# SEM

## Terms

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beta

The direct effect of an eta on another eta

effects of dependent variable on another dependent variable

beta matrix
effects of eta's on each other
calculating df's

# of variances=p

# of covariances= 1/2 [(p)*(p-1)]

total elements (#of variances plus # of covariances) 1/2[p*(p+1)]

degrees of freedom= number of total elements-#freed parameters

delta vector
q x 1 vector of measurement errors of x
determinant
the product of a diagonal.  indicates shared variance. large is bad.  if the determinant is zero or less, there is no solution (singular). if larger than zero, matrix is "positive definite"
disturbances
amount of variance unexplained
epsilon vector
a p x 1 vector of the measurement errors of y
eta vector
m x 1 vector of latent endogenous variables
free v fixed in a matrix

1= free to be estimated

0=fixed

Gamma

Effect of ksi's on etas

effects of indep variables on dep variables

gamma matrix
effects of ksi's on etas
identification
whether or not you can estimate all freed parameters given the known parameters
identity matrix

matrix with 1s on diagonals and zeros off diagonal

1 0 0

0 1 0

0 0 1

implied correlations
direct path between variables plus the sum of products of indirect paths plus non-causal
just identified model

(saturated model) has no df's

fit is perfect--cant be falsified

ksi
an exogenous (indep) latent variable
ksi vector
an n x 1 vector of latent exogenous variables
lambda-x
effects of ksi's on x's
lambda-x matrix
effects of etas on x's
lambda-y

effects of eta's on y's

lambda-y matrix
effects of etas on y's
matrix inverse
what you multiply a matrix by to get the identity matrix.  to see if your sigma matrix is close to the observed matrix, you multiply by the inverse and hope to get the identity matrix
Model Equations :  Structural
eta= beta (eta) +  gamma (ksi)+ zeta
Model Equations: Measurement (Y)
Y= lambda (eta)+ epsilon
Model Equations:  Measurement (X)
X= lambda (ksi) +delta
overidentified model
has enough degrees of freedom to estimate multiple solutions (df=positive)
Phi

covariance matrix of the ksi's

covariance between independent variables

along the diagonal

phi matrix
covariance of ksi's
Psi

covariance matrix of zetas

covariance of structural error with Psi's on diagonal

psi matrix
covariance of zeta
R^2
variance explained by whole model
theta-delta
covariance matrix of the disturbances (deltas) the measurement error of the X's
theta-epsilon

covariance matrix of epsilon's (measurement error of y's)

includes variances on diagonal (correlation with self) and any correlations between errors

theta-epsilon matrix
covariance of errors (epsilons) or deltas
underidentified model
not enough df's to generate a unique solution
x    vector
a  q x1 vector of observed exogenous variables
y vector
a p x 1 vector of observed endogenous variables
zeta matrix

m x 1 vector of residuals representing errors in the equation that relates eta and ksi

part of structural equation

a vector

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