Power analysis
Message/Author
 Daniel Rodriguez posted on Monday, March 31, 2003 - 8:00 am
Is there a way to assess power with LCGA?
 Linda K. Muthen posted on Monday, March 31, 2003 - 8:17 am
You can use the same strategy that is outlined in the following paper:

Muthén, L.K. and 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.
 Daniel Rodriguez posted on Monday, March 31, 2003 - 9:15 am
Hi, does this apply to the situation with ordered categorical indicator variables as well? Or do I just consider my indicators as non-normal factor indicators as in your example in the paper?
 Linda K. Muthen posted on Monday, March 31, 2003 - 3:45 pm
LCGA can have continuous or categorical indicators in Mplus. See Examples 25.11 and 25.11A for categorical indicators.
 Patrick Malone posted on Wednesday, May 28, 2003 - 7:26 am
Greetings.

I need to do a power analysis for an elaborate planned missingness design. It looks like I could do this using the techniques from the sample size and power 2002 paper, but for one thing: I'm interested in discriminant validity for a CFA, so the null hypothesis I need power for to reject is that the factor correlation equals one. It looks like the MONTECARLO output won't give me that. If I had a simpler design, I could use the power analysis approach from power.html, but I don't see how that would work with a mixture model (using classes to represent the planned missingness).

I could fall back and just use the estimated standard errors for the factor correlations from the MONTECARLO output, and not have it be formally "power." Any suggestions, though?

Thanks,
Pat
 bmuthen posted on Wednesday, May 28, 2003 - 8:32 am
Could you somehow turn the unit correlation into a test of a parameter being zero? I was first thinking of a second-order factor but didn't get far with that. What about loadings that are equal and rejecting that they are zero; can the problem be rephrased into that?
 Patrick Malone posted on Wednesday, May 28, 2003 - 11:33 am
I'm not sure how. Except for the missing data part, the problem is straightforward. Three correlated factors, with four items each -- I want to know if I can reject the hypothesis that the factor correlations (taken together or one at a time -- I'll take either one) are 1. The factors will be trivially correlated -- the indicators are measures of the same trait taken across three contexts.
 bmuthen posted on Thursday, May 29, 2003 - 6:07 pm
Sounds like you may have to do Monte Carlo simulation "externally", that is generating data, running Mplus using "RUNALL", and combining results from runs with unit and non-unit correlations. Lot of work.
 Patrick Malone posted on Friday, May 30, 2003 - 11:21 am
That did the trick; wasn't so bad.

 Jason Bond posted on Thursday, October 07, 2004 - 5:12 pm
I have taken a look at several papers I have found on power analysis for LGM (Linda and Bengt's paper in SEM entitled "How to use a monte carlo study to decide on sample size and determine power", Bengt and Patrick Curran's paper in Psych methods entitled "General longitudinal modeling of individual differences in experimental designs: a latent variable framework for analysis and power estimation", as well as the power example on this web site - and if anyone knows of any more, I would most appreciate hearing of them) but I haven't found any that explicitly discuss how to get at power to detect the number of classes. And I'm not sure exactly how to even define the concept of power for detecting a given number of classes. Perhaps it could be stated as the power to detect an additional class, given that k have already identified, for various true membership proportions in that additional group (the effect size). That is just a thought. Anyway, any input on this topic would be greatly appreciated.

Jason
 Bengt O. Muthen posted on Tuesday, October 12, 2004 - 5:13 pm
You can define power as the probability of rejecting a k-1 class model when a k class model is correct or the probability of rejecting a k + 1 model when a k class model is correct. A paper is being prepared by Nylund et al on this topic which you can request from bmuthen@ucla.edu.
 mart eussen posted on Thursday, October 15, 2009 - 1:46 am
Dear Dr. Muthen,

We would like to perform Latent Class Analysis on 18 or 23 binary items within a sample of n=134. Possible covariates are sex and age. Would we have enough power for reliable analysis?

Mart Eussen
 Linda K. Muthen posted on Thursday, October 15, 2009 - 10:20 am
Whether you have enough power depends on the separation of classes. You would need more observations if classes are not well-separated and fewer observations if the classes are well-separated. You would need to do a Monte Carlo study to determine how many observations you would need. See on the website:

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.
 luke fryer posted on Wednesday, September 08, 2010 - 8:33 am
Muthén and Muthén,

I have read your 2002 article and it was very helpful, conceptually. However, neither the paper nor the Manual seem to provide syntax examples for dichotomous data. I have a sample of 650, 30 dichotomous indicators and three factors. Fit is very good but as it is my first time analyzing non-continuous data, I want to be sure that my sample size is sufficient. Is syntax available for for such a model?

My results, if they are valid, will be very controversial. I want to get this right...

luke

p.s. sorry for my flurry of posts...
 Linda K. Muthen posted on Wednesday, September 08, 2010 - 11:20 am
All of the examples in the user's guide have data that were generated using Mplus. The Monte Carlo inputs for these are available on the Mplus CD and also on the website. Find an example with dichotomous data and take a look at that.
 Eric Thibodeau posted on Thursday, March 26, 2015 - 2:14 pm
Hi,

Trying a power analysis for a path analysis. See syntax below, am I on the right track? I have expected unstandardized slope estimates, but not sure what to do about the variances. I set them to 1. Do I also have to estimate means, intercepts, and residual variances?

Thanks! Eric

MONTECARLO: NAMES ARE y1-y3;
NOBSERVATIONS = 200;
NREPS = 10000;
SEED = 53487;
CLASSES = C(1);
GENCLASSES = C(1);
PATMISS = y2(.1);
PATPROB = 1;

ANALYSIS: TYPE = MIXTURE;
ESTIMATOR = MLR;
MODEL MONTECARLO:
%OVERALL%
y3 on y1*.15;
y3 on y2*.15;
Y2 on Y1*.15;

y1-y3*1;

MODEL:
%OVERALL%
y3 on y1*.15;
y3 on y2*.15;
Y2 on Y1*.15;
y1-y3*1;

OUTPUT: TECH9;
 Bengt O. Muthen posted on Thursday, March 26, 2015 - 3:32 pm
You can choose any variance you like for an IV, but the residual variances that you need to give for DVs have to correspond to reasonable R-square values for these DVs. You don't have to give means or intercepts, in which case the default of zero is used.

I don't know why you are using mixture here, but otherwise it looks ok.

I assume you know that every example in the UG has a Monte Carlo version posted on our website.
 Eric Thibodeau posted on Friday, March 27, 2015 - 12:45 pm
Thanks Dr. Muthen,

For a mediator in this case Y2, do I need both a residual variance and variance stated? I have done that in the syntax below and the % Sig Coef is unusually small for Y3 on Y2.

I assume a standardized effect of .15 for each slope and about 20% residual variance for Y3 and Y2 (if I supposed to state it).

MONTECARLO:
NAMES ARE y1-y3;
NOBSERVATIONS = 200;
NREPS = 500;
SEED = 4533;
PATMISS = y1(.1) y2(.1) y3(.1);
PATPROBS = 1;

MODEL POPULATION:

y3 on y1-y2*.15;
y2 on y1*.15;

y1-y2*1;

y3@.2;
y2@.2;

MODEL:

y3 on y1-y2*.15;
y2 on y1*.15;

y1-y2*1;

y3@.2;
y2@.2;

OUTPUT: TECH9;
 Bengt O. Muthen posted on Friday, March 27, 2015 - 2:44 pm
Note that

y2;

refers to a variance if y2 is an IV and a residual variance if it is a DV (see the basic description of the Mplius language in the UG). So if y2 is a mediator you give its residual variance.
 Andrea Norcini Pala posted on Wednesday, May 04, 2016 - 8:33 am
Hello,

I want to run a power analysis for a pilot study. I will have a 2X2 factorial design and I want to use Bayesian estimation to analyze the results. I want the 4 groups to have equal size.
Can you suggest an example I can use?

I thought of a regression model with X1 and X2 (two binary variables identifying the 2X2 groups) and their interaction, but I am not sure how to control the size of the groups (X1 and X2).

Then I thought of a latent class (4 classes), where I have control over the groups' size.
Any Idea? Thanks!
 Bengt O. Muthen posted on Wednesday, May 04, 2016 - 9:26 am
4 latent classes should be fine, so Bayes with Knownclass. The class sizes will vary across replications but perhaps that is realistic given that some people have missing data.
 Tirip Rashid posted on Thursday, September 21, 2017 - 11:22 am
The power estimates come out two-tailed. Is there a way to get one-tailed power estimates?
 Bengt O. Muthen posted on Thursday, September 21, 2017 - 3:57 pm
Not automatically.