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Message/Author
 Doris Rubio posted on Wednesday, November 03, 1999 - 8:25 am
When conducting multiple group analysis (MIMIC model), is it appropriate to test the model on one group and then use multiple group to test the equality of the parameters across both groups? And if the results suggests that the model does not fit across both groups what is the next logical procedure? to free the error variance?
So, if you find that the model does have different error variance and different parameter estimates, does that mean that the measure is biased across groups?
 Linda K. Muthen posted on Thursday, November 04, 1999 - 10:47 am
I would test the model separately on all groups before I attempted a multiple group analysis. I would include a set of background variables including the one that is ultimately the grouping variable to see if it has an effect. If the model did not fit for each group, I would analyze the groups separately. If it did, I would then do a multiple group analysis to test measurement invariance.

With categorical outcomes, a multiple group model must include thresholds and scale factors for identification purposes. Measurement invariance requires that the factor loadings and the thresholds be held equal across the groups. I would look at the derivatives (like modification indices for categorical) and see where the misfit is. Residual covariances could take care of part of the problem and they can vary across groups without violating measurement invariance. If differences exist in the factor loadings and thresholds, I would free them but not without a good reason. Partial measurement invariance is possible.
 MikeW posted on Wednesday, April 19, 2000 - 1:52 pm
I'm trying to estimate a multiple group
measurement model using dichotomous indicators.
Each time I run the model, an error msg regarding a floating point error flashes in the
DOS window that appears during estimation. Is there a way to "capture" that message? I've
tried running the model through both the windows
& DOS interface but the msg appears to quickly.

My out file is pasted below. I'm wondering whether using the "group" variable to both subset
cases and define groups in a MCFA setup is problematic?

Thanks for any assistance you might provide.

-MW

============Mplus syntax for MCFA===============

Mplus VERSION 1.03
MUTHEN & MUTHEN
04/19/2000 4:52 PM

INPUT INSTRUCTIONS

TITLE: MCFA of ADHD symptoms, males age 9 & 10

DATA: FILE IS e:\csem\mikew\research\gsms\mcfa\prtadhdsxs.txt;
FORMAT IS free;
TYPE IS individual;

NOBSERVATIONS ARE 1716;

VARIABLE: NAMES ARE
GSMSID GROUP P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8 P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18 WT2;

USEOBSERVATIONS = group LE 2;

USEVARIABLES = P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8 P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18;

CATEGORICAL = P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8 P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18;

GROUPING IS group (1=male9, 2=male10);

WEIGHT IS wt2;


ANALYSIS: TYPE = MEANSTRUCTURE;
!adding "mgroup" doesn't help;

ESTIMATOR = WLSM;

MODEL:
f1 BY P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8;
f2 BY P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18;
f1 with f2;

!factor correlation is free to vary, ;
!lambda & thresholds are fixed by default.;

OUTPUT: sampstat; residual;


=======output starts but doesn't finish========

INPUT READING TERMINATED NORMALLY

MCFA of ADHD symptoms, males age 9 & 10

SUMMARY OF ANALYSIS

Number of groups 2
Number of observations
Mplus VERSION 1.0 PAGE 2
MCFA of ADHD symptoms, males age 9 & 10

Group MALE9 254
Group MALE10 246

Number of y-variables 13
Number of x-variables 0
Number of continuous latent variables 2

Observed variables in the analysis
P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8
P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18

Grouping variable GROUP
Weight variable WT2

Categorical variables
P4NHY1 P4NHY2 P4NHY3 P4NHY4 P4NHY7 P4NHY8
P4NHY10 P4NHY12 P4NHY13 P4NHY15 P4NHY16 P4NHY17 P4NHY18

Continuous latent variables in the analysis
F1 F2

Estimator WLSM
Maximum number of iterations 1000
Convergence criterion .500D-04

Input data file(s)
e:\csem\mikew\research\gsms\mcfa\prtadhdsxs.txt

Input data format FREE

=========end of output file=================
 Maria Orlando posted on Tuesday, May 09, 2000 - 5:47 pm
I'm having the same problem as described by MikeW on Wednesday, April 19, 2000 - 01:52 pm. In my case, I am trying to estimate a Latent Class model using 58 dichotomous class indicators and 5 latent classes. The sample size is 24,505. The floating point error message flashes in the DOS window and the output terminates in the same place ("Input data format FREE").
 joeln posted on Friday, February 01, 2002 - 2:41 pm
I am planning to examine the equivalence of a measure across 5 groups. My data are significantly skewed and kurtotic, and transformations have not been effective. Due to sample size requirements for ADF estimators, I have chosen instead to report the Satorra-Bentler Scaled statistic. I have read Satorra's paper regarding the computation for the chi-square difference test when using the scaled chi-square.

I am seeking advice on what fit statistics in addition to the S-B chi-square are appropriate for examining differences in nested models where data are non-normal. I have seen the formulas for computing robust a CFI, but am uncertain whether this is appropriate. Recently, researchers have examined the RNI, GFI and NNFI in determining equivalence of nested models. Is it possible (and appropriate) to obtain “robust” versions of these other statistics? Thanks for any assistance.
 Linda K. Muthen posted on Saturday, February 02, 2002 - 8:39 am
If you are using MLM in Mplus, all chi-square based fit statistics (CFI, TLI, RMSEA) are based on the Satorra-Bentler chi-square. I am not familiar with the research on examining differences in nested models using fit indices. Mplus does not compute RNI, GFI, and NNFI.
 joeln posted on Monday, February 04, 2002 - 1:37 pm
Linda,

Thank you for your assistance. I plan to manually calculate the other fit indices and will use the S-B chi-square.
 Jim Davis posted on Sunday, August 25, 2002 - 12:58 am
I am planning to examine the equivalence of the factor structure of a measure with dichotomous indicators across 3 groups and took previously posted advice to test the model separately for all groups first. However, in the results for one group, the S.E., as well as Residual variance, for one item are listed as ********, and the factor loading for that item is listed as 32.791. Yet the model estimation terminated normally. I've checked the data set and the model but cannot determine what led to these results! Any advice would be greatly appreciated!
 bmuthen posted on Sunday, August 25, 2002 - 12:09 pm
When the standard errors are large enough to produce ***** in the output, the model is often (close to) non-identified. Perhaps you want to send the data and input to support@statmodel.com for further advice.
 Jim Davis posted on Wednesday, August 28, 2002 - 5:17 pm
A belated thank you for your suggestion!
 Carol W posted on Thursday, November 21, 2002 - 9:05 am
Hello,

I am trying to test whether the overall form of a factor model differs for men vs women. I have all categorical outcomes, and am using WLSMV, specifying 2 groups, and estimating a meanstructure (because I assume meanstructure is necessary for identification). When I run the model, I get this error in the output file:

*** ERROR
Based on Group 0: Group 1 contains
inconsistent categorical value for OB6: 7

"OB6" is an item (outcome) in my analysis which can take on the values 1, 2, 3, 4, 5, 6, or 7. I assume this error message relates to the fact that noone in group 0 gave response "7" to item OB6, but at least one person in group 1 gave response "7" to this item. But, why does that prevent the model from running? What should I be doing differently?
 bmuthen posted on Thursday, November 21, 2002 - 10:44 am
You are understanding the error message correctly. Mplus does not allow different number of categories across groups. You can collapse the top 2 categories - for group 1 this does perhaps not change things much since few individuals are in the highest category anyway. Collapsing can easily be done using the Mplus Define command.
 alexandra posted on Monday, April 07, 2003 - 1:18 am
Hello,

I am trying to do a multigroup modelling. First I tested a model for each of the two groups separately and I obtained good results. Then I tested the model in a multigroup modelling and the estimation has not converged. Last, I put off a correlation between two variables of the model, I tested again the model in a multigroup modelling and the model converged. But if I test again the second model separately for the two groups, I do not obtain as goog results as with the first one. What does it mean?
 Linda K. Muthen posted on Monday, April 07, 2003 - 9:11 am
When you restrict the covariance to zero, the model is more restrictive and therefore may have an easier time converging. It also may not fit as well. I suggest trying to get the model with the covariance to converge. There are suggestions about convergence problems on pages 160-162 of the Mplus User's Guide. If you still cannot get the model to converge, please send the output and data to support@statmodel.com and I will be happy to look at it.
 Chris Richardson posted on Sunday, January 04, 2004 - 12:26 am
Hi Bengt/Linda,
I am trying to assess the stability over time (2 assessments separated by 3 years)of a construct (with a second order facture structure) in 3 different age groups. The indicators are resposes to a 7-pt likert scale. The primary hypothesis I want to test does not involve relative levels of the construct across groups but rather it's stability across the assessment periods - the youngest group should show the least stability while the medium and older age groups should show relatively high stability. To do this I am trying to run a multi-group longitudinal factor analysis. From looking at the examples in the MPLUS User Guide I have come up with the following model (see below) and questions - Question 1: Do you think the approach I've taken in the model below is appropriate (I have a very large n for each group)? and Question 2 Are there limits on the number of indicator variables I can use in this type of analysis? Thanks for your time and any feedback you are able to provide as well as for all the great advice posted on this web site.
Regards
Chris Richardson

MPLUS SYNTAX

Title: Multigroup Longitudinal CFA of second order factor structure

DATA: FILE is soc.dat;

VARIABLE: NAMES ARE y1–y13 y1b y2b y3b y4b y5b y6b y7b y8b y9b y10b y11b y12b y13b Age;
CATECORICAL ARE y1-Age;
GROUPING IS Age (1=young 2=middle 3=older);

ANALYSIS: TYPE = MEANSTRUCTURE;

MODEL :
f1 BY y1 y9 y11 y13;
f2 BY y2 y5 y6 y7 y12;
f3 BY y3 y4 y8 y10;
f5 BY f1 f2 f3;

f6 BY y1b y9b y11b y13b;
f7 BY y2b y5b y6b y7b y12b;
f8 BY y3b y4b y8b y10b;
f10 BY f6 f7 f8;

f5 ON f10;

[y1$1 y1$2 y1$3 y1$4 y1$5 y1$6 y1b$1 y1b$2 y1b$3 y1b$4 y1b$5 y1b$6] (1);
[y2$1 y2$2 y2$3 y2$4 y2$5 y2$6 y2b$1 y2b$2 y2b$3 y2b$4 y2b$5 y2b$6] (2);
[y3$1 y3$2 y3$3 y3$4 y3$5 y3$6 y3b$1 y3b$2 y3b$3 y3b$4 y3b$5 y3b$6] (3);
[y4$1 y4$2 y4$3 y4$4 y4$5 y4$6 y4b$1 y4b$2 y4b$3 y4b$4 y4b$5 y4b$6] (4);
[y5$1 y5$2 y5$3 y5$4 y5$5 y5$6 y5b$1 y5b$2 y5b$3 y5b$4 y5b$5 y5b$6] (5);
[y6$1 y6$2 y6$3 y6$4 y6$5 y6$6 y6b$1 y6b$2 y6b$3 y6b$4 y6b$5 y6b$6] (6);
[y7$1 y7$2 y7$3 y7$4 y7$5 y7$6 y7b$1 y7b$2 y7b$3 y7b$4 y7b$5 y7b$6] (7);
[y8$1 y8$2 y8$3 y8$4 y8$5 y8$6 y8b$1 y8b$2 y8b$3 y8b$4 y8b$5 y8b$6] (8);
[y9$1 y9$2 y9$3 y9$4 y9$5 y9$6 y9b$1 y9b$2 y9b$3 y9b$4 y9b$5 y9b$6] (9);
[y10$1 y10$2 y10$3 y10$4 y10$5 y10$6 y10b$1 y10b$2 y10b$3 y10b$4 y10b$5 y10b$6] (10);
[y11$1 y11$2 y11$3 y11$4 y11$5 y11$6 y11b$1 y11b$2 y11b$3 y11b$4 y11b$5 y11b$6] (11);
[y12$1 y12$2 y12$3 y12$4 y12$5 y12$6 y12b$1 y12b$2 y12b$3 y12b$4 y12b$5 y12b$6] (12);
[y13$1 y13$2 y13$3 y13$4 y13$5 y13$6 y13b$1 y13b$2 y13b$3 y13b$4 y13b$5 y13b$6] (13);
 Linda K. Muthen posted on Monday, January 05, 2004 - 9:19 am
First of all, there are no limits on the number of indicator variables other than the limit of 500 variables in an analysis. It's just time and the size of your computer that may be limiting.

If you are not planning to look at the three groups together, that is, you see them coming from different populations, then I would analyze each one separately.

Regarding your setup, I wonder why you are not holding factor loadings equal over time, just thresholds. Also, I wonder about f5 ON f10;

You need to include scale factors for categorical indicators when you have a longitudinal model. Following is a generic setup that you can follow in which factor loadings and thresholds are held equal. Note also the inclusion of the factor means.

MODEL:
f1 BY u11
u21 (1);
f2 BY u12
u22 (1);
f3 BY u13
u23 (1);
f4 BY u14
u24 (1);
[u11 u12 u13 u14] (2);
[u21 u22 u23 u24] (3);
{u11-u21@1 u12-u24};
[f1@0 f2-f4];];
 Chris Richardson posted on Tuesday, January 06, 2004 - 8:07 pm
Hi Linda,
Many thanks for taking the time to reply - in trying to understand this longitudinal CFA model I ran into a couple of road blocks. Question 1: If I’m freely estimating latent means for time 2 in group 1 – what to do about fixing all latent means in group 1 to zero for the multi-group component of the analysis? Question 2: When constraining individual thresholds to be equal across time do I need to fix each individual threshold of an indicator on a separate line (my guess is yes but just wanted to check)?

With regard to modeling the groups separately, the age groups come from the same general population survey though based on the theory behind the scale they could be conceived of as different subpopulations. If I run a longitudinal CFA separately for each group (see model below) would it be appropriate to directly compare the time 1 time 2 correlations/R-squared of the 3 age groups - I also seem to remember being shown a formula to create 95 % confidence intervals for correlations. Thanks again for your advise - it is appreciated.
cheers
chris

REVISED MODEL

Title: Full Invariance Longitudinal CFA of second order factor structure

DATA: FILE is soc.dat;

VARIABLE: NAMES ARE y1–y13 y1b y2b y3b y4b y5b y6b y7b y8b y9b y10b y11b y12b y13b Age;
CATECORICAL ARE y1-Age;

ANALYSIS: TYPE = MEANSTRUCTURE;

MODEL :
f1 BY y1@1
y9 (1)
y11 (2)
y13 (3);
f2 BY y2@1
y5 (4)
y6 (5)
y7 (6)
y12 (7);
f3 BY y3@1
y4 (8)
y8 (9)
y10 (10);
f4 BY f1@1
f2 (11)
f3 (12);

f5 BY y1b@1
y9b (1)
y11b (2)
y13b (3);
f6 BY y2b@1
y5b (4)
y6b (5)
y7b (6)
y12b (7);
f7 BY y3b@1
y4b (8)
y8b (9)
y10b (10);
f8 BY f5@1
f6 (11)
f7 (12);

f4 WITH f8

! MPLUS automatically fixes the first factor loading in each BY statement to 1
! Which loading is fixed can be overridden using *(free) and @ (fix)
! Numbers in round brackets (1-12) indicate equal across time

{y1-y13 @1 y1b – y13b};
! Curly brackets constrain scale factors to be equal across time 1 and free across time 2

[f1-f4@0 f5-f8];
! Square brackets fix time 1 factor means to zero and free time 2 factor means

[y1$1 y1$2 y1$3 y1$4 y1$5 y1$6 y1b$1 y1b$2 y1b$3 y1b$4 y1b$5 y1b$6] (1);
[y2$1 y2$2 y2$3 y2$4 y2$5 y2$6 y2b$1 y2b$2 y2b$3 y2b$4 y2b$5 y2b$6] (2);
[y3$1 y3$2 y3$3 y3$4 y3$5 y3$6 y3b$1 y3b$2 y3b$3 y3b$4 y3b$5 y3b$6] (3);
[y4$1 y4$2 y4$3 y4$4 y4$5 y4$6 y4b$1 y4b$2 y4b$3 y4b$4 y4b$5 y4b$6] (4);
[y5$1 y5$2 y5$3 y5$4 y5$5 y5$6 y5b$1 y5b$2 y5b$3 y5b$4 y5b$5 y5b$6] (5);
[y6$1 y6$2 y6$3 y6$4 y6$5 y6$6 y6b$1 y6b$2 y6b$3 y6b$4 y6b$5 y6b$6] (6);
[y7$1 y7$2 y7$3 y7$4 y7$5 y7$6 y7b$1 y7b$2 y7b$3 y7b$4 y7b$5 y7b$6] (7);
[y8$1 y8$2 y8$3 y8$4 y8$5 y8$6 y8b$1 y8b$2 y8b$3 y8b$4 y8b$5 y8b$6] (8);
[y9$1 y9$2 y9$3 y9$4 y9$5 y9$6 y9b$1 y9b$2 y9b$3 y9b$4 y9b$5 y9b$6] (9);
[y10$1 y10$2 y10$3 y10$4 y10$5 y10$6 y10b$1 y10b$2 y10b$3 y10b$4 y10b$5 y10b$6] (10);
[y11$1 y11$2 y11$3 y11$4 y11$5 y11$6 y11b$1 y11b$2 y11b$3 y11b$4 y11b$5 y11b$6] (11);
[y12$1 y12$2 y12$3 y12$4 y12$5 y12$6 y12b$1 y12b$2 y12b$3 y12b$4 y12b$5 y12b$6] (12);
[y13$1 y13$2 y13$3 y13$4 y13$5 y13$6 y13b$1 y13b$2 y13b$3 y13b$4 y13b$5 y13b$6] (13);

! The above comments fix the thresholds to be equal from time 1 to time 2
 Linda K. Muthen posted on Wednesday, January 07, 2004 - 9:45 am
Regarding the means when you analyze the groups together, consider the following example for two groups (means only):

MODEL g1: [f1@0 f2-f4];
MODEL g2: [f1-f4];

Yes, you can have only one equality constraint per record/line.

If you are analyzing the groups separately, there can be no direct comparison across groups because the factors don't mean the same thing in all groups. You would have to have measurement invariance across the groups to do any comparisons.
 Stephanie West posted on Tuesday, May 18, 2004 - 8:31 pm
I want to see if there is a difference on the scores of respondents based on their gender. I've looked through the manual and online and came up with the following input for my model. Is this correct, and if so, how do I tell if responses differ by my grouping variable. If the answer is already indicated somewhere, please direct me to the appropriate source.

data:
file=F:\Final Results 4-04\RESNOMISS.dat;
format=free;
type=individual;
nobservations are 455;
ngroups=1;
variable:
names= V1 R1 A1-A9 B1-B9 C1-C30 D1-D4 E1-E30 S1;
usevariables= C1-C7 C9-C21 C23 C24 C27-C30;
categorical= C1-C7 C9-C21 C23 C24 C27-C30;
grouping is D1 (0=male 1=female);
analysis:
type=general;
model:
f1 by C7 C11 C20 C24;
f2 by C1 C2 C12 C21 C27;
f5 by C5 C14 C15 C28;
f6 by C17 C30;
f7 by C10 C16 C23;
f8 by C6 C18 C29;
f9 by C4 C9;
f10 by C3 C13 C19;
f2 with f1;
f5 with f1@0 f2;
f6 with f1@0 f2 f5;
f7 with f1 f2@0 f5 f6;
f8 with f1 f2 f5 f6 f7;
f9 with f1 f2 f5 f6 f7 f8;
f10 with f1 f2@0 f5 f6 f7 f8 f9;
output:
standardized sampstat tech1;
 Linda K. Muthen posted on Wednesday, May 19, 2004 - 10:31 am
Example 5.16 in the Mplus User's Guide shows a multiple group CFA with categorical factor indicators. To test measurement invariance, you would first run the default overall model where factor loadings and thresholds are held equal as the default. The second model is one where factor loadings and thresholds are unequal across groups. How to relax the default equality is shown in Example 5.16. Note that you do not need the NGROUPS option with individual data and that the number of groups is 2 not 1.
 Anonymous posted on Monday, October 04, 2004 - 8:26 am
I am fitting a multi-group irt model using the known class specification in a mixture analysis. I have 118 dichotomous items that load on a single factor in four groups. I hold the factor loadings and item thresholds fixed across groups and allow the factor means and variances to be free in groups 2, 3, and 4. Although I make no reference to the categorical latent class variable in the model statements I get means for the categorical latent variables in groups 1, 2, and 3.

I do not understand what these values represent. They seem to be related to the estimated factor means but I'm not sure. Is there any way to avoid estimating these parameters.
 bmuthen posted on Monday, October 04, 2004 - 9:17 am
They represent logit estimates corresponding to the proportion of individuals in each group, i.e. the proportions in the sample. They do not harm the estimation of the rest of the model. If you don't want them you can fix them at the correct values.
 Anonymous posted on Thursday, June 23, 2005 - 1:41 pm
Hi,

I'm new to Mplus and SEM in general...sorry if this is an easy one! My model was working fine before I defined my variables as categorical--now I'm getting the message:

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED.

Any insight would be great-Thx!

Here's my script:
Variable:
NAMES= age1 drug1 age2 gen2 drug2 zygo p1 p2;
USEVARIABLES = age1 drug1 age2 drug2 p1 p2 ;
CATEGORICAL = drug1 drug2 p1 p2 ;
GROUPING = zygo (1=MZ 2=DZ 3=FS 4=HS 5=NR);
MISSING = .;
Define:
cut p1 (0 3);
cut p2 (0 3);
cut drug1 (0 3);
cut drug2 (0 3);

Analysis:

TYPE = MEANSTRUCTURE MGROUP;
ITERATIONS = 10000;

MODEL:
A1 by p1@1;
C1 by p1@1;
E1 by p1@1;

A2 by p2@1;
C2 by p2@1;
E2 by p2@1;

A1* (AMZ);
C1* (2);
E1* (3);

A2* (AMZ);
C2* (2);
E2* (3);

A1 WITH C1@0 E1@0 C2@0 E2@0;
C1 WITH E1@0 A2@0 E2@0;
E1 WITH A2@0 C2@0 E2@0;
A2 WITH C2@0 E2@0;
C2 WITH E2@0 ;
C1 WITH C2* (2);
A1 WITH A2* (AMZ);

p1@0;
p2@0;
p1 WITH p2@0;
p1 WITH drug1@0 drug2@0;
p2 WITH drug1@0 drug2@0;

[A1@0 C1@0 E1@0];
[A2@0 C2@0 E2@0];

age1 WITH A1-E2@0 ;
age2 WITH A1-E2@0 ;


drug1 WITH drug2*;

drug1 ON A1* (8);
drug1 ON C1* (7);
drug1 ON E1@0;

drug2 ON A2* (9);
drug2 ON C2* (7);
drug2 ON E2@0;


p1 ON age1 ;
p2 ON age2 ;
drug1 ON age1 ;
drug2 ON age2 ;

age1 with p2 drug2;
age2 with p1 drug1;


MODEL DZ:
A1 WITH A2* (ADZ);
drug1 WITH drug2*;
E1* (9) ;
E2* (9);

MODEL FS:
A1 WITH A2* (ADZ);
drug1 WITH drug2*;
E1* (10);
E2* (10);

MODEL HS:
A1 WITH A2* (AHS);
drug1 WITH drug2*;
E1*(11);
E2*(11);

MODEL NR:
A1 WITH A2* (ANR);
drug1 WITH drug2*;
E1* (12);
E2* (12);

MODEL CONSTRAINT:
ADZ=.5*AMZ;
AHS=.25*AMZ;
ANR=0;

OUTPUT:
STANDARDIZED;
 BMuthen posted on Friday, June 24, 2005 - 2:02 am
It looks like you are estimating a twin model using A, C, and E factors. With categorical outcomes, the E factor parameter is not separately identified. See the Prescott article in Behavioral Genetics from about a year ago. It is on the website.
 abdr0005 posted on Tuesday, November 29, 2005 - 7:14 pm
Hi Linda/Bengt,

This is my first experience using MPLUS and performed the analysis of multigroup CFA. my intention is to examine whether the instrument that I used is invariance across three ethnic groups undertaken in this study. Based on the output can I say that the instrument is equivalence across groups? Is there any further analysis I should carried out? Attached the result:
Mplus VERSION 3.13
MUTHEN & MUTHEN
01/28/2005 12:07 AM

INPUT INSTRUCTIONS


TITLE: School leadership with real data

DATA:

FILE IS c:\NORM\REAL DATA\mgcfa.dat;
FORMAT is 34F1.0;
NGROUPS=3;

VARIABLE:

NAMES ARE t_ethnic item01-item31;
USEVARIABLE t_ethnic item02-item16 item18-item22
item24-item31;
GROUPING IS t_ethnic (1= Malay 2= Chinese 3= Indian);
MISSING ARE BLANK;

MODEL:

BGR BY item02@0.01 item03-item05 item07 item22@1;
RNWT BY item18* item19 item24 item25@1 item26 item28-item29
item30;
PGE BY item08* item09@1 item13 item14 item15 item21;
GCA BY item06* item10-item12 item16@1 item20 item27 item31;


LEADER BY BGR* RNWT@1 PGE GCA;

MODEL MALAY: ITEM04 WITH ITEM03;
ITEM08 WITH ITEM07;
ITEM11 WITH ITEM10;
ITEM14 WITH ITEM13;
ITEM18 WITH ITEM12;
ITEM21 WITH ITEM20;
ITEM22 WITH ITEM20;
ITEM22 WITH ITEM21;
ITEM25 WITH ITEM11;
ITEM27 WITH ITEM20;
ITEM27 WITH ITEM21;
ITEM27 WITH ITEM22;
ITEM27 WITH ITEM26;
ITEM28 WITH ITEM27;
ITEM29 WITH ITEM28;
LEADER BY BGR* RNWT PGE@1 GCA;
GCA@0.01
BGR@0.01
PGE@0.01
ITEM28 WITH ITEM26;
ITEM31 WITH ITEM30;
ITEM31 WITH ITEM26;




MODEL CHINESE: LEADER BY BGR* RNWT@1 PGE GCA;
PGE@0.01
ITEM04 WITH ITEM03;
ITEM08 WITH ITEM07;
ITEM09 WITH ITEM04;
ITEM11 WITH ITEM10;
ITEM13 WITH ITEM02;
ITEM13 WITH ITEM12;
ITEM14 WITH ITEM13;
ITEM22 WITH ITEM20;
ITEM22 WITH ITEM21;
ITEM25 WITH ITEM11;
ITEM25 WITH ITEM16;
ITEM27 WITH ITEM26;
ITEM28 WITH ITEM27;
ITEM29 WITH ITEM13;
ITEM30 WITH ITEM29;
GCA@0.01
ITEM31 WITH ITEM19;
ITEM26 WITH ITEM25;
ITEM26 WITH ITEM10;
ITEM28 WITH ITEM26;
ITEM21 WITH ITEM20;
ITEM15 WITH ITEM14;

MODEL INDIAN: ITEM30 WITH ITEM29;
ITEM05 WITH ITEM03;
ITEM05 WITH ITEM04;
ITEM08 WITH ITEM07;
ITEM14 WITH ITEM13;
ITEM22 WITH ITEM20;
ITEM22 WITH ITEM21;
ITEM24 WITH ITEM22;
ITEM27 WITH ITEM26;
ITEM28 WITH ITEM27;
ITEM29 WITH ITEM20;
ITEM29 WITH ITEM27;
ITEM29 WITH ITEM28;
ITEM30 WITH ITEM27;
ITEM31 WITH ITEM28;
ITEM31 WITH ITEM30;
GCA@0.01
ITEM04 WITH ITEM03;
ITEM21 WITH ITEM20;
ITEM30 WITH ITEM28;
ITEM31 WITH ITEM29;
ITEM06 WITH ITEM05;
ITEM06 WITH ITEM04;
ITEM11 WITH ITEM10;
ITEM21 WITH ITEM05;
ITEM19 WITH ITEM15;


ANALYSIS:

ITERATIONS=10000;



OUTPUT: TECH4 MODINDICES STANDARDIZED;



INPUT READING TERMINATED NORMALLY



School leadership with real data

SUMMARY OF ANALYSIS

Number of groups 3
Number of observations
Group MALAY 377
Group CHINESE 387
Group INDIAN 485

Number of dependent variables 28
Number of independent variables 0
Number of continuous latent variables 5

Observed dependent variables

Continuous
ITEM02 ITEM03 ITEM04 ITEM05 ITEM06 ITEM07
ITEM08 ITEM09 ITEM10 ITEM11 ITEM12 ITEM13
ITEM14 ITEM15 ITEM16 ITEM18 ITEM19 ITEM20
ITEM21 ITEM22 ITEM24 ITEM25 ITEM26 ITEM27
ITEM28 ITEM29 ITEM30 ITEM31

Continuous latent variables
BGR RNWT PGE GCA LEADER

Variables with special functions

Grouping variable T_ETHNIC

Estimator ML
Information matrix EXPECTED
Maximum number of iterations 10000
Convergence criterion 0.500D-04
Maximum number of steepest descent iterations 20

Input data file(s)
c:\NORM\REAL DATA\mgcfa.dat

Input data format
(34F1.0)



THE MODEL ESTIMATION TERMINATED NORMALLY



TESTS OF MODEL FIT

Chi-Square Test of Model Fit

Value 2886.044
Degrees of Freedom 1029
P-Value 0.0000

Chi-Square Test of Model Fit for the Baseline Model

Value 42828.265
Degrees of Freedom 1134
P-Value 0.0000

CFI/TLI

CFI 0.955
TLI 0.951

Loglikelihood

H0 Value -34698.436
H1 Value -33255.414

Information Criteria

Number of Free Parameters 189
Akaike (AIC) 69774.871
Bayesian (BIC) 70744.460
Sample-Size Adjusted BIC 70144.110
(n* = (n + 2) / 24)

RMSEA (Root Mean Square Error Of Approximation)

Estimate 0.066
90 Percent C.I. 0.063 0.069

SRMR (Standardized Root Mean Square Residual)

Value 0.044



MODEL RESULTS

Estimates S.E. Est./S.E. Std StdYX

Group MALAY

BGR BY
ITEM02 0.010 0.000 0.000 0.011 0.023
ITEM03 0.938 0.025 38.169 1.018 0.851
ITEM04 0.968 0.024 40.491 1.050 0.860
ITEM05 0.884 0.023 37.902 0.960 0.850
ITEM07 0.969 0.023 41.969 1.051 0.876
ITEM22 1.000 0.000 0.000 1.085 0.872

RNWT BY
ITEM18 0.817 0.021 39.818 0.973 0.865
ITEM19 0.846 0.024 34.860 1.008 0.800
ITEM24 0.965 0.022 43.286 1.150 0.907
ITEM25 1.000 0.000 0.000 1.192 0.832
ITEM26 0.838 0.022 38.920 0.998 0.849
ITEM28 0.824 0.022 37.402 0.982 0.859
ITEM29 0.822 0.021 38.767 0.980 0.871
ITEM30 0.848 0.021 40.425 1.011 0.872

PGE BY
ITEM08 0.859 0.019 44.556 1.008 0.877
ITEM09 1.000 0.000 0.000 1.173 0.913
ITEM13 0.847 0.018 47.596 0.994 0.886
ITEM14 0.884 0.019 46.428 1.037 0.877
ITEM15 0.983 0.022 44.543 1.154 0.868
ITEM21 0.889 0.021 42.893 1.043 0.874

GCA BY
ITEM06 0.859 0.021 41.070 0.982 0.855
ITEM10 0.982 0.022 44.348 1.123 0.870
ITEM11 0.980 0.021 46.458 1.121 0.901
ITEM12 0.867 0.018 47.526 0.992 0.895
ITEM16 1.000 0.000 0.000 1.143 0.901
ITEM20 0.871 0.021 41.303 0.995 0.845
ITEM27 0.861 0.020 42.611 0.985 0.854
ITEM31 0.900 0.022 39.996 1.029 0.815

LEADER BY
BGR 0.924 0.025 37.099 0.996 0.996
RNWT 0.996 0.029 33.926 0.977 0.977
PGE 1.000 0.000 0.000 0.996 0.996
GCA 0.974 0.024 40.457 0.996 0.996

ITEM04 WITH
ITEM03 0.164 0.024 6.905 0.164 0.112

ITEM08 WITH
ITEM07 0.083 0.019 4.457 0.083 0.060

ITEM11 WITH
ITEM10 0.078 0.019 4.063 0.078 0.049

ITEM14 WITH
ITEM13 0.104 0.018 5.866 0.104 0.079

ITEM18 WITH
ITEM12 0.080 0.016 4.907 0.080 0.064

ITEM21 WITH
ITEM20 0.138 0.022 6.379 0.138 0.098

ITEM22 WITH
ITEM20 0.144 0.023 6.351 0.144 0.098
ITEM21 0.126 0.021 6.005 0.126 0.085

ITEM25 WITH
ITEM11 0.116 0.024 4.867 0.116 0.065

ITEM27 WITH
ITEM20 0.125 0.021 6.094 0.125 0.092
ITEM21 0.103 0.019 5.456 0.103 0.074
ITEM22 0.110 0.020 5.570 0.110 0.077
ITEM26 0.123 0.019 6.331 0.123 0.090

ITEM28 WITH
ITEM27 0.082 0.017 4.806 0.082 0.062
ITEM26 0.068 0.020 3.468 0.068 0.050

ITEM29 WITH
ITEM28 0.090 0.019 4.841 0.090 0.070

ITEM31 WITH
ITEM30 0.080 0.023 3.472 0.080 0.055
ITEM26 0.071 0.023 3.097 0.071 0.048

Variances
LEADER 1.367 0.110 12.398 1.000 1.000

Residual Variances
ITEM02 0.225 0.016 13.729 0.225 0.999
ITEM03 0.396 0.031 12.859 0.396 0.276
ITEM04 0.389 0.030 12.792 0.389 0.261
ITEM05 0.353 0.027 12.888 0.353 0.277
ITEM06 0.355 0.027 12.957 0.355 0.269
ITEM07 0.336 0.027 12.651 0.336 0.233
ITEM08 0.306 0.024 12.743 0.306 0.231
ITEM09 0.274 0.022 12.262 0.274 0.166
ITEM10 0.404 0.032 12.793 0.404 0.243
ITEM11 0.290 0.023 12.533 0.290 0.188
ITEM12 0.243 0.019 12.577 0.243 0.198
ITEM13 0.270 0.021 12.628 0.270 0.215
ITEM14 0.323 0.025 12.720 0.323 0.231
ITEM15 0.436 0.034 12.840 0.436 0.247
ITEM16 0.304 0.024 12.507 0.304 0.189
ITEM18 0.319 0.025 12.562 0.319 0.252
ITEM19 0.571 0.044 13.036 0.571 0.360
ITEM20 0.396 0.030 12.996 0.396 0.285
ITEM21 0.338 0.026 12.777 0.338 0.237
ITEM22 0.372 0.029 12.700 0.372 0.240
ITEM24 0.283 0.024 11.881 0.283 0.176
ITEM25 0.633 0.049 12.854 0.633 0.308
ITEM26 0.385 0.030 12.725 0.385 0.279
ITEM27 0.362 0.027 13.303 0.362 0.272
ITEM28 0.342 0.027 12.624 0.342 0.262
ITEM29 0.305 0.025 12.454 0.305 0.241
ITEM30 0.322 0.026 12.485 0.322 0.240
ITEM31 0.536 0.041 13.181 0.536 0.336
BGR 0.010 0.000 0.000 0.008 0.008
RNWT 0.064 0.011 5.659 0.045 0.045
PGE 0.010 0.000 0.000 0.007 0.007
GCA 0.010 0.000 0.000 0.008 0.008

Group CHINESE

BGR BY
ITEM02 0.010 0.000 0.000 0.010 0.026
ITEM03 0.938 0.025 38.169 0.935 0.772
ITEM04 0.968 0.024 40.491 0.965 0.824
ITEM05 0.884 0.023 37.902 0.882 0.792
ITEM07 0.969 0.023 41.969 0.966 0.829
ITEM22 1.000 0.000 0.000 0.997 0.874

RNWT BY
ITEM18 0.817 0.021 39.818 0.917 0.844
ITEM19 0.846 0.024 34.860 0.950 0.794
ITEM24 0.965 0.022 43.286 1.083 0.901
ITEM25 1.000 0.000 0.000 1.123 0.795
ITEM26 0.838 0.022 38.920 0.940 0.813
ITEM28 0.824 0.022 37.402 0.925 0.824
ITEM29 0.822 0.021 38.767 0.923 0.837
ITEM30 0.848 0.021 40.425 0.952 0.859

PGE BY
ITEM08 0.859 0.019 44.556 0.916 0.824
ITEM09 1.000 0.000 0.000 1.066 0.876
ITEM13 0.847 0.018 47.596 0.903 0.855
ITEM14 0.884 0.019 46.428 0.942 0.855
ITEM15 0.983 0.022 44.543 1.048 0.832
ITEM21 0.889 0.021 42.893 0.948 0.836

GCA BY
ITEM06 0.859 0.021 41.070 0.904 0.816
ITEM10 0.982 0.022 44.348 1.034 0.848
ITEM11 0.980 0.021 46.458 1.032 0.859
ITEM12 0.867 0.018 47.526 0.913 0.878
ITEM16 1.000 0.000 0.000 1.053 0.865
ITEM20 0.871 0.021 41.303 0.917 0.831
ITEM27 0.861 0.020 42.611 0.907 0.834
ITEM31 0.900 0.022 39.996 0.948 0.797

LEADER BY
BGR 0.885 0.029 30.912 0.986 0.986
RNWT 1.000 0.000 0.000 0.990 0.990
PGE 0.955 0.028 33.655 0.996 0.996
GCA 0.943 0.027 35.507 0.995 0.995

ITEM04 WITH
ITEM03 0.154 0.028 5.462 0.154 0.109

ITEM08 WITH
ITEM07 0.130 0.024 5.476 0.130 0.100

ITEM09 WITH
ITEM04 0.125 0.022 5.822 0.125 0.088

ITEM11 WITH
ITEM10 0.099 0.022 4.527 0.099 0.068

ITEM13 WITH
ITEM02 0.033 0.010 3.303 0.033 0.081
ITEM12 0.079 0.015 5.371 0.079 0.072

ITEM14 WITH
ITEM13 0.053 0.015 3.417 0.053 0.045

ITEM22 WITH
ITEM20 0.118 0.020 5.842 0.118 0.094
ITEM21 0.125 0.021 6.029 0.125 0.096

ITEM25 WITH
ITEM11 0.114 0.027 4.298 0.114 0.067
ITEM16 0.112 0.028 4.068 0.112 0.065

ITEM27 WITH
ITEM26 0.218 0.024 9.082 0.218 0.173

ITEM28 WITH
ITEM27 0.180 0.023 7.844 0.180 0.147
ITEM26 0.136 0.024 5.742 0.136 0.105

ITEM29 WITH
ITEM13 0.088 0.017 5.308 0.088 0.075

ITEM30 WITH
ITEM29 0.082 0.019 4.336 0.082 0.067

ITEM31 WITH
ITEM19 0.097 0.028 3.412 0.097 0.068

ITEM26 WITH
ITEM25 0.096 0.025 3.846 0.096 0.059
ITEM10 0.069 0.019 3.709 0.069 0.049

ITEM21 WITH
ITEM20 0.076 0.021 3.582 0.076 0.061

ITEM15 WITH
ITEM14 0.066 0.022 3.045 0.066 0.048

Variances
LEADER 1.236 0.106 11.705 1.000 1.000

Residual Variances
ITEM02 0.153 0.011 13.910 0.153 0.999
ITEM03 0.593 0.045 13.057 0.593 0.404
ITEM04 0.439 0.034 12.825 0.439 0.320
ITEM05 0.463 0.036 12.968 0.463 0.373
ITEM06 0.411 0.031 13.202 0.411 0.334
ITEM07 0.426 0.034 12.654 0.426 0.314
ITEM08 0.395 0.030 13.097 0.395 0.320
ITEM09 0.345 0.027 12.657 0.345 0.233
ITEM10 0.418 0.032 12.997 0.418 0.281
ITEM11 0.378 0.029 12.927 0.378 0.262
ITEM12 0.247 0.019 12.705 0.247 0.229
ITEM13 0.300 0.023 13.106 0.300 0.269
ITEM14 0.327 0.025 12.840 0.327 0.269
ITEM15 0.487 0.037 13.017 0.487 0.307
ITEM16 0.374 0.029 12.855 0.374 0.252
ITEM18 0.338 0.026 12.889 0.338 0.287
ITEM19 0.528 0.040 13.210 0.528 0.369
ITEM20 0.377 0.029 13.097 0.377 0.310
ITEM21 0.386 0.030 13.003 0.386 0.300
ITEM22 0.308 0.026 11.964 0.308 0.237
ITEM24 0.274 0.023 12.101 0.274 0.189
ITEM25 0.732 0.055 13.298 0.732 0.367
ITEM26 0.452 0.034 13.397 0.452 0.338
ITEM27 0.361 0.028 13.098 0.361 0.305
ITEM28 0.406 0.031 13.033 0.406 0.322
ITEM29 0.365 0.028 12.990 0.365 0.300
ITEM30 0.322 0.025 12.705 0.322 0.262
ITEM31 0.517 0.039 13.287 0.517 0.365
BGR 0.027 0.010 2.627 0.027 0.027
RNWT 0.025 0.009 2.790 0.020 0.020
PGE 0.010 0.000 0.000 0.009 0.009
GCA 0.010 0.000 0.000 0.009 0.009

Group INDIAN

BGR BY
ITEM02 0.010 0.000 0.000 0.011 0.025
ITEM03 0.938 0.025 38.169 0.993 0.793
ITEM04 0.968 0.024 40.491 1.025 0.811
ITEM05 0.884 0.023 37.902 0.936 0.767
ITEM07 0.969 0.023 41.969 1.026 0.852
ITEM22 1.000 0.000 0.000 1.059 0.860

RNWT BY
ITEM18 0.817 0.021 39.818 0.963 0.863
ITEM19 0.846 0.024 34.860 0.998 0.787
ITEM24 0.965 0.022 43.286 1.138 0.894
ITEM25 1.000 0.000 0.000 1.179 0.867
ITEM26 0.838 0.022 38.920 0.988 0.827
ITEM28 0.824 0.022 37.402 0.972 0.787
ITEM29 0.822 0.021 38.767 0.970 0.815
ITEM30 0.848 0.021 40.425 1.000 0.854

PGE BY
ITEM08 0.859 0.019 44.556 0.983 0.848
ITEM09 1.000 0.000 0.000 1.144 0.899
ITEM13 0.847 0.018 47.596 0.969 0.875
ITEM14 0.884 0.019 46.428 1.011 0.868
ITEM15 0.983 0.022 44.543 1.125 0.850
ITEM21 0.889 0.021 42.893 1.017 0.780

GCA BY
ITEM06 0.859 0.021 41.070 0.980 0.818
ITEM10 0.982 0.022 44.348 1.120 0.866
ITEM11 0.980 0.021 46.458 1.118 0.876
ITEM12 0.867 0.018 47.526 0.990 0.887
ITEM16 1.000 0.000 0.000 1.141 0.881
ITEM20 0.871 0.021 41.303 0.993 0.812
ITEM27 0.861 0.020 42.611 0.983 0.822
ITEM31 0.900 0.022 39.996 1.027 0.826

LEADER BY
BGR 0.907 0.026 35.052 0.998 0.998
RNWT 1.000 0.000 0.000 0.987 0.987
PGE 0.976 0.027 36.707 0.993 0.993
GCA 0.976 0.026 37.561 0.996 0.996

ITEM30 WITH
ITEM29 0.202 0.023 8.904 0.202 0.145
ITEM27 0.132 0.019 7.041 0.132 0.094
ITEM28 0.130 0.023 5.575 0.130 0.090

ITEM05 WITH
ITEM03 0.176 0.030 5.944 0.176 0.115
ITEM04 0.221 0.030 7.376 0.221 0.143

ITEM08 WITH
ITEM07 0.104 0.020 5.284 0.104 0.075

ITEM14 WITH
ITEM13 0.091 0.017 5.461 0.091 0.071

ITEM22 WITH
ITEM20 0.174 0.022 7.847 0.174 0.115
ITEM21 0.191 0.025 7.613 0.191 0.119

ITEM24 WITH
ITEM22 0.103 0.017 6.141 0.103 0.066

ITEM27 WITH
ITEM26 0.150 0.021 7.120 0.150 0.105

ITEM28 WITH
ITEM27 0.174 0.024 7.331 0.174 0.118

ITEM29 WITH
ITEM20 0.054 0.016 3.313 0.054 0.037
ITEM27 0.128 0.021 6.020 0.128 0.090
ITEM28 0.236 0.028 8.574 0.236 0.160

ITEM31 WITH
ITEM28 0.151 0.025 6.044 0.151 0.099
ITEM30 0.146 0.021 7.015 0.146 0.101
ITEM29 0.112 0.023 4.922 0.112 0.076

ITEM04 WITH
ITEM03 0.242 0.030 8.111 0.242 0.153

ITEM21 WITH
ITEM20 0.236 0.029 8.019 0.236 0.148
ITEM05 0.088 0.024 3.695 0.088 0.055

ITEM06 WITH
ITEM05 0.100 0.024 4.086 0.100 0.068
ITEM04 0.086 0.022 3.886 0.086 0.057

ITEM11 WITH
ITEM10 0.087 0.020 4.265 0.087 0.053

ITEM19 WITH
ITEM15 0.087 0.027 3.251 0.087 0.052

Variances
LEADER 1.355 0.104 13.049 1.000 1.000

Residual Variances
ITEM02 0.185 0.012 15.572 0.185 0.999
ITEM03 0.581 0.040 14.666 0.581 0.371
ITEM04 0.547 0.037 14.616 0.547 0.342
ITEM05 0.613 0.041 14.928 0.613 0.412
ITEM06 0.475 0.032 14.814 0.475 0.331
ITEM07 0.396 0.028 14.041 0.396 0.274
ITEM08 0.377 0.026 14.421 0.377 0.281
ITEM09 0.312 0.023 13.622 0.312 0.192
ITEM10 0.418 0.029 14.386 0.418 0.250
ITEM11 0.379 0.027 14.281 0.379 0.233
ITEM12 0.264 0.019 14.186 0.264 0.213
ITEM13 0.288 0.021 14.005 0.288 0.235
ITEM14 0.335 0.024 14.104 0.335 0.247
ITEM15 0.487 0.034 14.412 0.487 0.278
ITEM16 0.376 0.026 14.278 0.376 0.224
ITEM18 0.317 0.022 14.228 0.317 0.255
ITEM19 0.613 0.041 14.828 0.613 0.381
ITEM20 0.510 0.034 14.918 0.510 0.341
ITEM21 0.667 0.045 14.986 0.667 0.392
ITEM22 0.396 0.028 14.250 0.396 0.261
ITEM24 0.327 0.024 13.734 0.327 0.202
ITEM25 0.458 0.032 14.173 0.458 0.248
ITEM26 0.450 0.031 14.569 0.450 0.315
ITEM27 0.462 0.031 15.123 0.462 0.324
ITEM28 0.582 0.039 14.943 0.582 0.381
ITEM29 0.476 0.032 14.792 0.476 0.336
ITEM30 0.371 0.026 14.488 0.371 0.271
ITEM31 0.490 0.033 14.768 0.490 0.317
BGR 0.004 0.010 0.420 0.004 0.004
RNWT 0.035 0.009 4.130 0.025 0.025
PGE 0.017 0.009 2.020 0.013 0.013
GCA 0.010 0.000 0.000 0.008 0.008


R-SQUARE

Group MALAY

Observed
Variable R-Square

ITEM02 0.001
ITEM03 0.724
ITEM04 0.739
ITEM05 0.723
ITEM06 0.731
ITEM07 0.767
ITEM08 0.769
ITEM09 0.834
ITEM10 0.757
ITEM11 0.812
ITEM12 0.802
ITEM13 0.785
ITEM14 0.769
ITEM15 0.753
ITEM16 0.811
ITEM18 0.748
ITEM19 0.640
ITEM20 0.715
ITEM21 0.763
ITEM22 0.760
ITEM24 0.824
ITEM25 0.692
ITEM26 0.721
ITEM27 0.728
ITEM28 0.738
ITEM29 0.759
ITEM30 0.760
ITEM31 0.664

Latent
Variable R-Square

BGR 0.992
RNWT 0.955
PGE 0.993
GCA 0.992

Group CHINESE

Observed
Variable R-Square

ITEM02 0.001
ITEM03 0.596
ITEM04 0.680
ITEM05 0.627
ITEM06 0.666
ITEM07 0.686
ITEM08 0.680
ITEM09 0.767
ITEM10 0.719
ITEM11 0.738
ITEM12 0.771
ITEM13 0.731
ITEM14 0.731
ITEM15 0.693
ITEM16 0.748
ITEM18 0.713
ITEM19 0.631
ITEM20 0.690
ITEM21 0.700
ITEM22 0.763
ITEM24 0.811
ITEM25 0.633
ITEM26 0.662
ITEM27 0.695
ITEM28 0.678
ITEM29 0.700
ITEM30 0.738
ITEM31 0.635

Latent
Variable R-Square

BGR 0.973
RNWT 0.980
PGE 0.991
GCA 0.991

Group INDIAN

Observed
Variable R-Square

ITEM02 0.001
ITEM03 0.629
ITEM04 0.658
ITEM05 0.588
ITEM06 0.669
ITEM07 0.726
ITEM08 0.719
ITEM09 0.808
ITEM10 0.750
ITEM11 0.767
ITEM12 0.787
ITEM13 0.765
ITEM14 0.753
ITEM15 0.722
ITEM16 0.776
ITEM18 0.745
ITEM19 0.619
ITEM20 0.659
ITEM21 0.608
ITEM22 0.739
ITEM24 0.798
ITEM25 0.752
ITEM26 0.685
ITEM27 0.676
ITEM28 0.619
ITEM29 0.664
ITEM30 0.729
ITEM31 0.683

Latent
Variable R-Square

BGR 0.996
RNWT 0.975
PGE 0.987
GCA 0.992


MODEL MODIFICATION INDICES

Minimum M.I. value for printing the modification index 10.000

M.I. E.P.C. Std E.P.C. StdYX E.P.C.
Group MALAY


BY Statements

BGR BY ITEM18 14.170 0.130 0.141 0.126
RNWT BY ITEM18 13.311 0.078 0.093 0.083
PGE BY ITEM18 14.691 0.123 0.144 0.128
GCA BY ITEM18 14.674 0.126 0.144 0.128
LEADER BY ITEM18 14.497 0.122 0.143 0.127

ON/BY Statements

GCA ON GCA /
GCA BY GCA 15.983 -1.315 -1.315 -1.315

WITH Statements

ITEM06 WITH ITEM05 11.143 0.065 0.065 0.050
ITEM09 WITH ITEM04 20.232 0.074 0.074 0.047
ITEM11 WITH ITEM09 10.675 0.049 0.049 0.030
ITEM14 WITH ITEM09 10.073 -0.049 -0.049 -0.033
ITEM15 WITH ITEM07 10.719 0.067 0.067 0.042
ITEM16 WITH ITEM11 17.202 0.065 0.065 0.041
ITEM24 WITH ITEM22 12.245 0.057 0.057 0.036
ITEM25 WITH ITEM16 11.290 0.079 0.079 0.043
ITEM26 WITH ITEM15 10.349 0.067 0.067 0.043
ITEM27 WITH ITEM15 17.879 -0.076 -0.076 -0.050
ITEM29 WITH ITEM27 15.078 0.061 0.061 0.047
ITEM30 WITH ITEM04 12.901 -0.062 -0.062 -0.044

Variances/Residual Variances

GCA 15.979 -0.026 -0.020 -0.020

Group CHINESE


WITH Statements

ITEM16 WITH ITEM06 13.990 -0.078 -0.078 -0.058
ITEM16 WITH ITEM11 15.982 0.079 0.079 0.054
ITEM18 WITH ITEM06 13.459 -0.074 -0.074 -0.062
ITEM21 WITH ITEM13 10.435 -0.048 -0.048 -0.040
ITEM24 WITH ITEM05 18.489 -0.086 -0.086 -0.064
ITEM24 WITH ITEM15 10.179 -0.064 -0.064 -0.042
ITEM24 WITH ITEM18 10.307 0.057 0.057 0.043
ITEM27 WITH ITEM11 34.835 -0.088 -0.088 -0.067
ITEM29 WITH ITEM22 11.954 0.052 0.052 0.042
ITEM30 WITH ITEM19 10.497 -0.068 -0.068 -0.052

Group INDIAN


ON/BY Statements

RNWT ON GCA /
GCA BY RNWT 10.074 1.893 1.831 1.831
GCA ON RNWT /
RNWT BY GCA 10.066 0.539 0.557 0.557

WITH Statements

ITEM08 WITH ITEM03 10.417 0.061 0.061 0.042
ITEM09 WITH ITEM04 12.302 0.060 0.060 0.037
ITEM09 WITH ITEM08 11.280 0.057 0.057 0.039
ITEM12 WITH ITEM10 11.566 -0.054 -0.054 -0.038
ITEM13 WITH ITEM12 14.232 0.049 0.049 0.040
ITEM15 WITH ITEM08 10.856 -0.066 -0.066 -0.043
ITEM16 WITH ITEM04 10.016 -0.059 -0.059 -0.036
ITEM16 WITH ITEM12 15.292 -0.062 -0.062 -0.043
ITEM18 WITH ITEM12 14.406 0.055 0.055 0.044
ITEM19 WITH ITEM16 11.609 0.078 0.078 0.048
ITEM20 WITH ITEM18 14.390 0.064 0.064 0.047
ITEM21 WITH ITEM09 11.787 -0.068 -0.068 -0.041
ITEM25 WITH ITEM12 15.359 -0.068 -0.068 -0.045
ITEM25 WITH ITEM18 16.494 -0.079 -0.079 -0.052
ITEM26 WITH ITEM12 15.171 -0.062 -0.062 -0.047
ITEM27 WITH ITEM09 12.490 -0.056 -0.056 -0.037
ITEM31 WITH ITEM25 10.561 0.069 0.069 0.041
GCA WITH RNWT 10.062 0.019 0.014 0.014



TECHNICAL 4 OUTPUT


ESTIMATES DERIVED FROM THE MODEL FOR MALAY


ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 1.177
RNWT 1.258 1.420
PGE 1.263 1.362 1.377
GCA 1.230 1.326 1.332 1.307
LEADER 1.263 1.362 1.367 1.332 1.367


ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 1.000
RNWT 0.973 1.000
PGE 0.992 0.974 1.000
GCA 0.992 0.973 0.993 1.000
LEADER 0.996 0.977 0.996 0.996 1.000


ESTIMATES DERIVED FROM THE MODEL FOR CHINESE


ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 0.994
RNWT 1.093 1.260
PGE 1.044 1.180 1.136
GCA 1.031 1.165 1.113 1.109
LEADER 1.093 1.236 1.180 1.165 1.236


ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 1.000
RNWT 0.977 1.000
PGE 0.982 0.986 1.000
GCA 0.982 0.986 0.991 1.000
LEADER 0.986 0.990 0.996 0.995 1.000


ESTIMATES DERIVED FROM THE MODEL FOR INDIAN


ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 1.120
RNWT 1.230 1.391
PGE 1.200 1.323 1.308
GCA 1.201 1.323 1.291 1.302
LEADER 1.230 1.355 1.323 1.323 1.355


ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
BGR RNWT PGE GCA LEADER
________ ________ ________ ________ ________
BGR 1.000
RNWT 0.985 1.000
PGE 0.991 0.981 1.000
GCA 0.994 0.983 0.990 1.000
LEADER 0.998 0.987 0.993 0.996 1.000


Beginning Time: 00:07:50
Ending Time: 00:07:53
Elapsed Time: 00:00:03



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 Linda K. Muthen posted on Wednesday, November 30, 2005 - 6:10 pm
Please do not post outputs on Mplus Discussion. It is not meant for long posts.

Testing measurement invariance requires several steps. I suggest that you purchase the new Day 1 short course handout when it is available. The steps for testing measurement invariance for continuous outcomes is shown in detail in this document.
 abdr0005 posted on Thursday, December 01, 2005 - 3:43 pm
I'm sorry. thank you for your suggestion
 Shicheng Yu posted on Tuesday, February 14, 2006 - 3:55 pm
Dear Linda/Bengt,

I am dealing with a factor indicator, frequency of handling needles, the codings of this variable are shown below:

1 = 1-5 /week
2 = 6-10 /week
3 = 11-20 /week
4 > 20 /week
0 = not applicable (some people don't handle needles at all, such as manager and clerk in a hospital)

Can censored-inflated regression model be used? Can I define this inflation variable as "censored (bi)" in model syntax? If wrong, what is your suggestion to deal with this variable?

Thanks for your help.
 bmuthen posted on Tuesday, February 14, 2006 - 5:03 pm
Given the small number of scale steps, I would suggest treating it as a categorical variable - i.e. an ordinal (ordered polytomous) outcome.
 Jeffrey Hall posted on Wednesday, May 24, 2006 - 9:05 am
Is there a way to generate fit statistics for subgroups when using multigroup SEM? Results currently obtained partain to the overall model and provide only info on the contribution of the subgroups to the overall model chi-square. Thanks for your assistance.
 Linda K. Muthen posted on Wednesday, May 24, 2006 - 10:22 am
In Version 4 and up, chi-square contributions for each group are given but nothing for other fit statistics.
 Shane Allua posted on Monday, August 21, 2006 - 9:57 am
Hello,
I would like to do a multiple group path analysis model using THETA, but I understand that there are differences with categorical predictors and possibly the THETA param.

From what I have read, invariance testing is different for cat variables:

Model 1 - This is the default model in Mplus. The thresholds are held equal across groups and the factor loadings are held equal across groups. The scale factor is fixed to one in the first group and free in the others. The factor means are zero in the first group and free in the others.

Model 2 - The thresholds and factor loadings are free across groups. Scale factors are one in all groups and factor means are zero in all groups.

Is this still valid for a path model using THETA parameterization?

Syntax:CATEGORICAL ARE csedmin dvigmin dwtcat ;
MISSING = BLANK ;
CLUSTER = rschool ;
GROUPING IS sex (1= male 2 = female) ;

ANALYSIS: TYPE = GENERAL COMPLEX MISSING H1 MEANSTRUCTURE ;
PARAMETERIZATION = THETA ;
H1ITERATIONS = 3000 ;

MODEL:
tdiet csedmin dvigmin ON
tdiet2 refdiet4 tdiet8
refpa_neg tpa_pos tpa_self ;

dwtcat ON tdiet csedmin dvigmin ;

dwtcat ON tpa_self ;

csedmin ON tdiet ;

Your help is greatly appreciated.
 Linda K. Muthen posted on Monday, August 21, 2006 - 3:48 pm
The two models you mention above are models used for testing measurement invariance of factors. You don't have any factors in your model. So this would not apply to your model.
 Shane Allua posted on Tuesday, August 22, 2006 - 8:26 am
In a multiple group path model (as described above) using GROUPING IS, it appears that there are no default constraints. How are constraints modeled in a path model (such as in the previous post)?

Also, can the Rsquare be interpreted as with OLS when the DV is dichotomous with categorical and continuous predictors?

Many thanks.
 Linda K. Muthen posted on Tuesday, August 22, 2006 - 10:20 am
There are no default equality constraints when there are no factors. You can set equalities as follows:

MODEL:

y ON x (1);

The (1) specifies that the regression coefficient is held equal across groups. See Chapter 13 for a more thorough description of multiple group equalities.

The R-square will be for u* not for u.
 B Lee posted on Tuesday, November 14, 2006 - 1:09 pm
We are conducting a multigroup CFA with 13 ordered polytomous indicators.

While items for both groups were offered the same response option categories, a ceiling effect for one group resulted in some indicators in one group having a different endorsed range than the other group. We thought this was fixed by specifying categorical is x1-x11 (*).

1. What is the problem causing the error message? We tried Estimation=WLSMV as well, but it doesn't accept the notation (*).

2. Is there a solution for this problem other than collapsing categories (which is conceptually problematic)?

Thanks!

DATA:
file is C:\Datamplus.dat;
format is FREE;

VARIABLE:
names are x1-x11 group;
usevar are x1-x11 group;
categorical is x1-x11 (*);
grouping is group (1=GroupA 2=GroupB);

ANALYSIS:
Type = Basic;
Estimator = ML;

MODEL:
F1 by x1 x2 x4 x11;
F2 by x3 x6 x9;
F3 by x5 x7 x8 x10;

MODEL GroupA:
F1 by x2 x4 x11;
F2 by x6 x9;
F3 by x7 x8 x10;


*** ERROR in Analysis command
ALGORITHM = INTEGRATION is not available for multiple group analysis.
Try using the KNOWNCLASS option for TYPE = MIXTURE.
 Linda K. Muthen posted on Tuesday, November 14, 2006 - 1:34 pm
This * option is available only for maximum likelihood estimation.
 B Lee posted on Wednesday, November 15, 2006 - 8:19 am
Thanks for your reply. Can you explain the error message (Algorithm=Integration not available for multiple group analysis)? It seems that we need to use ML to accommodate the different range of response options for the two groups, but as output above shows, the model still wouldn't run in ML.
 Linda K. Muthen posted on Wednesday, November 15, 2006 - 8:39 am
With maximum likelihood, you need to use the KNOWNCLASS option and TYPE=MIXTURE instead of the GROUPONG option. If you need numerical integration and have more then 3 or 4 dimensions of integration, your model may be to computationally demanding. You might want to consider staying with weighted least squares and collapsing categories.
 paula elosua posted on Friday, December 29, 2006 - 4:13 am
I'm trying to carry out one invariance analysis with categorical data using intercepts, thersholds and loadings. This is my model,could you tell me please what's it wrong?
The u5 loading of the u5 variable has been modified in the second group.
Thanks a lot
DATA:
FILE = CONDI023.dat;
FORMAT IS f12.6 9f13.6 f3.0;
NGROUPS=2 ;
VARIABLE:
NAMES ARE u1-u10 g;
USEVARIABLES ARE u1-u10 g;
CATEGORICAL ARE U1-U10;
GROUPING IS g (1=g1 2=g2);
ANALYSIS:
TYPE=MEANSTRUCTURE;
PARAMETERIZATION=THETA;
MODEL:
f1 by u1;
f2 by u2;
f3 by u3;
f4 by u4;
f5 by u5;
f6 by u6;
f7 by u7;
f8 by u8;
f9 by u9;
f10 by u10;
f1@1;
f2@1;
f3@1;
f4@1;
f5@1;
f6@1;
f7@1;
f8@1;
f9@1;
f10@1;
[f1-f10];
f11 by f1 f2 f3 f4 f5 f6 f7 f8 f9 f10;
MODEL g2:
f11 BY f5;
 Boliang Guo posted on Friday, December 29, 2006 - 5:14 am
the posible problem is
NGROUPS=2 ;which from LISREL?
remove this sentence and try, pls.
 paula elosua posted on Friday, December 29, 2006 - 5:51 am
I'm trying without Ngroups=2, but the problems continues.
THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
 Linda K. Muthen posted on Friday, December 29, 2006 - 6:22 am
Please send your input, data, output, and license number to support@statmodel.com.
 B Lee posted on Friday, December 29, 2006 - 12:48 pm
I'm conducting a multi-group CFA with categorical indicators so am using knownclass with type=mixture. Membership in the 2 groups is known (with sample size for group1=306 and group2=211). However, output for the analysis suggests that 234 are in group 1 and 282 in group 2. Am I not signifying group membership correctly? The output seems to suggest that new groups have been created.

Relevant input:******************
classes=c(2)
knownclass=c(group=1 group=2)
ANALYSIS:
Type = Mixture;
Estimator = ML;

MODEL:
%OVERALL%
F1 by y1 y2 y4 y11;
F2 by y3 y6 y9;

%c#2%
F1 by y2 y4 y11;
F2 by y6 y9;
 Linda K. Muthen posted on Friday, December 29, 2006 - 12:55 pm
This is a support question. Please send your input, data, output, and license number to support@statmodel.com.
 Boliang Guo posted on Friday, December 29, 2006 - 1:19 pm
for multiple group CFA, it is straightforward to use group but not knownclass command,i think. pls refer soecial issue for multiple group CFA in manual.
fyi
group is ***(1=group1, 2=group2):
MODEL:
F1 by y1 y2 y4 y11;
F2 by y3 y6 y9;

model group2
F1 by y2 y4 y11;
F2 by y6 y9;
 Linda K. Muthen posted on Friday, December 29, 2006 - 1:52 pm
With the CATEGORICAL option and maximum likelihood estimation, the GROUPING option is not available. In this case, the KNOWNCLASS option and TYPE=MIXTURE is used. The GROUPING option is available for catgorical outcomes when the weighted least squares estimator is used.
 B Lee posted on Friday, December 29, 2006 - 2:07 pm
Thanks for your help! I was able to work out the knownclass language.

However, is there a counterpart for type=meanstructure when using knownclass and type=mixed analysis? I manually specified thresholds to check invariance, but is it possible to examine invariance of the factor variance/covariance without meanstructure?
 Linda K. Muthen posted on Friday, December 29, 2006 - 3:04 pm
No, means are automatically inlcuded with TYPE=MIXTURE. Having unstructured means as part of the model is the same as not having means the model.
 Boliang Guo posted on Saturday, December 30, 2006 - 2:36 am
thanks, professor Muthen.
 Lois Downey posted on Saturday, December 15, 2007 - 11:58 am
I ran a clustered 3-group single-factor CFA with 6 dichotomous indicators, allowing the lambdas to be freely estimated within groups.

Group 1 had 209 cases in 134 clusters.
Group 2 had 120 cases in 76 clusters.
Group 3 had 598 cases in 310 clusters.

The chi-square for overall fit was 24.782 on 24 df, with p = 0.4177.

Contributions of the 3 groups to chi-square were as follows:
Group 1 -- 7.684
Group 2 -- 5.418
Group 3 -- 11.680
This led me to believe that the best fit of the model was obtained in Group 2 and the worst fit in Group 3.

I then ran clustered CFAs in the 3 separate groups, with the following results:
Group 1 -- chi-square = 3.684, 7df, p=0.8154
Group 2 -- chi-square = 7.169, 6df, p=0.3055
Group 3 -- chi-square = 11.270, 8df, p=0.1868
The rank ordering of the chi-square values is now different, making me think perhaps the model fits Group 1 better than Group 2.

Is either of these interpretations accurate? Or is it impossible to make any statement about the relative fit of the model to the 3 groups based on this information?
 Lois Downey posted on Saturday, December 15, 2007 - 2:42 pm
What are the implications when one gets a chi-square suggesting adequate fit (p > 0.12) in a multi-group analysis with lambdas freely estimated, but significant misfit when the model is fit to the groups separately?
 Linda K. Muthen posted on Sunday, December 16, 2007 - 10:10 am
I suspect that a couple of things are going on here. First of all, when you run the multiple group analysis, thresholds and factor loadings are being held equal across groups as the default. If you have not relaxed these equalities, then the separate analyses would not be comparable to the multiple group analysis. Also, I think you are using the WLSMV estimator. The chi-square and degrees of freedom for WLSMV are not interpretable in the same was as for WLS.
 Josue Almansa Ortiz posted on Tuesday, May 06, 2008 - 9:10 am
I want to analyse invariance across three timepoints, with categorical outcomes.

1) Is there any difference using a multigroup approach, with a grouping variable indicating the measurement timepoint, respect to analyse it as three separated set of variables?

2) In case of adjusting the same model to 3-timepoints' sets of variables: Should Scale factors be fixed at one and factor means at zero as in multigroup analyses?
 Tait Medina posted on Tuesday, May 06, 2008 - 10:14 am
I am new to multiple-group cfa and am trying to follow the recommendations given in chapter 13 for models for categorical outcomes. This question might be a bit out of bounds for this forum, but in case it's not I am hoping you might be able to point me in the right direction:

If my ultimate goal is not to compare means across groups but to compare the effects of covariates across groups, should my measurement model show total measurement invariance of thresholds and factor loadings?

Thank you.
 Josue Almansa Ortiz posted on Tuesday, May 06, 2008 - 11:11 am
I've followed EXAMPLE 5.16 but I obtained an estimation "warning". Model is a Bifactor-model with categorical outcomes, testing invariance of the general factor.
Do you know if did something wrong?


GROUPING IS Time (1=T1 2=T2 3=T3);

MODEL:
f1 BY D110CI D115CI D175CI D210CI D310CI D330CI D350CI D570CI D630CI D660CI D710CI ;
f2 BY D110CI D430CI D440CI D450CI D910CI D920CI ;
GF by D110CI-D920CI;
GF with F1-F2@0; F1 with F2@0;

MODEL T2:
GF by D110CI-D920CI ;
[D110CI$1-D920CI$3];
{D110CI-D920CI@1};
[GF@0];

MODEL T3:
GF by D110CI-D920CI ;
[D110CI$1-D920CI$3];
{D110CI-D920CI@1};
[GF@0];



Output says:
"THE MODEL ESTIMATION TERMINATED NORMALLY

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 369.

THE CONDITION NUMBER IS 0.241D-18."

Parameter 369 is the variance of GF in group T2.
 Linda K. Muthen posted on Tuesday, May 06, 2008 - 12:37 pm
Josue: (1) You do not want to use multiple group analysis with repeated measures data. Multiple group analysis assumes that the observations in the groups are independent. (2) Yes.

In the group-specific MODEL commands, you should not mention the first factor loadings. When you mention them, they are no longer fixed at one to set the metric of the factors.
 Linda K. Muthen posted on Tuesday, May 06, 2008 - 12:38 pm
Tait: If you want to compare regression coefficients across groups, you would want measurement invariance.
 Boliang Guo posted on Wednesday, May 07, 2008 - 1:34 am
Dear Josue,
did you find following paper?
Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4-69.

there is an example to do ME/I for longitudinal data, I just finished a study on this topic with Mplus.
 Josue Almansa Ortiz posted on Wednesday, May 14, 2008 - 8:37 am
In the suggested paper (Vandenberg & Lance 2000) says that the wide-data approach "increased likelihood of non-convergent or improper solutions". I have 36 items and three time-points, quite a lot ...((3*36)^2 covariance-matrix elements).
Every model I've tried (Restricted and unrestricted, two and three time-points) produced wrong results (THETA and PSI are NOT POSITIVE DEFINITE) with factor correlations grater than 1. Could this misfit due to the large size of the model? or, Could I send you my inputs to you check if I made any mistake?
 Linda K. Muthen posted on Wednesday, May 14, 2008 - 10:10 am
You should send your input, data, output, and license number to support@statmodel.com.
 fite posted on Saturday, April 11, 2009 - 6:27 am
I am estimating the following multiple group model that includes all observed variables. The outcome is dichotomous. When I run this model I only get degrees of freedom and WRMR for model fit indices - no chisquare. Is there a reason I do not get a chisquare value? Is there a way to compare models?


GROUPING is race (1 = white 2 = black);

CATEGORICAL IS dicharrest;

Missing = all (-9999);

Analysis:
Type = Missing;

MODEL:

dicharrest on acad comm neigh census
peerdel ses peerej zinathyp cal cd odd dep anxiety
Zgx3a9000 Zneigharstp12;

[acad comm neigh census
peerdel ses peerej zinathyp cal cd odd dep anxiety
Zneigharstp12];

MODEL BLACK:
dicharrest on acad comm neigh census
peerdel ses peerej zinathyp cal cd odd dep anxiety
Zgx3a9000 Zneigharstp12;

MODEL WHITE:
dicharrest on acad comm neigh census
peerdel ses peerej zinathyp cal cd odd dep anxiety
Zgx3a9000 Zneigharstp12;
 Linda K. Muthen posted on Saturday, April 11, 2009 - 6:33 am
If you are using an old version of Mplus, you need to have TYPE=MISSING H1; to obtain fit statistics. If this is not the case, please send your input, data, output, and license number to support@statmodel.com.
 Emil Coman posted on Wednesday, February 17, 2010 - 1:51 pm
[simple saturated model - endogenous vs. exogenous]
Hi guys, I have a question so basic it's hard to deal with...
I am trying to test for equality of covariance matrices between 2 ethnic groups on say 3 binary indicators [no latent in the model, just the 3 observed variables, no model at all in fact].
The way I did it was to specify in a multi-group model all covariances
x1 with x2;
x1 with x3;
x2 with x3;
SAVEDATA: DIFFTEST IS xxx.dat;
then run 2nd model with
x1 with x2 (1);
x1 with x3 (2);
x2 with x3 (3);
ANALYSIS: DIFFTEST IS xxx.dat;
I got the 'Chi-Square Test for Difference Testing', but what I noticed is that all my observed variables are seen as 'dependent', even though there's only a saturated model specified, with only covariances between them.
I did this in AMOS 16 too, and there they are seen as observed - exogenous variables.
Is there a way to do this in MPlus that preserves the variables as exogenous? Thanks, Emil
 Bengt O. Muthen posted on Wednesday, February 17, 2010 - 5:16 pm
If x1-x3 are the only variables in your model, Mplus calls them "y's", not "x's". In Mplus, x's are what you call exogenous variables, where x's are variables for which there is no model. The SEM literature is a bit misleading on this in my opinion, sometimes applying a model to exogenous (x) variables. That's not done in econometrics which is where the exogenous term comes from.
 Emil Coman posted on Thursday, February 18, 2010 - 11:08 am
Thanks for clarifying it, Bengt.
[I asked Semnet about this too, and Cam and Stas have chipped in too].
Emil
 Emil Coman posted on Thursday, March 04, 2010 - 12:58 pm
I have a short question: when doing a 1 factor-1 group 10-categorical indicators CFA, I can get with TECH4 the 'ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES', which shows covariances between all my indicators and the latent, but for a 2 group similar CFA I only get the covariance of my factor with itself, but I would like to get the covariances between indicators too.
Is there a way to get this? Thanks!
 Linda K. Muthen posted on Thursday, March 04, 2010 - 2:21 pm
It sounds like in one analysis you must have put a factor behind each observed variable or there is more to the model than just the factor. You can do this in the other analysis and you will obtain what you want in TECH4.
 Emil Coman posted on Friday, March 05, 2010 - 5:17 am
I don't think now that something I did was wrong...
I re-ran things with bare minimum:
1 group
USEOBSERVATION ARE (Ethn60 EQ 1);
MODEL: CESD BY cd1-cd10;
then 2 groups
GROUPING IS Ethn60 (1 = PR 2 = BAA);
MODEL: CESD BY cd1- cd10;
That's all. The 2 groups output only lists
'ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
CESD
________
CESD 0.890 '
while the 1 group one has a full 11x11 covariance matrix.

I need the estimated covariance matrix to compute factor score coefficients, i.e. wanted to use the inverse of it multiplied by factor loadings to compute factor score coefficients then compute individual total scores [1 question was whether these scores would replicate the individual scores saved by SAVE = FSCORES].
I was able to get the covariance matrices by groups too, with a trick... I got my loadings and thresholds from the 2 group CFA, and fixed them back in 2 separate 1 group CFAs, then looked at the covariance matrices... Thank you.
 Linda K. Muthen posted on Friday, March 05, 2010 - 8:37 am
Please send the two outputs and your license number to support@statmodel.com.
 Michael Green posted on Friday, April 30, 2010 - 9:37 am
I have constructed a fairly simple path analysis model using dichotomous variables and I am doing a groups analysis using the type=mixture and knownclass options. I've identified some significant differences between groups on the thresholds for some variables. Ideally I would like to express these differences as odds ratios with confidence intervals. Am I correct in thinking I can just use the exponential of the difference between the thresholds to get the odds ratio? If not, is there another way to do this? If yes, is there a way of also producing 95% confidence intervals for those odds ratio?

Thanks, MG
 Bengt O. Muthen posted on Saturday, May 01, 2010 - 3:19 pm
Q1 Yes. See pp. 462-463 of

Muthén, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S., Carlin, J., & Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biostatistics, 3, 459-475.

which is on our website under Growth Mixture Modeling.

Q2 Because odds have less normal distributions than logodds, I would take the usual approach of getting confidence limits from the logodds and then exponentiating those limits to get them on the odds scale. You can get the logodds SE by defining a New parameter in Model Constraint.
 Michael Green posted on Tuesday, May 04, 2010 - 3:14 am
Thanks for this, just to be clear I've understood you correctly, would the input then look something like this?

(where p1 and p2 are the two parameter estimates I'd like to compare)

model constraint:

new (d1);
d1=p1-p2;

And then I can use the exponents of d1 and plus or minus its error to get the odds and confidence intervals?

Thanks again, MG
 Linda K. Muthen posted on Tuesday, May 04, 2010 - 9:53 am
Yes. Yes.
 Patrick Nowlin posted on Tuesday, June 22, 2010 - 1:11 am
Hi, I am running a logistic regression model (dv has 4 categories) with two continuous mediators. I can get the model to run perfectly fine (using MLR estimation) until I start to test for model variance across three ethnic groups (using the KNOWNCLASS Option).

Specifically, if I take the original model and add the KNOWNCLASS option to the syntax, I get the following error:

*** WARNING in Variable command
CLASSES option is only available with TYPE=MIXTURE.
CLASSES option will be ignored.
*** WARNING in Variable command
KNOWNCLASS option is only available with TYPE=MIXTURE.

But if I change the analysis type from general to mixture, then I'm given this error message:

*** WARNING in Analysis command
The INTEGRATION option is not available with this analysis.
INTEGRATION will be ignored.

*** ERROR
The following MODEL statements are ignored:
[basically Mplus omitted all variables predicting the categorical DV]

*** ERROR
One or more MODEL statements were ignored. These statements may be
incorrect or are only supported by ALGORITHM=INTEGRATION.

So, is there a way to compare logistic models across multiple groups if monte carlo integration is required?
 Linda K. Muthen posted on Tuesday, June 22, 2010 - 6:19 am
Please send the full output and your license number to support@statmodel.com.
 Regan posted on Thursday, September 16, 2010 - 7:18 pm
Hi,
I am having the same problem as Patrick.

I am running a binary logistic regression path model and would like to do a 3 group analysis.

The model runs in each of the three groups separately. Mplus warning prior suggested using montecarlo integration, which helped me out initially, but when I try to run the multiple group analysis I get the same warnings as he has described.

I got the multiple group analysis to run using "groupings" command, by switching to Theta parameterization with WLS, option, but I wanted to use the maximum likelihood robust option for missing data and skewness of continous variables.

Is there a way to know how his problem was solved?

thank you!
 Linda K. Muthen posted on Friday, September 17, 2010 - 9:22 am
I can't see what the answer was to this. Please send the full output and your license number to support@statmodel.com.
 roofia galeshi posted on Monday, February 28, 2011 - 12:54 pm
Hello,

I have a multiclass analysis with dichotomous variables. My program is very slow, it does iterate but every iteration takes an hour to advance to the next one.
Thanks
 Linda K. Muthen posted on Monday, February 28, 2011 - 4:22 pm
Please send your input, data, and license number to support@statmodel.com.
 harvey brewner posted on Monday, March 14, 2011 - 12:05 pm
based on the steps outlined in chapter 14, i am trying to figure out how to deal with correlated residual variances in multi-group factor analysis. in the separate cfa of my two groups i found extremely large MI for several items on one of my factors, eg. f1a with f1d and f1b and f1g. i want to do a mgfa with categorical variables using wlsm and theta. in chapter 14, to show invariance:
1) test # factors; residual variances set to 1 in all groups.
2) test invariant thresholds/loadings; residual variances set to 1 in one group.
3) test invariant residual variances; residual variances set to 1 in all groups.

how would you handle the correlated residual variances (eg., f1a with f1d and f1b and f1g) in these three steps?

is there a section that explains how to test for invariance of the structural parameters (for categorical data)? can you even test structural parameters in mgfa in mplus?
 Linda K. Muthen posted on Tuesday, March 15, 2011 - 11:12 am
We don't require residual variances and covariances to be the same across groups for a sufficient degree of measurement invariance to be established.

See the Topic 1 course handout at the end of the multiple group section. Testing of structural parameters is shown here. It is the same for continuous and categorical factor indicators. In both cases, the factors are continuous.
 Jacquelyn Mize (nickname is Jackie) posted on Tuesday, March 15, 2011 - 11:46 am
Hi,
I apologize for how simple this is.

I'm trying to do a multiple group analysis by defining two groups. Have tried both "Define" using "If...Then" statements and using "cut."

Examples - one with if-then, one with cut:

THANK YOU SO MUCH.

usevar kaggtot preaggto wake2po tcchange meddum hiloagg;
MISSING are all (999);
Define:
IF (preaggto > 2.05) THEN hiloagg = 1;
IF (preaggto < 2.0499999999999999) THEN hiloagg = 0;
GROUPING is hiloagg (lo_Agg=0 hi_Agg=1);
analysis:
model lo_agg:
hiloagg eq 0;
kaggtot on meddum tcchange;
tcchange on wake2po;
model hi_agg:
hiloagg eq 1;
kaggtot on meddum tcchange;
tcchange on wake2po;

output: sampstat standardized residual;

*** ERROR in DEFINE command
Error in assignment statement for GROUPING

---------------------------------------

cut preaggto (2.05);

analysis:
model:
kaggtot on meddum tcchange preaggto;
tcchange on wake2po;


output: sampstat standardized residual;

*** ERROR in VARIABLE command
Unknown option:
cut
 Linda K. Muthen posted on Tuesday, March 15, 2011 - 12:13 pm
It looks like you don't have options under the right command. For example, the GROUPING option should be in the VARIABLE command. It looks like it is in the DEFINE command. The CUT option should be in the DEFINE command. It does not look like it is. If this does not help, please send the full output and your license number to support@statmodel.com.
 harvey brewner posted on Wednesday, March 16, 2011 - 10:39 am
in response to my inquiry on march 14 (included below), i guess what i am asking is, if you specify in a model correlations between item residual variances, based on large MI, would the "f1a with f1d" and "f1b and f1g" be freed in the non-invariance model, freed in the invariance model, and constrained equal in the model, if you were to test for invariance of residual variances? or would "f1a with f1d" and "f1b and f1g" be constrained invariant in all models?

[original question march 14]:
based on the steps outlined in chapter 14, i am trying to figure out how to deal with correlated residual variances in multi-group factor analysis. in the separate cfa of my two groups i found extremely large MI for several items on one of my factors, eg. f1a with f1d and f1b and f1g. i want to do a mgfa with categorical variables using wlsm and theta. in chapter 14, to show invariance:
1) test # factors; residual variances set to 1 in all groups.
2) test invariant thresholds/loadings; residual variances set to 1 in one group.
3) test invariant residual variances; residual variances set to 1 in all groups.

how would you handle the correlated residual variances (eg., f1a with f1d and f1b and f1g) in these three steps?
 Bengt O. Muthen posted on Wednesday, March 16, 2011 - 4:55 pm
Invariance of residual variances does not necessitate invariance of the residual covariances and vice versa. And neither is necessary for studying factor mean, variance and covariance differences across groups. It is up to you to decide on which restrictions to impose - which ones you are interested in.
 Jo Brown posted on Wednesday, May 29, 2013 - 10:17 am
Hi Drs,

I would like to run a model to see how alcohol use changes over time (I have 4 waves) and see if the trajectories vary for boys and girls.

I am quite new to MPlus and have no idea where to start. Could you direct me to a relevant example on the manual/workshop?

Thanks.
 Linda K. Muthen posted on Wednesday, May 29, 2013 - 10:25 am
See the Topic 6 video and handout on the website. See the examples in Chapter 8 of the Mplus User's Guide. These cover LCGA and GMM. If you are not familiar with growth modeling in general, see the Topic 3 course handout and video and Chapter 6 examples.
 Jo Brown posted on Thursday, May 30, 2013 - 2:08 am
Thanks Linda!
 Jo Brown posted on Thursday, May 30, 2013 - 8:07 am
Hi Linda,

I had a look at the manual and I think the best approach for my question is to use multiple indicator linear growth models as I am planning to use latent variables for my alcohol measures.

I now have a couple of questions that I am hoping you could help with:

1. In the example in the manual (6.14) it seems that the same measure is collected over time.

However, I am using a different alcohol questionnaire in one of my 3 waves - is this an issue? does it affect the way I specify measurement invariance across waves?

2. my measures are at age 14, 16 and 17 would I specify my model as follows ?

i s | f1@0 f2@2 f3@3

3. I would like to test whether the intercept and slope are different for boys and girls; how can I include this - using model constraint?

4. would I need to test for measurement invariance across the measurement model?

Thanks a lot for your help!
 Linda K. Muthen posted on Thursday, May 30, 2013 - 3:53 pm
You need to have the same variables measured over time for a growth model.

The steps for multiple indicator growth modeling including testing for measurement invariance across time are described in either the Topic 3 or 4 course handout and video.
 Richard E. Zinbarg posted on Monday, September 16, 2013 - 9:21 pm
I am conducting a survival analysis with a latent variable as a predictor of survival. I am trying to test whether the regression of the survival function on the latent variable predictor is moderated by sex. I have set this up as a multiple group analysis using the KNOWNCLASS statement and TYPE=MIXTURE and have run two different versions. In one version, the regression is free to vary across groups and in the second the regression is constrained to be equal across groups (by only including the overall model). If this were a multiple group CFA with continuous variables, I would know how to do the chi-square difference test to test whether freeing the regression to vary across groups leads to a significant improvement in model fit. What indices do I use for this test in the survival analysis? Do I get the difference of the Likelihood Ration Chi-Squares for the tests of model fit for the binary and ordered (ordinal) outcomes and the difference in their dfs? Many thanks!
 Linda K. Muthen posted on Tuesday, September 17, 2013 - 12:26 pm
Use a loglikelihood difference test. Use the difference in the number of free parameters.
 Richard E. Zinbarg posted on Tuesday, September 17, 2013 - 5:44 pm
great! thanks Linda!
So, my understanding is that if my constrained model has a loglikelihood of -16383.944 iwth 78 free parameters and the model allowing the regression to vary across groups has a loglikelihood of -16383.468 with 79 free parameters, the difference test would equal 2(16383.944 -16383.468) or .952 with 1 df. Does that look right? Again, many thanks!
 Linda K. Muthen posted on Wednesday, September 18, 2013 - 9:53 am
That seems right.
 thanoon younis posted on Wednesday, February 12, 2014 - 6:44 pm
dear dr. Muthen
my question can i use for example uniform function as a link function to conduct WLS for categorical data.
regards
 Bengt O. Muthen posted on Friday, February 14, 2014 - 10:47 am
No, WLSMV uses only probit link when declaring variables as categorical.
 Emily Haroz posted on Tuesday, July 15, 2014 - 8:24 am
Dear Drs. Muthen,

I am running some measurement invariance testing (between two groups) with one latent factor and 15 categorical indicators. I am confused by something and would love some clarification or to be pointed in the right direction. When I use the new measurement invariance language (MODEL = CONFIGURAL METRIC SCALAR) I note that my residual variances are constrained to be 1 across groups. I want to also test Strict invariance as well, but I am confused. In my understanding configural invariance is same factor structure, metric is constraining factor loadings to be equal, scalar is constraining factor loadings and thresholds to be equal, and strict should be constraining loadings, thresholds and residual variances to be equal across groups. However, it appears that the Scalar output would be the same as strict output. Am I mistaken? Why are the residual variances constrained to be 1 across groups in the three models (Configural, Metric, and Scalar)? Thanks in advance for your help!
 Bengt O. Muthen posted on Wednesday, July 16, 2014 - 11:55 am
Perhaps you are using ML for your categorical variable analysis. Residual variances are not free parameters in this case (IRT research has not provided this). With WLSMV, the residual variances can be different across groups (fixed at 1 for one group), except for configural.
 Philip Parker posted on Sunday, December 14, 2014 - 5:56 pm
I am using the approach to mediation suggested by Bengt in "Applications of Causally Defined Direct and Indirect Effects in Mediation Analysis
using SEM in Mplus"

However, I read in articles like:

"Comparing Logit and Probit Coefficents Across Groups" - Paul Allison,

"Logistic Regression: Why we cannot do what we think we can do, and what we can do about it" - Carina Mood

That multi-group models may not be so straight forward here. What is the best way to undertake multi-group models represented in Bengt's paper above so as to account for unobserved heterogeneity. I want to compare the size of direct and indirect effect across groups.
 Bengt O. Muthen posted on Monday, December 15, 2014 - 5:09 pm
I am not familiar with those two articles - what is the concern they discuss? Note that with a binary Y the causal effects are not in the metric of slope coefficients but in the metric of Y probabilities for a given change in x (say from 0 representing control group to 1 representing treatment group).
 Philip Parker posted on Tuesday, December 16, 2014 - 1:27 am
Hi Bengt,

Thanks for the reply. Williams summarizes the issue "Allison (1999) notes that comparisons of logit and probit coefficients across groups can lead to invalid conclusions because differences in residual variation are confounded with estimates of variable effects...The problem is actually worse than Allison indicates. Allison focuses on omitted variable bias, but omitted variable bias is simply one of the possible causes of heteroskedasticity, i.e. unequal error variances across cases. There are others; and unfortunately, unlike OLS, heteroskedastic errors in binary and ordinal regression models result in biased parameter estimates"

- Using Heterogeneous Choice Models
To Compare Logit and Probit Coefficients Across Groups
 Philip Parker posted on Tuesday, December 16, 2014 - 1:28 am
p.s. at the moment I am focusing on the solution proposed by Mood of using Linear Probability Models. But this is really less than satisfactory.
 Bengt O. Muthen posted on Tuesday, December 16, 2014 - 9:20 am
I see, so the concern is similar to that which prompted the modeling of residual variance differences across groups as used in WLSMV with Delta and Theta parameterization. ML approaches don't use those more flexible models. The context for freeing residual variances was that of multiple indicators of a factor, where measurement invariant thresholds and loadings made is possible to identify residual variance differences across groups for the indicators. Not sure that identification would work out with regular path models with a single indicator.

There is certainly precedence for ignoring this issue - I may be wrong, but I don't think for instance the epidemiological causal effect literature considers this issue. Switching to a linear probability model doesn't seem like a solution because then we are back to treating a binary variable as continuous.
 Bengt O. Muthen posted on Tuesday, December 16, 2014 - 10:09 am
Thinking more about it, I don't think this is a concern for comparing indirect and direct causal effects. The authors' concern is about comparing coefficients (slopes) across groups where these slopes are confounded by residual variance differences (they get "baked together"). Indirect and direct effect comparisons across groups in the causal effect framework don't compare such slopes but focus on the resulting probability differences across groups. These probability differences don't care if they stem from different slopes or different residual variances. I may be wrong, but I think this holds.
 Philip Parker posted on Tuesday, December 16, 2014 - 8:46 pm
Thanks for the feedback.
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