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 Jack Noone posted on Wednesday, December 19, 2007 - 2:52 pm
Firstly, I have a SEM model with two endogenous variables (categorical indicators) three
exogenous/endogeous variables (continuous indicators), two exogenous variables (continuous indicators) and two observed
continuous exogenous variables. N=1,500 and two groups.

1) the default estimator is WLSMV - if my variables (besides the ones indicated by categorical variables) are reasonably normally distributed what other estimators would be suitable? (any refs? I also have a weighting variable and missing data)

2) can i still use the missing data option? - and if yes, what method (FIML?) does it use?

3) How do i calculate power?

4) I have two groups and i want to see if a)the factor means (and means of observed exogenous variables) are different across groups and b) if the path co-efficients are different. Is this possibile? if yes, how do i do this? I get confused with which parameters to hold constant etc (refs welcomed here as well!

thanks for your help

 Bengt O. Muthen posted on Wednesday, December 19, 2007 - 5:44 pm
1) You can use ML.

2) Yes.

3) See the Mplus User's Guide chapter 11 Monte Carlo example 11.2

4) See pages 398-401 in the Mplus Version 5 User's Guide.

Note also the upcoming Mplus short course at the Johns Hopkins University in March where many related issues are discussed.
 Jack Noone posted on Thursday, December 20, 2007 - 5:00 pm
thanks for your quick response.

for question 1 which estimator would be best if the variables were not normally distributed?

 Jack Noone posted on Thursday, December 20, 2007 - 5:04 pm
oh, and mplus won't let me use ML with the "weight" command - what would be the next best option?
 Bengt O. Muthen posted on Thursday, December 20, 2007 - 9:22 pm
MLR is the answer in both cases. It gives SEs that are robust against non-normality and it incorporates the sampling weights.
 jack noone posted on Wednesday, July 09, 2008 - 7:01 pm
1)I need to test differences in latent variable means across 2 groups.
2) I also need to test whether the correlation between y and Z is different across groups

But i get a bit confused at which parameters need to be held constant for each type of analysis.
Could you fill in the syntax for me below?

grouping is x(1=male 2=female);
y by y1 y2 y3 y4;
z by z1 z2 z3 z4;
y on z;

Feel free to explain exactly what is going on!
 Linda K. Muthen posted on Thursday, July 10, 2008 - 9:08 am
See the Topic 1 course handout on the website. The input for this comparison is shown at the end of the multiple group discussion. See also the video from Johns Hopkins March 2008 workshop on this topic.
 Jack Noone posted on Thursday, July 10, 2008 - 10:04 pm
Thank you, the video was very helpful.

I have discovered that i need to take a multiple group approach to testing group means - but i have a couple of extra questions.

I have 4 endogenous latent variables and 2 exogenous variables (in an SEM model). Do i have to do tests for measurement invariance/population heterogeneity for each latent variable in separate runs or can i test them all simultaneously? I ask because if there is VERY SLIGHT non-invariance across all the latent variables would these not all add up to show a worsening of the entire model fit? Thus leading one to conclude non-invariance when it is just a cumulative effect of small differences which on their own would still be invariant?

When testing for group mean differences one fixes the means of the second group to zero - Chi square tests then tell us if the means are different between the two groups. How can we tell which group had higher mean scores and to what degree?

Also, 2 of my latents have categorical indicators which makes it awkward for chi square diff tests when using WLSMV. is it OK to use the WLS estimator instead when just testing for invariance - then going back to WLSMV for testing direct/indirect relationships?
 Linda K. Muthen posted on Friday, July 11, 2008 - 9:55 am
I would look at all of the latent variables together.

To see the mean differences, look at the means of the unconstrained model.

I would use the DIFFTEST option with WLSMV or use WLSM.
 Jack Noone posted on Friday, July 11, 2008 - 8:12 pm

Just to get the steps for testing measurement invariance across groups right in my head (this assumes the model fits for both groups):

1)free equlity constraint on factor loadings (using command "model male:" for example).

2)run default model which constrains factor loadings across groups.

compare chi square for 1 and 2 for factor loading invariance

3) we then add a meanstructure (this frees equality constraints on intercepts right?)

compare chiquare between 3 and 4 for intercept invariance.
 Linda K. Muthen posted on Saturday, July 12, 2008 - 6:54 am
Please see Chapter 13 of the user's guide at the end of the multiple group section. The models for testing measurement invariance are described there. See also Topic 1 of the course handouts that are on the website where inputs are given for testing measurement invariance using multiple groups.
 jack noone posted on Tuesday, July 22, 2008 - 4:18 pm
HI there, i am doing a monte carlo to determine power (normal/mising) -

The example you give in your 2002 paper use CFA but can i change the "with" statements to "on" statements as i am doing SEM?

Also, can you simply add covariates and specify the estimated correlation between the covariate and the latent variable? Or are there other steps you must follow?

can i assume that your answers to the above also apply to non-normal/missing?

 Linda K. Muthen posted on Tuesday, July 22, 2008 - 4:59 pm
Yes, you can change WITH to ON. You might want to find an example in the user's guide closer to what you want and start with the input for the Monte Carlo counterpart of that example. Find an example with covariates to see how this is done.

The models in Chapter 13 apply to non-normal missing.
 jack noone posted on Tuesday, July 22, 2008 - 7:10 pm

does changing "with" to "on" actually impact on estimated power?
 jack noone posted on Tuesday, July 22, 2008 - 7:24 pm
also, is there a limit on the nomber of variables you can use in a monte carlo simulation? I have 80 loading onto 16 factors.

but the error message comes up:

Numerical format error in PATMISS option:

I can't see any errors - should i send it to your help desk?
 Linda K. Muthen posted on Wednesday, July 23, 2008 - 9:09 am
This could change the power.

The limit is 500 variables as in regular analyses in Mplus. However, in a Monte Carlo simulation where the analysis is replicated many time, it may be very time-consuming.

If you can't see your error, please send the output and your license number to support@statmodel.com.
 jack noone posted on Wednesday, July 23, 2008 - 2:53 pm
yes, VERY time consuming! Is there another option for calculating power that isn't too complicated?

I am unable at this stage to update from version 4.21 to version 5.1 (i am currently in contact with tech support regarding this) so i am struggling a bit testing for measurement invariance across groups.

the problem is to do with the meanstructure command - more specifically when i add a meanstructure (as per the video) it makes no difference to the chi square and degrees of freedom. This is true regardless of whether factor loadings are constrained or free.

any ideas? I understand that meanstructure is the default for v5.1.
 jack noone posted on Wednesday, July 23, 2008 - 4:33 pm
HI Linda, ignore last comment. I've got v5.1 now.

 jack noone posted on Wednesday, July 23, 2008 - 7:42 pm
actually i get the following error message when i run nomeanstructure:

MODEL=NOMEANSTRUCTURE is not allowed in conjuction with TYPE=MISSING.
Request for MODEL=NOMEANSTRUCTURE will be ignored.

I understand that missing is the default, but why will it not allow nomeans?
 Linda K. Muthen posted on Thursday, July 24, 2008 - 6:51 am
Having no means or unstructured means does is the same. Certain parts of the program include means.
 Jack Noone posted on Thursday, July 24, 2008 - 3:44 pm
I'm sorry i don't understand. I am testing for measurement invariance across groups using the following commands but the error message i talked about earlier comes up. This command is based on your video at John Hopkins.

usev are
sex jsat2 jsat4
jsat8 jsat13
jsat14 jsat15 involve4 involve5
involve6 afinan1
afinan4 afinan5
radj2 radj3 radj4 expid1
expid3 expid4;
Missing = all(-9999) ;

grouping is sex (1=male 2=female);

involve by involve4@1 involve5 involve6;
satis by jsat2@1 jsat4 jsat8 jsat13 jsat14 jsat15;
afinan by afinan1@1 afinan4 afinan5;
radj by radj2@1 radj3 radj4;
expid by expid1 expid3 expid4;

analysis: model = nomeanstructure;

output: stand ;
 Linda K. Muthen posted on Thursday, July 24, 2008 - 5:12 pm
We changed the input for that after the course when we realized that means were needed. See the Topic 1 course handout on the website.
 Jack Noone posted on Thursday, July 24, 2008 - 7:54 pm
Ok - i was beginning to think i was a moron!

(still possible i guess.)
 Jack Noone posted on Sunday, July 27, 2008 - 6:01 pm
I just took a look at the topic 1 handout as you suggested (slide #207) - could you please explain what the square brackets are doing with the variables...

[rlit@0 math@0]



for example is rlit@0 an equality constraint?

 Jack Noone posted on Sunday, July 27, 2008 - 6:09 pm
also, when you can establish partial measurement invariance is it still appropriate to test for population heterogeneity?

say, you only needed to remove equality constraints on the intercept for one variable.
 linda beck posted on Monday, July 28, 2008 - 6:31 am
square brackets indicate a mean... "@" is not an equality constraint, instead it symbolizes "fixed at a certain value", e. g. zero. in sum: the means of rlit and math are fixed at zero.
you should read more about the basics in the mplus manual.
 Linda K. Muthen posted on Monday, July 28, 2008 - 6:50 am
You might want to listen to the Topic 1 video on the website where measurement invariance is covered.
 Jack Noone posted on Saturday, August 23, 2008 - 8:11 pm
Is it possible to test for invariance and heterogeneity when factor indicators are a mixture of continuous and categorical variables? (4 factors have continuous indicators and 2 factors have cat. indicators. All factors are continuous though.)

If yes can you still use a difftest with WLSMV?

I had a try combining the commands from handout 1 and 2 but with little success.
 Jack Noone posted on Saturday, August 23, 2008 - 8:32 pm
I forgot to say that i using missing data and survey weights
 Jack Noone posted on Saturday, August 23, 2008 - 9:41 pm
I actually had the command wrong but when i got to the last step the following error came up:


from the command

categorical are
think spouse friends savings sharfund
rental home;
Missing = all(-9999) ;
grouping is sex (1=male 2=female);
radjust by radj2 radj3 radj4;
planA by think spouse friends ;
planB by savings sharfund rental home ;
afinan by Afinan1 Afinan4 Afinan5 ;
involve by involve1 involve4 involve5 involve6;
satis by jsat2 jsat4 jsat8 jsat14 jsat15;

output: stand modindices (3.84);

can you let me know what i did wrong please.
 Linda K. Muthen posted on Sunday, August 24, 2008 - 10:40 am
Please send your files and license number to support@statmodel.com.
 Alex Z posted on Tuesday, August 26, 2008 - 9:24 pm
I have a 3 factor MGCFA. I want to compare the factor means. My model showed measurement invariance for loadings, thresholds, residuals, and factor variances BUT failed to show measurement invariance for the factor means.

Q1. does failure of invariance of the 'Factor Means' imply that the factor means are significantly different?

Q2. Should the model for testing measurement invariance for factor models be nested within the model testing meas inv for factor variance?

Q2. I understand that when comparing factor means I should use an unconstrained model. Should any other parameters, eg factor variances, also be unconstrained or just the factor means?

 Linda K. Muthen posted on Wednesday, August 27, 2008 - 6:49 am
Factor means, variances, and covariances are not measurement parameters. They are structural parameters. Once you have established measurement invariance, you want to examine the structural parameter differences. You can do this using a series of nested models. Please see the Topic 1 course handout where this type of analysis is shown in detail.
 Jack Noone posted on Tuesday, October 07, 2008 - 7:09 pm
Hello again, i am trying to get latent variable means and SDs (across differnt groups) using the tech4 output. However i notice that my LV means are negative across all the groups. The indicators were dichotomous and coded either 1 or 2.

the same thing happens when i try to get the latent mean for the whole sample (ie taking out the grouping option)

why are they negative?

thanks jack
 Linda K. Muthen posted on Wednesday, October 08, 2008 - 9:12 am
Factor scores are z-scores with a mean of zero.
 Jack Noone posted on Wednesday, October 08, 2008 - 1:54 pm
Oh, I had no idea - could you point me towards some extra reading on this subject please?
 Linda K. Muthen posted on Wednesday, October 08, 2008 - 4:27 pm
Go to the Technical Appendix document on the website. Technical Appendix 11 discusses factor score estimation in Mplus. See also the references in this appendix.
 Jack Noone posted on Thursday, October 09, 2008 - 7:35 pm
Thanks, i'll have a look at those.
is it possible to test for group mean differences on observed (continuous exogenous) variables? This would be equivalent to a t-test i guess.

My idea was too impose an equality constraint on the mean of the observed variable (lets call it OBS)

OBS (1);

and do a difftest.

Would that work? If not - any other ideas?
 Linda K. Muthen posted on Friday, October 10, 2008 - 11:03 am
That would work. You could also use MODEL TEST.
 Linda K. Muthen posted on Friday, October 10, 2008 - 11:04 am
Note that obs refers to a variance or residual variance. A mean or intercept is referred to in brackets:

[obs] (1);
 Alex Z posted on Wednesday, October 15, 2008 - 3:59 am
i have run a series of nested models to test for measurement invariance across 3 groups. Measurement Invariance was found.
I then tested for Structural invariance of factor variances (found to be invariant) and then I tested for invariance of factor covariances (not found to be invariant).

I ran a final model to compare the 3 groups by setting factor variances to 1 and means to zero in a reference group and freely estimating variances and means in the other 2 groups. THis produced different factor variances for each group.

My questions are:

How can I find structural invariance for the factor variances but also produce different factor variances for each group when I run the final model (as described above)?

If i have found structural invariance of the factor variances, does it makes sense to compare variances across the groups as i have done in my final model?
 Alex Z posted on Wednesday, October 15, 2008 - 4:07 am
Adding to my last post:

Rather than compare variances across groups, I should have said,is it valid to comment on the different values of the factor variances, e.g. if one is significantly bigger than the others.
 Linda K. Muthen posted on Wednesday, October 15, 2008 - 10:08 am
If you have concluded that the variances are equal, I am not sure why you want to again test their equality.
 Alex Z posted on Wednesday, October 15, 2008 - 12:43 pm
even though the factor variances have been shown to be invariant, when I do the three group comparison and let the variance be freely estimated, the variances are different. One group has the smallest variance for all factors. Another group has the largest variance for a single factor.

Is valid to comment on why one group has the smallest variances, e.g. they are a more homogeneous group than the other groups? Or a characteristic of the other group has caused them to have the largest variance
 Linda K. Muthen posted on Wednesday, October 15, 2008 - 2:59 pm
If you concluded from your difference testing that the variances are invariant, the differences you see are not statistically significant. The differences you see are due to sampling variability not differences in the population.
 Jack Noone posted on Tuesday, December 02, 2008 - 4:05 pm
i need to use listwise deletion, but only on selected variables.

is this possible?

 Linda K. Muthen posted on Tuesday, December 02, 2008 - 5:17 pm
There is no automatic way to do this. You could probably figure something out using the DEFINE command.
 Jack Noone posted on Sunday, December 14, 2008 - 5:39 pm
Can mplus handle a nominal observed variable (6 categories) which is endogenous and exogenous?
 Linda K. Muthen posted on Monday, December 15, 2008 - 8:32 am
A set of dummy variables should be created for an observed exogenous variable. An observed endogenous variable should be put on the NOMINAL list. See Example 3.6.
 Jack Noone posted on Saturday, December 20, 2008 - 4:06 pm
OK sounds good.

another question on group means:

On your website you give a fantastic example of how to test for group factor means differences - using a CFA example. In this case you do a difftest where step two constrains the second group mean to zero.

In SEM where factor means are endogenous, do you do the same or do you impose equality constraints on factor means instead? I notice in my tech4 that factor means are given for both groups, while an exogenous factor has 0 for the first group (like the CFA example).

To me this suggests i should impose an equality constraint on endoegous factors while constraining factor means at 0 for the exogenous factor. Is this correct?
 Jack Noone posted on Saturday, December 20, 2008 - 4:52 pm
Just to add to above.
if i run just a CFA with latent variables and constrain group 2 factor means to zero - this shows up in tech 4 and everything works out fine

if i turn it into SEM (making factoros enodeogous and exogenous and adding covariates), the latent factor means in the first group are esimated, and constrining the factor means to zero in the second group does not change the means in tech4.

I'm a bit confused.
 Linda K. Muthen posted on Sunday, December 21, 2008 - 6:46 am
I think you are confusing means and intercepts. Means are estimated for exogenous factors. Intercepts are estimated for endogenous factors. TECH4 provides models estimated means, variances, and covariances for the factors in the model. I would have to see your output to fully understand what you are describing. If my comments are not sufficient, please send the outputs and your license number to support@statmodel.com.
 Jack Noone posted on Sunday, December 21, 2008 - 2:00 pm
sadly my license has run out but.....

can i still test for group mean differences on endogenous variables?

From what i understand above the tech4 output shows intercepts rather than means for enodogenous variables?
 Linda K. Muthen posted on Sunday, December 21, 2008 - 6:32 pm
In the model if a variable is endogenous, an intercept is estimated not a mean. TECH4 does not give intercepts. It gives means. Look at the output. I'm sorry I cannot help you further on this without going through support.
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