? Latent Constructs

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 also need to assess if you have any missing data. Once your data has been keyed into a data software program like Excel, SAS, or SPSS, the first thing

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 of an acceptable range, you need to go to your SPSS file, select the “Analyze” option at the top, and then select “Descriptive Statistics”. Next, you will select the