Alan Acock posted on Wednesday, February 11, 2009 - 12:53 pm
I want to know how to estimate the score on an observed outcome and get a confidence interval on the estimate when I have an exogenous latent variable with a direct effect and an indirect effect on the outcome variable.
Here is an example. Campus wide intervention to reduce binge drinking behavior. 1. exogenous latent variable is exposure to the content using three indicators. 2. intervening latent variable is attitude toward binge drinking. 3. A second exogenous latent variable is peer pressure to binge drink and it has a direct effect on outcome. outcome is a measure of binge drinking.
I would like two predictions. 1. a person who has a score of zero on each indicator of exposure, hence has zero on the latent exposure variable 2. a person who has an average score on the latent exposure variable.
I want a confidence interval fore each estimation.
where y is the binge drinking outcome, f_a is the attitude factor, f_p is the peer pressure factor, and f_e is the exposure factor. So you insert 2 into 1 to get the prediction equation (leaving out the e's) using estimated a's and b's. You can express this equation in Model Constraint, defining parameter labels in the Model command. The Model constraint equation would use (condition on) certain f values and get the predicted y. It will also give you a SE taking into account the (co-)variation in the estimates. This SE can then be used to create a CI.
The score on the factor would not be zero for zero indicator values unless the intercepts for the indicators were zero (which they would be if the indicators are centered).