As Crhistoph suggested, Barbara's book is very simple to follow, specifically for using AMOS. The book also provides data set in its companion website which is. I think the classical book of Kline can help you. "principles and practice of Structural Equation Modeling" by Rex B Kline. It covers several practical aspects with a. Arjun, in addition to SSI's publications Barbara Byrne's book (Structural Equation Modeling With Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and.
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how to best use structural equation modeling (SEM) to answer critical all applications of SEM described in this book are picture perfect, but neither are actual. Unlike most SEM texts, this book is notable for making a sophisticated, often- difficult statistical technique understandable to non-statisticians without watering . Randall Schumacker and Richard Lomax's book introduces structural equation modeling (SEM) to researchers with some previous background in applied.
Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling SEM. Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a flexible tool to analyze their data with an easy-to-use interface and graphical displays of data and analysis results. Key features: Presents a useful reference guide for applications of SEM whilst systematically demonstrating various advanced SEM models, such as multi-group and mixture models using Mplus. Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes. Provides step-by-step instructions of model specification and estimation, as well as detail interpretation of Mplus results.
The book demonstrates both of these approaches. Throughout the text, the examples use the sem command.
Each chapter also includes brief discussions on drawing the appropriate path diagram and performing estimation from within the SEM Builder. The first two chapters introduce the building blocks of SEM. Then, building on these concepts, Acock demonstrates how to perform confirmatory factor analysis, discusses a variety of statistics available for assessing the fit of the model, and shows a more general measurement of reliability that is based on confirmatory factor analysis.
Chapter 2 focuses on using SEM to perform path analysis.
It includes examples of mediation, moderation, cross-lagged panel models, and nonrecursive models. Numerous examples that help readers match research questions to appropriate analyses and interpret results. Reviews practical issues related to model specification and estimation to reinforce connections. Analyzes continuous and discrete binary and ordinal variables throughout for breadth not found in other sources.
Reviews key SEM concepts for those who need a refresher Ch. Emphasizes how to apply and interpret each model through realistic data examples. The chapters can be read out of order but it is best to read chapters 1 — 4 first because most of the later chapters refer back to them.
The book opens with a review of latent variables and analysis of binary and ordinal variables. Chapter 2 applies this information to assessing longitudinal measurement invariance. SEM tests of dependent means and proportions over time points are explored in Chapter 3, and stability and change, difference scores, and lagged regression are covered in Chapter 4. The remaining chapters are each devoted to one major type of longitudinal SEM -- repeated measures analysis models, full cross-lagged panel models and simplex models, modeling stability with state-trait models, linear and nonlinear growth curve models, latent difference score models, latent transition analysis, time series analysis, survival analysis, and attrition.
Missing data is discussed in the context of many of the preceding models in Chapter Yes, remembering that dichotomous and ordered categorical measures can fall under the class of quantitative data. Yes, provided sample size issues are addressed. That is, some time series analyses and other analyses at aggregated levels can have samples too small for these methods.
No, moderation implies an interaction type of effect between variables. Chapter 12 will address moderating effects. Equivalent models are those that predict the exact same pattern of relationships between measures. For example, Job—Success—Family is mathematically equivalent to Figure 1. Because the models always start with theory, one should have chosen a model from among equivalent ones that matches the hypothesized relationships.
That of course does not make the model correct, but it affirms plausibility of the theory. Chapter 2.
Yes, technically speaking, path analysis always uses standardized data. Yes, for identified or over-identified models, multiple regression yields optimal estimates. Yes, path coefficients are partial regression coefficients. Again speaking technically, no , for when data are longitudinal, covariance matrices need to be analyzed. On the other hand, if nonstandardized coefficients are examined, then regression techniques can be used to analyze longitudinal data.
Those coefficients sometimes were called path regression coefficients in the path analysis literature. Degrees of freedom for path models are determined by the number of pieces of information that are available to use for solving for path coefficients.
In the same way that subjects are bits of information for many analyses, each correlation covariance is one piece of information for path models. Degrees of freedom provide the opportunity for models to diverge from the data, and therefore allow the possibility of model disconfirmation.
Under-identified models cannot be solved. If their plausibility is of interest, they need to be reconceptualized to make them identified. Surprisingly, the answer is Yes, even though there are few cases in which they are appropriate, for they are far inferior to the latent variable structural equation techniques described later in this book.
Chapter 3. Because path analysis is regression analysis, it analyzes correlation or covariance matrices that are used in regression analysis. Partial correlation attempts to completely eliminate the relationships of the controlled variable with the remaining variables and their relationships with one another, while partial regression attempts to spread common variance across the various predictors.
Partial correlation would be picked to look at residual relationships after removing some variable or variables. Although path analysis approaches do not formally talk about working with partial correlation matrices, there may be instances in which, due to sample size limitations, control variables like age or gender would need to be partialed out so the sample is sufficient for SEM techniques.
Remember, however, that decisions to partial need to be guided theoretically, and therefore likely should not be done if the variable to be partialed is expected to display different causal structures at different levels. The signs of the nonstandardized coefficients will be the same as the standardized coefficients, and the nonstandardized values are very descriptive insofar as they describe the relationship in raw score units.
Stepwise regression can be guided by theory, and is when used for decomposing effects. If it is not, yes, it can be misleading. Remember, however, that at the last step of the regression analysis, if all variables are entered into the equation, the order of entry used does not matter; all orders of entry yield the same final outcome provided the same variables are in the equation.
Yes, the logic of decomposition of effects is the same across all different types of SEM techniques. The matrix form is very appealing, for it works for over-identified as well as just-identified models. The other approaches work as well, requiring that coefficients that are omitted from the model take on a value of 0. ANOVAs are not used, although path analysis can be used to model experimental studies.
Path modeling can be particularly effective if some variable is viewed as a mediating variable. There it can be used to test plausibility of a mediation model. It also can be valuable if there are questions about the conceptual variable that is being assessed by some independent or dependent variable. It may be possible to use SEM techniques to aggregate measures into conceptual variables. The information on variability within the sample is very important, and it is lost in converting to correlations.
Here, if we are talking about assumptions of regression, viz. As will be explained later, tests of fit are all based upon residuals, the part of relationships that are not accounted for by models.
Sometimes, it will be obvious by looking at a correlation matrix that a hypothesized model will not fit. For example, if a set of four measures is hypothesized as assessing a single construct, but two of the measures have a correlation twice that of all the others, it is clear that a single factor model will not work well.
Other times, the pattern of relationships will be more complicated, and can be examined only through looking at the residual matrix and the measures of model fit.
To go from standardized to nonstandardized coefficients or vice versa, it is the standard deviations, not the standard errors, that are used. Yes, there is a fairly simple conversion from one to the other that requires only dividing by or multiplying by a ratio of two standard deviations. There has been a controversy in the literature about the meaning of standardized versus nonstandardized coefficients and how to explain that difference. From my perspective, it is most important to think of it conceptually.
Standardized coefficients describe relations in standard deviation units, whereas nonstandardized coefficients describe relations in real raw score units. Decisions about relationships between methods should be driven at the data collection stage. At the same time, one needs to trade off difficulty in collecting data where methods do not exert influence on [Page ] answers versus simplicity in getting needed data. If one decides that the best decision is to collect data from measures that have method variance, then that variability needs to be modeled so variability can be adequately partitioned.
Systematically attending to method variability is clearly as important today as it was in the past. Using multiple methods is highly desirable. Yet, as will be described in Chapter 7 , MTMM matrices produce problems of estimation in certain types of models, which reduces somewhat their value. Chapter 6. Lag refers to the passage of time. The exact amount of time varies with the nature of the conceptual issues. I suspect that I am guilty of accepting ways of talking about stability that do not fit with some other uses of terms, and, more importantly, I have not been as clear in my usage as I should have been.
To clarify hopefully: Stability as I have used it refers only to single variables. In the absolute sense, stability means absence of change in some variable across some time period.
With respect to covariances, however, stability means only that the relative position of a group of individuals on some dimension does not change. For example, if all children in a class grew at a common rate, their height scores would all increase by a constant, and their heights at the first time before growing would correlate perfectly with their heights at the second time after growing , and height would be perfectly stable.
Said differently, height at time 1 perfectly predicts height at time 2. Finally, if a relationship between 2 variables is called stable, then their covariance should not have changed from some point in time to some later time. Factor analysis and AIC. Psychometrika , 52 , — Arbuckle , J. Analysis of moment structures. Psychometrika , 59 , — AMOS users'guide: Version 3.
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