mxLISRELObjective(LX=NA, LY=NA, BE=NA, GA=NA, PH=NA, PS=NA, TD=NA, TE=NA, TH=NA,
TX = NA, TY = NA, KA = NA, AL = NA,
dimnames = NA, thresholds = NA, vector = FALSE, threshnames = dimnames)
Matrix | Word | Abbreviation | Dimensions | Expression | Description |
\(\Lambda_x\) | Lambda x | LX | NX x NK | Exogenous Factor Loading Matrix | |
\(\Lambda_y\) | Lambda y | LY | NY x NE | Endogenous Factor Loading Matrix | |
\(B\) | Beta | BE | NE x NE | Regressions of Latent Endogenous Variables Predicting Endogenous Variables | |
\(\Gamma\) | Gamma | GA | NE x NK | Regressions of Latent Exogenous Variables Predicting Endogenous Variables | |
\(\Phi\) | Phi | PH | NK x NK | cov(\(\xi\)) | Covariance Matrix of Latent Exogenous Variables |
\(\Psi\) | Psi | PS | NE x NE | cov(\(\zeta\)) | Residual Covariance Matrix of Latent Endogenous Variables |
\(\Theta_{\delta}\) | Theta delta | TD | NX x NX | cov(\(\delta\)) | Residual Covariance Matrix of Manifest Exogenous Variables |
\(\Theta_{\epsilon}\) | Theta epsilon | TE | NY x NY | cov(\(\epsilon\)) | Residual Covariance Matrix of Manifest Endogenous Variables |
\(\Theta_{\delta \epsilon}\) | Theta delta epsilson | TH | NX x NY | cov(\(\delta, \epsilon\)) | Residual Covariance Matrix of Manifest Exogenous with Endogenous Variables |
\(\tau_x\) | tau x | TX | NX x 1 | Residual Means of Manifest Exogenous Variables | |
\(\tau_y\) | tau y | TY | NY x 1 | Residual Means of Manifest Endogenous Variables | |
\(\kappa\) | kappa | KA | NK x 1 | mean(\(\xi\)) | Means of Latent Exogenous Variables |
\(\alpha\) | alpha | AL | NE x 1 | Residual Means of Latent Endogenous Variables |
#####------------------------------#####
##### Factor Model
mLX <- mxMatrix("Full", values=c(.5, .6, .8, rep(0, 6), .4, .7, .5),
name="LX", nrow=6, ncol=2,
free=c(TRUE,TRUE,TRUE,rep(FALSE, 6),TRUE,TRUE,TRUE))
mTD <- mxMatrix("Diag", values=c(rep(.2, 6)), name="TD", nrow=6, ncol=6,
free=TRUE)
mPH <- mxMatrix("Symm", values=c(1, .3, 1), name="PH", nrow=2, ncol=2,
free=c(FALSE, TRUE, FALSE))
# Create a LISREL objective with LX, TD, and PH matrix names
objective <- mxLISRELObjective(LX="LX", TD="TD", PH="PH")
testModel <- mxModel(model="testModel", mLX, mTD, mPH, objective)
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