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I would like to perform a power analysis following the procedure of Satorra and Saris (1985). How can I output the model implied covariance matrix and mean vector? 


You do a run where you fix all the parameters to the desired values and request RESIDUAL to get the estimated mean vector and covariance matrix. In this run you can use means and covariance input with dummy values, for example using zeros for the means and an identity matrix for the covariance matrix. We have a couple of pages that describe the steps for SatorraSaris power calculation in a growth model setting which we discuss in our courses and we will shortly post this information on our web site. This includes how to get the power value from the noncentrality parameter (the "chisquare" value). 


Dear Dr. Muthen: In Muthen & Curran (1996) and Curran & Muthen (1996), parameter values in the growth model were chosen so that the difference between the treatment and control group means at the last time point scaled by the pooled s.d. at the last time point represented a effect size of 0.20. Could you please explain how to shoose parameter values (e.g., slope mean and variance, correlation between the intercept and slope, et al.) in the first step for SatorraSaris power calculation for a given effect size (e.g., 0.20)? Thank you very much for your help. Sincerely, Jichuan Wang, Ph.D. School of Medicine Wright State University Dayton, OH 45435 

bmuthen posted on Tuesday, November 21, 2000  3:49 pm



You need to know how to calculate means and variances for the outcomes given a certain growth model with a certain choice of population parameter values. Given this, the simplest way is choosing parameter values that give the desired effect size using trial and error. 


Hi there, I am new to mplus and am confused about setting the start values in monte carlo for an LTA model. I would like to run an mc for a power analysis and am trying to use example 8.13 as a guide. I would like to see what power I have at N=300, 400 and 500 to test the possibility that x (continuous variable), is posititvely correlated with membership in highrisk drinking classes c2#1 and c1#1. I want to test the x effects as small, med and large effects over the different sample sizes. I originally wanted to use the classic cohen values, r=.1, .3 and .5 to represent small, med, and large effects, respectively, but realize that this is more like a logistic regression and am thus confused as to what start values I should use to test these different effect size levels. In the example 8.13, you suggest "c2#1 ON c1#1*.5 x*1;" but I have no idea what x*1 would actually be in terms of an effect size. Can you tell me how best to represent different effect sizes in the mplus code? I was also curious why "c2#1 on x*.2;" under the specific model "%c1#1%" while it appears differently in the %overall% command (i.e., c2#1 ON c1#1*.5 x*1;) Thanks so much for your help! Susan 


Effect size has a different meaning when the dependent variable is categorical and is not as easily settled. You are interested in an effect of x on c in the multinomial logistic regression of c on x. So instead you have to ask yourself how much the probability of being in a certain c class changes as a function of x changing, say by 1 SD. You have to decide what a small/medium/large probability change is. Note, however, that the probability change is different for a 1 SD x change at low, medium, and high x values. You can use UG Chapter 13 formulas to compute the probabilities. You may also take a look at logistic regression books to see if any counterpart to effect size appears, but I doubt that. Regarding your last question, the overall c2#1 on x will apply to the last class whereas the c1#1specific statement refers to the first class. This is how you represent the model picture's broken line. 


Hi: I ran a mixture model in mplus with two latent classes. I am now interested in simulating a 2 class model with 235 observations to see how much power I’d have. I can’t seem to get the thing to run. Especially, for two classes I get two estimates for threshold (one for each class). My question is, how I can specify twi threshold GENERATE command under MONTECARLO. Thanks, Shahadut Hossain UBC school of nursing 


Find the example in Chapter 7 that is like your model. Then use the Monte Carlo counterpart of that example as a starting point. If you run into problems, send your output and license number to support@statmodel.com. 


Hello, Can we do power analysis for path analysis model? I just saw examples for CFA and growth model. Thank you Owis 


You can do a power analysis for any model. 


Thank you for the reply. I have run power analysis, does "% Sig coff" indicate the power? Thank you, Owis 


The column labeled % Sig Coeff gives the proportion of replications for which the null hypothesis that a parameter is equal to zero is rejected at the .05 level (twotailed test with a critical value of 1.96). The statistical test is the ratio of the parameter estimate to its standard error, an approximately normally distributed quantity (zscore) in large samples. For parameters with population values different from zero, this value is an estimate of power with respect to a single parameter, that is, the probability of rejecting the null hypothesis when it is false. For parameters with population values equal to zero, this value is an estimate of Type I error, that is, the probability of rejecting the null hypothesis when it is true. 


So when I get zero for all parameters means that my null hypothesis is true but I reject it. But I already got pvalue<0.05 for some of these parameters! Does that also mean the model does not have enough power to run with the current sample size? Thank you, Owis 


Please send your output and license number to support@statmodel.com. Be explicit about where in the output you are looking. 


Hi, I like to do a poweranalysis for my Latent Profile Analysis model. However, I'm using zscores as input for the LPA. If I specify the power analysis with the values the LPA gave me, this error occurs: *** FATAL ERROR THE POPULATION COVARIANCE MATRIX THAT YOU GAVE AS INPUT IS NOT POSITIVE DEFINITE AS IT SHOULD BE. Is it possible to do the power analysis? And what would be the best way to do this? Thank you in advance! 


Please send the output and your license number to support@statmodel.com. 


I am trying to perform power analysis for my path model with all continuous variables. However, I get the following error: A POPULATION VARIANCE FOR A COVARIATE IS ZERO. Below is the model I am testing. MODEL POPULATION: [TL1@0 CR1@0 MEA1@0 MEP1@0 LF1@0]; TL1@1 CR1@1 MEA1@1 MEP1@1 LF1@1; Mot2 on Att1*1 Norms1*.3 Ctrl1T1*.3 Age1*.3; Att1 Norms1 Ctrl1T1 on TL1*1 CR1*.3 MEA1*.3 MEP1*.3 LF1*.3 Age1*.3; Att1 with Norms1*.3 Ctrl1T1*.3; Norms1 with Ctrl1T1*.3; TL1 with CR1*.6 MEA1*.6 MEP1*.5 LF1*.5; CR1 with MEA1*.6 MEP1*.5 LF1*.5; MEA1 with MEP1*.5 LF1*.5; MEP1 with LF1*.5; MODEL: Mot2 on Att1*1 Norms1*.3 Ctrl1T1*.3 Age1*.3; Att1 Norms1 Ctrl1T1 on TL1*1 CR1*.3 MEA1*.3 MEP1*.3 LF1*.3 Age1*.3; Att1 with Norms1*.3 Ctrl1T1*.3; Norms1 with Ctrl1T1*.3; TL1 with CR1*.6 MEA1*.6 MEP1*.5 LF1*.5; CR1 with MEA1*.6 MEP1*.5 LF1*.5; MEA1 with MEP1*.5 LF1*.5; MEP1 with LF1*.5; OUTPUT: Tech9; What am I doing wrong? 


Please send the full output and your license number to support@statmodel.com. 


Hi Drs. Muthen, I am running a power analysis for a GMM. In my output, I get warnings at the end for some replications: REPLICATION 30: WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1 IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/ RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE I. Sometimes the warning is for Variable I, sometimes Variable S. Not all replications have warnings. Should I interpret this as an unstable solution? Thank you for your help! 


Not necessarily. But the model is a bit fragile at this sample size. This can for instance happen if variances are close to zero and then slip into negative values for some replications. 


Thank you! I have a follow up question: When I add a covariate to the monte carlo model, I get a fatal error that the pop covariance matrix is not positive definite. Can you help me understand where I am going wrong? I've tried using an observed vs. latent variable, changing the sample size, changing coefficients, adding "algorithm=integration". Montecarlo: NAMES ARE y1 y2 y3 y4 y5 y6 y7; nobservations=1000; nreps=100; seed= 53487; genclasses= c(3); classes = c(3); save= Dissertation Power GMM3_withcov.sav.; analysis: type= mixture; estimator= ml; algorithm=integration; model montecarlo: %overall% i s  y1@0 y2@1 y3@2 y4@3; f1 BY y5*1 y6*.48 y7*.45; i*.05; s*.5; i with s*.1; y1y4*.3; i ON f1*.40; s ON f1*.585; %c#1% [i*.03 s*1.38]; %c#2% [i*.21 s*2.43]; %c#3% [i*1.96 s*1.01]; model: (same info as above) output: tech9 


You need to provide the variance of f1. 


Thank you! I just tried that with the same error: model montecarlo: %overall% i s  y1@0 y2@1 y3@2 y4@3; f1 BY y5*1 y6*.48 y7*.45; f1*.2; i*.05; s*.5; i with s*.1; y1y4*.3; i ON f1*.40; s ON f1*.585; 


You don't give values for the residual variances of y5y7. If that doesn't help, send your output to Support along with your license number. 

Nicole Tuitt posted on Wednesday, September 12, 2018  4:46 pm



Hello, Is Monte Carlo power simulation still applicable when using a Bayesian estimator for GMM? I guess a more general question, when using a Bayesian estimator can I make the assumption that I will be able to detect effects given the advantages of Bayes for limited data or would you recommend still conducting a power analysis? Thanks, Nicole 


I would recommend a power analysis which can be done with Bayes as well. 

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