Monte Carlo setup for Growth Model Po...
Message/Author
 Marc Glassman posted on Thursday, March 15, 2007 - 3:30 pm
In "How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power", (SEM v9, n4, 2002) a monte carlo analyis for a growth model with a covariate is discussed (p. 604). The mean and variance of the covariate, x, are 0.5 and .25, respectively (p. 604). However, when setting up the monte carlo analysis in MPLUS (p. 614) the mean and variance for the covariate, x, are fixed to 0 and 1 (p.614).

My question is simply why 0 and 1 instead of the values given on p. 604 of the article, i.e., .5 and .25? Does it possibly have to do with centering the covariate so that the intercept growth factor will estimated at the average value of the covariate ?

Any help/clarification would be much appreciated.
 Bengt O. Muthen posted on Thursday, March 15, 2007 - 5:11 pm
The 0, 1 values are for the continuous normal x that is then dichotomized at the mean using the CUTPOINTS = x(0) statement at the top of the input. The resulting dichotomous variable is 0.5, 0.25.
 Daniel Rodriguez posted on Tuesday, July 10, 2007 - 9:38 am
Hello,
I'm working on a Monte Carlo analysis for an ordered categorical variable with 6 thresholds (8 waves). I'm proposing development is linear. In the model population, I add variances with start values that increase over time. However, I'm unsure what to use as the scale start values. The coding from one of your examples includes the comment: "this sets the scale factors at the inverted SDs for the u* variables, so that the estimates are in the metric of the Delta parametrizations" How do I do this in my study?
 Bengt O. Muthen posted on Tuesday, July 10, 2007 - 12:34 pm
Act as if the u*s are continuous observed outcomes that have been categorized. Often the variance of such an observed continuous outcome increases over time. This implies a decreasing delta value (inverted SD).
 Daniel Rodriguez posted on Wednesday, July 11, 2007 - 7:32 am
Ok, thanks. Yes I understand that. I was wondering if the inverted SD meant taking the square root of the variance estimate and then dividing it into 1 (1/x). But that doesn't work out exactly as the values in the example. Am I wrong?
 Bengt O. Muthen posted on Wednesday, July 11, 2007 - 7:51 am
Yes, inverted SD is taking the square root of the variance and then computing 1 divided by that. Note that the variance is the total variance of the u*, not just the residual variance.
 Daniel Rodriguez posted on Wednesday, July 11, 2007 - 8:12 am
Ok, now I got it. Thanks for your help
DR
 Hanna posted on Sunday, November 25, 2007 - 2:32 pm
Hello, I am a graduate student using the 4.1 demo version to determine the sample size necessary for my dissertation research. I am using LGM to identify trajectories of a continuous outcome variable measured at 3 timepoints. I have 2 covariates (1 dichotomous, 1 continuous), and I also want to regress the slope growth factor on a continuous variable.

I've gotten a bit stuck using Monte Carlo syntax from Muthen and Muthen (2002), as well as from Chapter 11 of the MPlus User's guide. Could you point me in the right direction given that I'm using the demo version at the moment? Thanks!
 Linda K. Muthen posted on Monday, November 26, 2007 - 9:41 am
Most of the user's guide examples come with input for the Monte Carlo counterpart used to generate the data for the example. I would find an example in the user's guide close to what I want and start with the Monte Carlo counterpart for that example.
 Susan Collins posted on Saturday, January 06, 2018 - 3:01 am
I am setting up a monte carlo simulation study for a power analysis. I want to test the effect of a dummy-coded treatment variable on the slope factor of a growth model with 5 binary measured indicators. I have understood that even though the indicators are binary, the slope and intercept factors are continuous.

So, after accounting for the binary measured indicators, can I use the same slope coefficients as you discuss in your 2002 article, where .2 is a "medium" effect and .1 is a "small" effect for the slope growth factor? (I don't have access to any good pilot data.)

 Bengt O. Muthen posted on Saturday, January 06, 2018 - 12:05 pm
I believe the 2002 article considered effect size as the change in the slope divided by its SD. That would be relevant also in your case. It would be useful to also know how that translates to size of effect in terms of probability for a binary outcome, for instance at the last time point (a statistical consultant could help with that).
 Susan Collins posted on Sunday, January 07, 2018 - 12:44 am
As always, thank you for your quick response. Yes, your 2002 article indicated that the "medium" effect size (gamma=.2) is based on the differences in the slope means for the intervention and control groups divided by the slope SD. Based on the parameter values provided in the paper:

.2 / Sqrt (.04*.25 + .09) = .63

.2=regression coefficient for slope on the tx group
.04=.2^2 (i.e., the mean of the slope squared)
.25=intercept variance
.09=slope variance
.63=cohen’s d ("medium")

Do you have any articles to recommend on, as you say, "translating" or bridging the binary measured outcome (probabilities) to the continuous slope factor? I would much appreciate that! Masyn et al (2013) was very helpful with an orientation to growth modeling with binary outcomes but I couldn't find anything on conducting Monte Carlo simulation studies for growth models with binary measured outcomes. Whenever I don't have adequate pilot data, I struggle more with coming up with realistic parameter start values.

(Also, if you have a consultation service attached to your program, please let me know! I have wonderful stats savvy colleagues, but few who foray into this particular territory, and our available stats consults are biostatisticians who don't have expertise in monte carlo simulation studies for latent variable modeling.)
 Bengt O. Muthen posted on Sunday, January 07, 2018 - 3:16 pm
You don't have the correct description above. It should say:

.2=regression coefficient for slope on the tx group
.04=.2^2 (the regression coeff. of the slope growth factor regressed on x, squared)
.25= the x variance
.09= residual variance in the slope growth factor regression
.63=cohen’s d ("medium")

Regarding binary growth, see also our Topic 3 should course video and handout slides 185-212. To see how (growth) factors influence probabilities of binary outcomes, see Topic 2; this is discussed around slide 162. The story is about MIMIC modeling (CFA with covariates), but that is the same kind of model as a growth model with covariates.

We don't have time to provide consulting. But you may want to ask on SEMNET.
 Susan Collins posted on Sunday, January 07, 2018 - 4:39 pm
Thank you very much for the edits to my notes, and for the slide suggestions. That is really helpful!
 IW posted on Thursday, January 31, 2019 - 3:40 pm
Which paper 2002 paper is Susan referring to?
 Bengt O. Muthen posted on Thursday, January 31, 2019 - 4:15 pm
Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620. Mplus inputs and outputs used in this paper can be viewed and/or downloaded from the Examples page.