Predicting Dummy Covariate from LGM M...
Message/Author
 Aaron Elkins posted on Friday, October 09, 2009 - 11:58 am
I'm a new Mplus user that has been slowly replacing my repeated measures ANOVA models with LGM models.

To clarify, here is my model:

MODEL: i s | avj3@0 avj4*1 avj5@2 avj6*3
avj9*6 avj10@7 avj11@8 avj12@9;

i s ON female cond age ;

(Note: The above model is missing some important behavioral covariates for simplicity)

The above model corresponds to a recent experiment that involved subjects being instructed to alternate between deceptive and truthful responses to questions over time.
Each time point represents a vocalic behavior measure (avj) at each time point. The "cond" dummy covariate denotes if the participant was lying or telling the truth.

While the relationship between the covariates, time, and the behavioral response variables are interesting. My audience will want to know how this model help predict the lie or truth condition.

What would be the best way to use my model which currently predicts the continuous behavior measure to predict the dichotomous "cond" dummy covariate instead?

Thank you for any help or advice you can provide on modeling these kinds of data with Mplus.
 Bengt O. Muthen posted on Friday, October 09, 2009 - 5:23 pm
Depending on your cond design, you may find it useful to look at the Topic 5 handout pages 32-33 on randomized response modeling and the SEM journal reference given there which uses Mplus.

It sounds, however, as if the cond status is not known or randomized and perhaps in addition it changes randomly over time. Without knowing the cond status for some individuals it would seem hard to predict the cond status from the avj.
 Aaron Elkins posted on Saturday, October 10, 2009 - 3:53 pm
Dr. Muthen,

Thank you for your prompt response. Regarding the condition assignment in the experiment.

We had all subjects follow either one of two randomly assigned sequences over the 8 questions or time points in an interview:

(T=truth, L=lie)
Seq 1: LL TT TT LL
Seq 2: TT LL LL TT

During the interview they were instructed to lie via a teleprompter that was obscured from their interviewer.

The questions I am trying to answer are, does lying or telling the truth first affect your behavioral trajectory on subsequent questions.

Are there mean differences between liars and truth tellers on these behavioral measurements after accounting for individual differences (conditional model) that contribute to slope/intercept variance. Looking overall and at the individual question level (8 time points).

Additionally, I want to identify question effects, which time points resulted in departures from the linear trajectory.

After answering or at least starting to address the above questions, my audience will want to see how well the model can predict deception over an above regular logistic regressions which do not consider random effects.

Thanks again for your response. I will look at the Topic 5 handouts you recommend I review.

Kind Regards,

Aaron
 Bengt O. Muthen posted on Sunday, October 11, 2009 - 12:09 pm
I see; so the lie/thruth status is known, which it isn't in the article I referred to.

I don't see the growth modeling angle that you mention ("behavioral trajectory"). It is not clear to me that there is a developmental process at hand. Without knowing the context, it seems like the lying can make the outcome jump up and down at will.

The responses are correlated over time for a given subject, but that can be handled in any multivariate model. For instance, a latent class or factor mixture model could be applied to look at mean profiles - the "mean differences between liars and truth tellers" that you mention.
 Aaron Elkins posted on Sunday, October 11, 2009 - 12:39 pm
You are correct the outcome does jump around quite a bit. My thought process in using the growth model was to show that including individual difference covariates and the lie/truth treatment as a dummy variable we can smooth the curve by accounting for the variance in growth and show a particular trajectory.

The Interpersonal Deception Theory, predicts that non-strategic behaviors or cues to deception decrease over time. Is it an incorrect interpretation of my growth model with a good fit to the data and most of the variance in the slope explained and significant, to interpret a negative slope as supporting this prediction?

And further, to recenter the model around the different time points to see if the lie condition is significant for each question and report intercepts for liars and truth tellers.
 Aaron Elkins posted on Sunday, October 11, 2009 - 1:25 pm
I allowed the some slope loadings to be estimated, after reviewing the mod indices to suggest questions that causes significant departures from the smoothed linear trajectory. And was using this to identify questions that have effects on the response variable and should be further explored.

Thanks again for your help.