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
Observed variables are symbolized by squares or rectangles.
103
84
121
76
. . .
97
81
Observed
Variable
Latent Variables are symbolized by Circles or ellipses.
106
78
115
80
. . .
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 doubleheaded arrows.
"Cor / Cov"
Arrow
Observed
Variable B
"Cor / Cov"
Arrow
Observed
Variable A
103
84
121
76
. . .
97
81
101
90
128
72
. . .
93
80
Latent
Variable B
Latent
Variable A
106
78
115
80
. . .
93
83
104
79
114
79
. . .
92
81
"Causal" or "Predictive" or “Regression” relationships between variables are represented by singleheaded arrows
Latent
Variable
Observed
Variable
"Causal"
Arrow
Latent
Variable
Observed
Variable
"Causal"
Arrow
Latent
Variable
"Causal"
Arrow
Latent
Variable
"Causal"
Arrow
Observed
Variable
Observed
Variable
Exogenous Observed Variables
"Correlation"
Arrow
Observed
Variable
"Causal"
Arrow
Observed
Variable
Exogenous variable connect to other variables in the model through either a “causal” arrow or a correlation
"Correlation"
Arrow
Latent
Variable
"Causal"
Arrow
Latent
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
error
Random
error
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 catchall 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.
GREV
GREQ
r_{VQ}
2. Simple correlations between three observed variables.
GREV
GREQ
GREA
r_{VQ}
r_{QA}
r_{VA}
3. Simple regression of an observed dependent variable onto one observed independent variable.
Note that the endogenous variable is caused in part by catchall influences.
Note that the endogenous variable is caused in part by catchall influences.
GREQ
P511G
e
B or
4. Multiple Regression of an observed dependent variable onto three observed independent variables.
GREV
B_{V} or _{V}
P511G
GREQ
B_{Q} or _{Q}
e
UPGA
B_{U} or _{U}
