Observed Variable
Endogenous variable (En ~~ In)
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- Correlations or covariances between variables are represented by double-headed arrows.
- "Causal" or "Predictive" or “Regression” relationships between variables are represented by single-headed arrows
- Exogenous Latent Variables
Endogenous variable (En ~~ In)A variable whose values are explained within the theory with which we’re working. We account for all variation in the values of endogenous variables using the constructs of whatever theory we’re working with. Causes of endogenous variables originate within the model. Basic EFA, CFA, SEM Path Analytic Notation
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Latent Variables are symbolized by Circles or ellipses. 106
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93 83 Latent Variable Values of individuals on latent variables are not observable, hence the dimmed text. Correlations or covariances between variables are represented by double-headed arrows."Cor / Cov" Arrow
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Exogenous variable connect to other variables in the model through either a “causal” arrow or a correlation
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Latent
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Variable Exogenous latent variables also connect to other variables in the model through either a “causal” arrow or a correlation Endogenous Observed Variables - Endogenous Latent Variable Random
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Observed Variable Latent Variable "Causal" Arrow
"Causal" Arrow
Endogenous variables connect to other variables in the model by being on the “receiving” end of one or more “causal” arrows. Specifically, endogenous variables are typically represented as being “caused” by 1) other variables in the theory and 2) random error. Thus, 100% of the variation in every endogenous variable is accounted for by either other variables in the model or random error. This means that random error is an exogenous latent variable in SEM diagrams. Random error is a catch-all concept representing all “other” things that are affecting the endogenous variable. Summary statistics associated with symbols Mean, Variance Mean, Variance Observed Variable
Latent
Variable Our SEM program, Amos, prints means and variances above and to the right. Typically the mean and variance of latent variables are fixed at 0 and 1 respectively, although there are exceptions to this in advanced applications. "Correlation" Arrow
r or Covariance "Causal" Arrow
B or Path Diagrams of Analyses We’ve Done Previously Following is how some of the analyses we’ve performed previously would be represented using path diagrams. 1. Simple correlation between two observed variables. GRE-V GRE-Q rVQ 2. Simple correlations between three observed variables. GRE-V GRE-Q GRE-A rVQ rQA rVA 3. Simple regression of an observed dependent variable onto one observed independent variable. Note that the endogenous variable is caused in part by catch-all influences. Note that the endogenous variable is caused in part by catch-all influences. GRE-Q
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4. Multiple Regression of an observed dependent variable onto three observed independent variables. GRE-V
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