How to test group differences in path...
Message/Author
 Daniel posted on Thursday, September 25, 2003 - 1:26 pm
Hi Dr. Linda,

I could not find answers for the following questions from Mplus book:

(1). Generally, Est/S.E. in output can be used as critical t-value (or normal distribution) for checking significance level of Estimates. Can it also be used for checking significance level of Std and StdYX? If not, how to know that of Std and StdYX? The reason for that question is, we often use "Std" or "StdYX" instead of "Estimates", So significance level for these two is so important.

(2). In multiple group analysis, we can compare the means of Latent variables between two groups. But how to calculate the differences and its significance level of path coefficients of latent factors between two groups? Please give me an example of such program (model).

(3) Could you give me an exampel of how to intepret scale factor from output of multiple group analysis?

(4) Finally, how to test, as a whole, whether difference between two groups is significant or not?
 Linda K. Muthen posted on Thursday, September 25, 2003 - 4:45 pm
1. No, you would need the standard error for the standardized estimate to do that. I guess you would have to compute the standard errors using the Delta method.
2. Chi-square difference testing can be used to test the significance of any parameter. You just run a model where the parameter is held equal across groups and another model where the parameter is free across groups.
3. The scale factor is the inverse of the standard deviation of the y* variable.
4. Run two models - one with parameters free across groups, one with parameters fixed across groups. Do a chi-square difference test.
 Daniel posted on Friday, September 26, 2003 - 7:36 am
Dr. Linda,

I read the following paragraph from Multiple Group Analysis discussion:

"If you send me your fax number, I will fax you several pages we use when we teach. These show setups for a variety of multiple group models that test a variety of hypotheses. "

Could you please send me the material mentioned above. I need it badly. My fax number is

1-416-736-5647

Thanks
 Linda K. Muthen posted on Friday, September 26, 2003 - 8:27 am
I have tried to fax twice. The first time said poor line condition. The second time it just rang and rang. If you can clear up the problem, I will fax the pages.
 daniel posted on Monday, October 06, 2003 - 6:28 am
Hi Dr. Linda,

It's very kind of you. Thank you so much. I have just received eight pages including cover page. Please resend last two pages again.

Many thanks again
Daniel
 Linda K. Muthen posted on Monday, October 06, 2003 - 9:46 am
I'll be back in a week and do it then.
 Daniel posted on Wednesday, October 15, 2003 - 6:25 am
Dr. Linda,

I have received the last two pages.

Thanks

Daniel
 Daniel posted on Thursday, October 16, 2003 - 12:19 pm
Hi Dr. Linda,

I am still not quite sure I understand well. I have a simplified model for categrecal data as follows:

grouping is sext1 (1=male 2=female);
categorical are all;
usevariables are sext1 y1-y12;

model:
f1 by y1 y2 y3;
f2 by y4 y5 y6;
f3 by y7 y8 y9;
f4 by y10 y11 y12;

f2 on f1;
f3 on f1 f2;
f4 on f3 f1;

I am interested in the comparison of the regression coefficients (not factor loadings) of factors between the two groups. What syntax should I add?
 Linda K. Muthen posted on Thursday, October 16, 2003 - 12:25 pm
f2 ON f1 (1);
f3 ON f1 (2)
f2 (3);
f4 on f3 (4)
f1 (5);
 Daniel posted on Friday, October 17, 2003 - 8:59 am
Hi Dr. Linda,

I tried that model.

model:
f1 by y1 y2 y3;
f2 by y4 y5 y6;
f3 by y7 y8 y9;
f4 by y10 y11 y12;

f2 ON f1 (1);
f3 ON f1 (2)
f2 (3);
f4 on f3 (4)
f1 (5);

The results, if I interpret correctly, can show the differences of factor means between two groups, not differences of regression coefficients of factors between the two groups because the regression coefficients of factors between the two groups are already constrained equal. So I am afraid I have not made it clear to you.

My question is: are the differences of regression coefficients of factors between the two groups significant? In this case how to write syntax in model command?
 Linda K. Muthen posted on Friday, October 17, 2003 - 9:58 am
Please send your output to support@statmodel.com and clearly point out which parameter you want to hold equal or not hold equal. Regression coefficients specified by ON statements are not held equal across groups. Regression coefficients specified by BY statements are held equal across groups. I don't think you are interpreting your output correctly.
 jack noone posted on Sunday, May 11, 2008 - 8:41 pm
good day,
I notice above you have faxed a copy of your notes regarding multiple group hypotheses - could you fax them to me as well please? (if you still have them from 2003!)

I am after any info i can get regarding testing differences in latent variable means.

my fax is

(+64) 6 3505673

regards Jack Noone (please attention fax to me)
 Linda K. Muthen posted on Monday, May 12, 2008 - 10:30 am
All of our short course handouts are available at http://www.statmodel.com/trainhandouts.shtml.
Topic 1 covers this for continuous outcomes. See the slides for multiple group analysis.
 Keke Hiller posted on Wednesday, December 14, 2011 - 11:09 am
Hello Linda,
I am struggeling using categorical variables with the GROUPING command. Using N=182 & ML for the following analysis: four latent and two dichotomous variables (sal and cod) are used to explain one dependent latent variable. Satisfactory fit is achieved (Chi-sq=295.111; df=217; CFI=0.945; TLI=0.933; RMSEA=0.044; SRMR=0.053).

Next, I use sal & cod with the command GROUPING to check for differences in the relationships. The syntax is as follows:

MODEL:
PID BY cid_2-cid_5;
UPB BY upb1-upb6;
CARSI BY career1-career6;
IMP BY impr1-impr3;
AUT BY aut1-aut3;
UPB ON PID sal cod IMP AUT sameval CARSI tenure contstat;
PID ON IMP AUT contstat;

The grouping model for e.g. "sal" where I excluded cod to see the sole effect of sal:

GROUPING IS sal (0=no 1=yes);
MODEL:
PID BY cid_2-cid_5;
UPB BY upb1-upb6;
CARSI BY career1-career6;
IMP BY impr1-impr3;
AUT BY aut1-aut3;
UPB ON PID IMP AUT sameval CARSI tenure contstat;
PID ON IMP AUT contstat;

Although R^2 increases in grouping models, I get lower fit indices, as for "sal"-grouping I get Chi-sq=534.066 // Contr group yes (N=64): 271.514; Contr group no (N=118): 262.552; df=217; CFI=0.911; TLI=0.899; RMSEA=0.060; SRMR=0.083. Similar results I get for "cod"-grouping. Could you please tell me what the reason might be and whether that is ok?
 Linda K. Muthen posted on Wednesday, December 14, 2011 - 1:13 pm
The fit statistics will differ between the MIMIC and multiple group models because the sample statistics used for the analyses differ.
 Keke Hiller posted on Wednesday, December 14, 2011 - 1:17 pm
Linda, thank you very much for the fast reply!
As such, I do not have to worry about that fact? Can I increase the model fit indices?Which one should I report?

Thank you very much for your help!
 Linda K. Muthen posted on Wednesday, December 14, 2011 - 1:24 pm
No, you don't need to worry that they differ. You should report the fit indices for the model you decide to report.
 Cornelia Schoor posted on Thursday, May 08, 2014 - 7:37 am
Hi,

I have the same problem Daniel described in (2) in the first posting: I would like to compare path coefficients between groups. Unfortunately, I cannot do a chi-square difference test, as chi-square is not available due to replicate weights. Is there another way to check for differences?
 Linda K. Muthen posted on Thursday, May 08, 2014 - 2:15 pm