I am trying to run an SEM with the Theory of Planned Behavior. This is what my model looks like and that I want to test:
Attitude, Subjective Norm, Perceived Behavioral Control and Intention are latent variables, measured each by 4 indicators (questions) on a 7point likert scale. The Behavior is an observed binary variable (0=did not show behavior / 1 = did show behavior).
I treat the likert-scale inputs as continuous variables, but I am unsure about how to deal with the real behavior (0/1) as binary variable?
My code looks like:
mymodel <- "
attitude =~x1 + x2 + x3 + x4
subjectivenorm =~ x5 + x6 + x7 + x8
behcontrol =~ x9 + x10 + x11 + x12
intention =~ x13 + x14 + x15 + x16
intention ~ attitude + subjectivenorm + behcontrol
behavior ~ intention"
In this context, I have two questions:
- I have seen that some use „ordered“ to treat these variables as ordered (ordinal) variables - is that the only way to do it?
- e.g., fit <- sem(model = mymodel, data = df, ordered = "behavior") - like this?
- Why do I need to indicate my binary variable as ordinal variable, although it is categorical?
- What is the interpretation of the betas?
- I am not quite sure how lavaan actually scales the latent variable?
- How can I check the "values" of the latent variables?
- If beta/ the regression coefficient of Attitude—>Intention is "0.4" - are we talking about 1 unit increase in Attitude —> "0.4" unit increase in Intention? (if so, what is the scale / units?)
- Or are we talking about 1 standard deviation increase in Attitude —> "0,4" standard deviation increase in Intention?
- (Where do I find the mean and SD of my latent variable?)
- How can I interpret a 0.4 from intention --> behavior?
- A 1 unit increase in Intention --> "0.4" unit increase in behavior? (Again here, the interpretation also depends on the scale of the latent variable intention - if intention as latent variable has the same likert scale of 1 to 7, it is something different as to whether if its scale was 0 to 1)
I first did quite some research online and in different books and simply could not find the answers I needed, so I appreciate very much any comment, advice, suggestion, reading tip, etc.
- What is the interpretation of the betas?Same as any regression slopes. But the effect of intention on binary behavior is a probit regression slope, so its effect is in the scale of a normally distributed latent response (consult the standardized output to assume it is a z score, which is the default in lavaan, so it probably matches the unstandardized slope).
In Lavaan - where do I find the beta-0? / what is the intercept for my probit regression?