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 Chuck Cleland posted on Monday, December 23, 2002 - 7:18 am
I am trying to estimate power for a relatively simple LGM. The model specifies linear growth over 4 time points which is unrelated to intial status but dependent on a single covariate (a dummy variable). Here is what I think the correct Mplus specification of the model is:

i BY y1-y4@1;
s BY y1@0 y2@1 y3@6 y4@12;
[i*0 s*.1];
i WITH s*0;
i ON x1*.0;
s ON x1*.125;

I think this corresponds to a squared multiple correlation for the slope factor of about .04, ( (.125 - 0) / (.09^.5)). The Monte Carlo approach to power for the s ON x1 effect suggests that power is only .75 with 200 subjects (no missing data, normal data). I then used the Satorra-Saris method on the same model and find .80 power for only 52 subjects. The approximate noncentrality parameter obtained when misspecifying s ON x1 to 0 was 75.760 with n = 500).

1 - pchisq(qchisq(.95, df=1), 1, (52/500)*75.760)
= 0.801503

Are there mistakes in my use of either MC or SS? Could anyone comment on the differences I seem to get using the MC and SS approaches? I can provide the Mplus input files for either MC or SS.


 bmuthen posted on Monday, December 23, 2002 - 9:26 am
Muthen-Curran (1997) compared SS with MC power; see p. 383. They found reasonably good agreement at total n=200 (with a 50-50 split on the x variable). SS may be off at the low n=52. What does SS give at n=200?
 bmuthen posted on Monday, December 23, 2002 - 9:56 am
Your results do seem a bit strange. If you send me the input for both the MC and SS runs (all steps for SS) I'll take a quick look to see if I spot any input errors.
 Linda K. Muthen posted on Monday, December 23, 2002 - 2:13 pm
In the MC power calculation, you specified the mean of x1 to be .5 in the MONTECARLO command and cut it at zero resulting in a mean of .691. Note that the x1 mean in the MONTECARLO command refers to the mean of x1 before it is cut. In the SS power calculation, you have a mean of .5 for x1. When I change the mean for x1 from .5 to 0 for the MC run, so that the mean for the x1 variable used in the analysis is .5, the power is .889 at n=250 which is probably closer to the SS power. I am sending you the output.
 wendy posted on Thursday, July 27, 2006 - 8:41 am
Hi, Dr. Muthen:I have a question in terms of estimating effect size of slope factor regressed oin a covariate equivalent to your paper Muth and Muthen 2002. There, the covariate predicting growth rate factor is a categorical variable, I just wonder if the covariate is continuous, how to calculate the effect size of the regression coefficient,that is slope regressoned on x.
 Bengt O. Muthen posted on Thursday, July 27, 2006 - 4:46 pm
I don't know that there is generally agreed upon way to do this. But how about looking at mean differences in the outcome (divided by SD) for a 1 SD change in the continuous covariate? Or any amount of change that can be seen in practice.
 anonymous posted on Saturday, February 14, 2009 - 1:54 pm
I recently conducted a multiple group LGM analysis (2 groups, n=72 and n=69, total N=141). The model includes four time-invariant covariates (correlated), an intercept, linear slope, and quadratic slope, with seven time points contributing to their estimation. In all, the model includes 7 dependent variables, 4 independent variables, and 3 continuous latent variables.
I am wondering if there is any way I can justify adequate power of this analysis without conducting a Monte Carlo Power Analysis (as this might be beyond my skill level). Do you know of any literature or other output data I can use to support an analysis of this type with my sample size?
 Linda K. Muthen posted on Sunday, February 15, 2009 - 10:56 am
I know of no way to support this other than a Monte Carlo study.
 anonymous posted on Monday, February 16, 2009 - 2:06 pm
Hello again,
Thanks very much for your suggestion. I am now attempting to conduct the Monte Carlo analysis, but running into some warnings and errors due to incorrect syntax. Here are two issues:
1. Duplicate warnings for my MODEL and MODEL POPULATION command
Is there a way to address these? I am guessing that I've incorrectly specified the MODEL and MODEL POPULATION for the 2-group LGM.
2. And the following error: ERROR in MODEL MISSING command No MODEL statements for MODEL MISSING. True values must be specified.
The model is missing data on dependent variables, however I am not certain what to specify for the Model Missing command for a 2-group model.
Any help or examples would be very much appreciated.
 Linda K. Muthen posted on Monday, February 16, 2009 - 4:57 pm
Please send our output and license number to support@statmodel.com.
 Hemant Kher posted on Monday, November 01, 2010 - 7:18 am
Hello Professors Muthen & Muthen,

I fit a growth model to a sample n=150. The measured variable is self efficacy which is the sum of all items at each of the 4 time points. The intercept and the slope have means of 65 and 6 respectively, and the growth is non-linear with slopes of 0, 0, 1 and 2 (no change in periods 1 and 2).

Realizing that effect size is large (regression coefficient of 6), can I use the Monte Carlo procedure to determine minimum sample size for a power of 0.8 or more? Is it reasonable to input observed means (and variances and other required parameters) from my analysis for this?
 Linda K. Muthen posted on Monday, November 01, 2010 - 9:05 am
You can use your sample values as population parameter values if you believe they are good approximations of the population values. With a sample size of 150, this may or may not be a reasonable assumption. This may be the best information you have about your population.
 Hemant Kher posted on Monday, November 01, 2010 - 9:26 am
Thank you for your response Professor Muthen. Yes, this is the best guesstimate of population parameters as prior studies have only considered 2-point designs and have not used LGM for analysis.

I also tried other sample sizes given my estimated paramter values to get an idea as to when the sample size would be too small based on a power of 0.80. It seems that a sample of 150 appears adequate.
 Hemant Kher posted on Wednesday, November 10, 2010 - 2:56 pm
Hello Professors Muthen & Muthen,

I am writing about the issue of power analysis. Your answer above was very helpful. Just to confirm:

(1) the final column in the Monte Carlo output, labeled %Sig Coeff is the power estimate (% times the null hypothesis of zero was rejected)

(2) I also assume that the power analysis also holds for other outcomes, such as the variance of the intercept and slope, as well as the covariance between them

Thank you as always for your time
 Bengt O. Muthen posted on Wednesday, November 10, 2010 - 4:14 pm
1. Yes.

2. Yes, although variance testing is complicated by the fact that you are testing on the border of the admissible parameter space, so I am not sure how good the power estimate is there.
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