Binary, ordinal and nominal variables are considered categorical (not continuous). It makes a big difference if these categorical variables are exogenous (independent) or endogenous (dependent) in the model.
If you have a binary exogenous covariate (say, gender), all you need to do is to recode it as a dummy (0/1) variable. Just like you would do in a classic regression model. If you have an exogenous ordinal variable, you can use a coding scheme reflecting the order (say, 1,2,3,…) and treat it as any other (numeric) covariate. If you have a nominal categorical variable with $K > 2$ levels, you need to replace it by a set of $K-1$ dummy variables, again, just like you would do in classical regression.
The lavaan 0.5 series can deal with binary and ordinal (but not nominal) endogenous variables. There are two ways to communicate to lavaan that some of the endogenous variables are to be treated as categorical:
declare them as ‘ordered’ (using the
ordered function, which is part of
base R) in your data.frame before you run the analysis; for example, if you
need to declare four variables (say,
ordinal in your data.frame (called
Data), you can use something like:
Data[,c("item1", "item2", "item3", "item4")] <- lapply(Data[,c("item1", "item2", "item3", "item4")], ordered)
ordered argument when using one of the fitting functions
(cfa/sem/growth/lavaan), for example, if you have four binary or ordinal
item4), you can use:
fit <- cfa(myModel, data = myData, ordered = c("item1","item2", "item3","item4"))
If all the (endogenous) variables are to be treated as categorical, you can
ordered = TRUE as a shortcut.
ordered= argument is used, lavaan will automatically switch to the
WLSMV estimator: it will use diagonally weighted least squares (
estimate the model parameters, but it will use the full weight matrix to
compute robust standard errors, and a mean- and variance-adjusted test
stastistic. Other options are unweighted least squares (ULSMV), or pairwise
maximum likelihood (PML). Full information maximum likelihood is currently not