MIMIC growth model
Message/Author
 Sanjoy Bhattacharjee posted on Thursday, September 20, 2007 - 12:52 pm
Prof. Muthen,

In short I have the following statistical/econometric model to estimate … For a particular time period "t", we have a simple MIMIC (multiple indicator multiple cause) model … i.e. Y(t) a vector, is regressed on a latent variable "eta", which in turn is regressed on a vector of strict covariate X(t) …. We have t=T number of time periods. For simplicity, let us assume the vectors Y and X are observed for each time period …

Q1. Our model requires "eta" to be estimated over the entire "T" time periods assuming errors are correlated over the time periods, and I want to estimate the path or trajectory of "eta" for each as well as for the entire sample of size "n", so that as an extension of the model, we can do some mixture analysis to see how the "locus of eta" could be grouped together ... could u kindly suggest me some article, if any, which had dealt with this type of situation ... I would like to coin this situation as MIMIC growth model

Q2. It would be very helpful if you kindly suggest me how to proceed with the code-syntax

Thanks and regards
Sanjoy
 Linda K. Muthen posted on Thursday, September 20, 2007 - 4:01 pm
Example 6.14 is a multiple indicator growth model. Without the growth it is a longitudinal CFA model. If you add covariates, it is a longitudinal MIMIC model. This can be extended to the mixture setting. You may be interested in the Factor Mixture Analysis papers on the website.
 Sanjoy Bhattacharjee posted on Friday, September 21, 2007 - 8:23 am

Regards
Sanjoy
 Michael Hallquist posted on Friday, April 08, 2011 - 7:53 am
Hi Bengt and Linda,

I have a mult. indic. growth model with three waves of data, which fits well and is meas. invar.

I am interested in predicting initial status and change using several variables (i.e., a long. MIMIC model). I have regressed the second-order growth factors on the covariates (some latent), now I would like to plot the magnitude of each effect.

In the usual LGM case, I would construct model-estimated trajectories by writing out the reg. eqn. for all covariates at their mean. Then one can plot a given covariate at the mean +/- 1 SD to see its effect.

But in the long. MIMIC case, I'm unsure of how the latent vars are scaled. The I growth factor has a fixed intercept at 0 and typically latent vars are scaled sd=1. TECH4 indicates I mean=1.019, sd=.63, and S mean=-.032, sd=.32.

I have a latent covariate, X, that is a factor from a CFA. TECH4 indicates X has mean=0, sd=.86. Using this factor as a covariate in the growth model, it has a est. of .135 for the I ON X effect.

With that setup:

1) Would I use the TECH4 for I in the growth model (1.019) as the B0 in reconstructing my estimated trajectory? And is the I variable scaled m=0, sd=1, or m=1.019, sd=.63?

2) Is the interpretation that an individual one sd above the mean on X (.135 * .86=.116) increases I by .116, which is a .18 sd (.116/.63) increase in I?

Thanks,
Michael
 Bengt O. Muthen posted on Friday, April 08, 2011 - 8:39 pm
1) I has intercept fixed at 0 but its mean is a function of the covariates as well and that is what TECH4 reports. Tech4 also gives the total I variance/

2) Yes

But perhaps it is easier to look at how the means of a key factor indicator changes over time. You get that by expressing the indicator in terms of the X (the indicator is a function of I and S which are in turn functions of X).
 EFried posted on Monday, April 08, 2013 - 8:08 am
Dear experts,

We want to compare two models. In model I, covariates influence change of a latent variable over time. In model II, the covariates are directly allowed to influence change of the indicators of the latent. This is the longitudinal equivalent of a MIMIC model, applied to change.

We were unable to find literature or MPLUS syntax regarding that rather specific question, and were wondering whether you had suggestions.

In 2007, Linda described a model (6.14) that could be adapted to create a longitudinal MIMIC model, but are not sure whether the model allows to predict _change_ (in contrast to predicting the latent at time 1 and then latent at time 2, setting paths of covariates to be equal across time).

Thank you
 Bengt O. Muthen posted on Monday, April 08, 2013 - 5:12 pm
If your change of a latent variable over time is represented by a growth model for the latent variable, you can simply regress the change (slope) factor on covariates.

If you are talking about latent difference modeling, you can also study change as a function of covariates - but you would have to consult SEMNET on how to do this.

In line with not being able to identify the influence of a covariate on both factors and their indicators directly in MIMIC modeling, I don't think you can do both in a change context either. But again, in this case such general modeling questions may be better suited for SEMNET.
 EFried posted on Tuesday, April 09, 2013 - 3:16 am
Thank you very much, Bengt!
 EFried posted on Sunday, April 28, 2013 - 6:37 am
Dear Prof Muthens,

We want to test DIF in a longitudinal model: do the risk factors x1-x3 have significant indirect effects on increases of indicators from time 1 to time 2, or do they only affect increases of the latent? We have been unable to find examples for this in MPLUS yet, could you take a look whether we specified this correctly?

Baseline model
-----------------
f1 by y1t1-y3t1; ! time 1
f2 by y1t2-y3t2; ! time 2

f2 ON f1 x1-x3;
f1 ON x1-x3;

y1t2 ON y1t1;
y2t2 ON y2t1;
y3t2 ON y3t1;

y1t1 with y2t1; ! determined through mod indices
y2t2 with y3t2; ! determined through mod indices

The DIF model
----------------

y1t2 ON x2;
y2t2 ON x1 x2;
y3t2 ON x3;

MODEL INDIRECT:
y1t2 IND f2 x2;
y2t2 IND f2 x1 x2;
y3t2 IND f2 x3;

(this is the final DIF model, a previous full DIF model included all effects of all x on all yt2, we dropped the non-significant ones as recommended in cross-sectional DIF models)

Output looks ok and we don't get errors, but we're not sure if we made sure to implement everything that is required.

Thank you
E.
 Linda K. Muthen posted on Sunday, April 28, 2013 - 9:59 am
See the beginning of the multiple indicator growth model in either the Topic 3 or Topic 4 course handout on the website. This shows how to test for measurement invariance in a longitudinal model.