I am totally new to CFA, and am trying to use lavaan CFA for my master's thesis, which measures how disposition to risk-taking affects marijuana usage. I have 6 likert-scale variables (5-point) measuring risk-taking, and I am running CFA with two latent variables. All variables in my model come from survey data and are discrete, and each variable in my model is binary aside from the manifest items used for factor analysis, which as I said are on a 5-point scale. My data is highly non-normal and therefore I do not want to treat my risk-taking vars as continuous. All variables are ordered, and I have not provided any weights.
Here is my model:
myModel = '
# 1. latent variable definitions
cfaFA.score1 =~ RSK.kick.dangerous + RSK.test.risky + RSK.do.fright
cfaFA.score2 =~ RSK.frnd.exciting + RSK.explore.strange + RSK.break.rule
# 2. regression
MJ.try.if.legal ~ cfaFA.score1+cfaFA.score2+MJ.rsk.try.1or2+female+age.18.over+race.hispanic+race.black+pop.dens.med+pop.dens.high+geo.northeast+geo.south+geo.northcentral+father.edu.hs.grad+father.edu.clg.grad+mother.edu.hs.grad+mother.edu.clg.grad+hshld.father+hshld.mother+hshld.sib+money.other.11to50.week+money.other.over50.week+pol.belief.cons+pol.belief.lib
Here is my CFA call:
cfaFA = cfa(myModel, data = synth, ordered = ord.vars)
I know that lavaan CFA uses WLS estimator when variables are set as ordered. What I am unclear on is:
1) What exactly are the steps of the CFA function in this case? I need to understand this well to explain it in my thesis. What does it mean that the "estimator" is WLS - is this the regression type, or is WLS somehow used in estimating the latent factors?
2) What is the benefit of WLS over unweighted least squares?
3) How does the program calculate weights if no weight matrix is input?