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? 


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 yvariables 13 Number of xvariables 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 .500D04 Input data file(s) e:\csem\mikew\research\gsms\mcfa\prtadhdsxs.txt Input data format FREE =========end of output file================= 


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 SatorraBentler Scaled statistic. I have read Satorra's paper regarding the computation for the chisquare difference test when using the scaled chisquare. I am seeking advice on what fit statistics in addition to the SB chisquare are appropriate for examining differences in nested models where data are nonnormal. 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. 


If you are using MLM in Mplus, all chisquare based fit statistics (CFI, TLI, RMSEA) are based on the SatorraBentler chisquare. 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 SB chisquare. 

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) nonidentified. 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? 


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 160162 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. 


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 7pt 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 multigroup 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 y1Age; 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); 


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); {u11u21@1 u12u24}; [f1@0 f2f4];]; 


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 multigroup 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/Rsquared 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 y1Age; 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 (112) indicate equal across time {y1y13 @1 y1b – y13b}; ! Curly brackets constrain scale factors to be equal across time 1 and free across time 2 [f1f4@0 f5f8]; ! 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 


Regarding the means when you analyze the groups together, consider the following example for two groups (means only): MODEL g1: [f1@0 f2f4]; MODEL g2: [f1f4]; 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. 


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 404\RESNOMISS.dat; format=free; type=individual; nobservations are 455; ngroups=1; variable: names= V1 R1 A1A9 B1B9 C1C30 D1D4 E1E30 S1; usevariables= C1C7 C9C21 C23 C24 C27C30; categorical= C1C7 C9C21 C23 C24 C27C30; 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; 


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 multigroup 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 categoricalnow 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 greatThx! 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 A1E2@0 ; age2 WITH A1E2@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 item01item31; USEVARIABLE t_ethnic item02item16 item18item22 item24item31; GROUPING IS t_ethnic (1= Malay 2= Chinese 3= Indian); MISSING ARE BLANK; MODEL: BGR BY item02@0.01 item03item05 item07 item22@1; RNWT BY item18* item19 item24 item25@1 item26 item28item29 item30; PGE BY item08* item09@1 item13 item14 item15 item21; GCA BY item06* item10item12 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 0.500D04 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 ChiSquare Test of Model Fit Value 2886.044 Degrees of Freedom 1029 PValue 0.0000 ChiSquare Test of Model Fit for the Baseline Model Value 42828.265 Degrees of Freedom 1134 PValue 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 SampleSize 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 RSQUARE Group MALAY Observed Variable RSquare 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 RSquare BGR 0.992 RNWT 0.955 PGE 0.993 GCA 0.992 Group CHINESE Observed Variable RSquare 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 RSquare BGR 0.973 RNWT 0.980 PGE 0.991 GCA 0.991 Group INDIAN Observed Variable RSquare 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 RSquare 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 MUTHEN & MUTHEN 3463 Stoner Ave. Los Angeles, CA 90066 Tel: (310) 3919971 Fax: (310) 3918971 Web: www.StatModel.com Support: Support@StatModel.com Copyright (c) 19982005 Muthen & Muthen 


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 = 15 /week 2 = 610 /week 3 = 1120 /week 4 > 20 /week 0 = not applicable (some people don't handle needles at all, such as manager and clerk in a hospital) Can censoredinflated 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. 


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 chisquare. Thanks for your assistance. 


In Version 4 and up, chisquare 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. 


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. 


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 Rsquare 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 x1x11 (*). 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 x1x11 group; usevar are x1x11 group; categorical is x1x11 (*); 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. 


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. 


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. 


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 u1u10 g; USEVARIABLES ARE u1u10 g; CATEGORICAL ARE U1U10; 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; [f1f10]; 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. 


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. 


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 multigroup 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; 


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; 


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? 


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 3group singlefactor 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 chisquare for overall fit was 24.782 on 24 df, with p = 0.4177. Contributions of the 3 groups to chisquare 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  chisquare = 3.684, 7df, p=0.8154 Group 2  chisquare = 7.169, 6df, p=0.3055 Group 3  chisquare = 11.270, 8df, p=0.1868 The rank ordering of the chisquare 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 chisquare suggesting adequate fit (p > 0.12) in a multigroup analysis with lambdas freely estimated, but significant misfit when the model is fit to the groups separately? 


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 chisquare and degrees of freedom for WLSMV are not interpretable in the same was as for WLS. 


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 3timepoints' sets of variables: Should Scale factors be fixed at one and factor means at zero as in multigroup analyses? 


I am new to multiplegroup 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. 


I've followed EXAMPLE 5.16 but I obtained an estimation "warning". Model is a Bifactormodel 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 D110CID920CI; GF with F1F2@0; F1 with F2@0; MODEL T2: GF by D110CID920CI ; [D110CI$1D920CI$3]; {D110CID920CI@1}; [GF@0]; MODEL T3: GF by D110CID920CI ; [D110CI$1D920CI$3]; {D110CID920CI@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 0.241D18." Parameter 369 is the variance of GF in group T2. 


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 groupspecific 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. 


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, 469. there is an example to do ME/I for longitudinal data, I just finished a study on this topic with Mplus. 


In the suggested paper (Vandenberg & Lance 2000) says that the widedata approach "increased likelihood of nonconvergent or improper solutions". I have 36 items and three timepoints, quite a lot ...((3*36)^2 covariancematrix elements). Every model I've tried (Restricted and unrestricted, two and three timepoints) 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? 


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; 


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 multigroup 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 'ChiSquare 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 


If x1x3 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 factor1 group 10categorical 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! 


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 reran things with bare minimum: 1 group USEOBSERVATION ARE (Ethn60 EQ 1); MODEL: CESD BY cd1cd10; 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. 


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


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 


Q1 Yes. See pp. 462463 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, 459475. 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. 


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=p1p2; 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 


Yes. Yes. 


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? 


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! 


I can't see what the answer was to this. Please send the full output and your license number to support@statmodel.com. 


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 


Please send your input, data, and license number to support@statmodel.com. 


based on the steps outlined in chapter 14, i am trying to figure out how to deal with correlated residual variances in multigroup 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? 


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. 


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 ifthen, 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 


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. 


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 noninvariance 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 multigroup 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? 


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. 


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! 


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. 


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 chisquare 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 ChiSquares for the tests of model fit for the binary and ordered (ordinal) outcomes and the difference in their dfs? Many thanks! 


Use a loglikelihood difference test. Use the difference in the number of free parameters. 


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! 


That seems right. 


dear dr. Muthen my question can i use for example uniform function as a link function to conduct WLS for categorical data. regards 


No, WLSMV uses only probit link when declaring variables as categorical. 


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! 


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. 


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 multigroup models may not be so straight forward here. What is the best way to undertake multigroup 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. 


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). 


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 


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. 


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. 


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. 


Thanks for the feedback. 


I am running a logistic regression model with binary predicting and outcome variables. I’d like to define multigroup analysis with 4 groups using CLASSES and KNOWNCLASS options (MLR estimator). Is it possible to specify the groups by creating a new variable within the VARIABLE section as follow? DEFINE: IF (as_2 = 0 AND nbeet =0) THEN Group = 0; IF (as_2 = 0 AND nbeet >0) THEN Group = 1; IF (as_2 = 1 AND nbeet =0) THEN Group = 2; IF (as_2 = 1 AND nbeet >0) THEN Group = 3; CLASSES = CDS(4); KNOWNCLASS = CDS(Group = 03); Using this syntax, I get the following error message: *** ERROR in VARIABLE command CLASSES option not specified. Mixture analysis requires one categorical latent variable. Thank you for your help 


The CLASSES and KNOWNCLASS option belong in the VARIABLE command. The DEFINE command cannot be put in the VARIABLE command. It must come before it or after it. 

Alvin posted on Friday, October 23, 2015  7:13 pm



Hi Bengt/Linda, I ran a multigroup MIMIC model with categorical indicators (and continuous and categorical predictors) with WLSMV as the default estimator. I wondered about the coefficients between predictors and latent factors and whether these were based on probit regression? Would it be possible to estimate logits? 


With categorical factor indicators and WLSMV, the factor loadings are probit regression coefficients. You would need to use maximum likelihood to obtain logistic regression coefficients. 


I have a categorical moderator (high or low goal clarity) between two observed variables (personal interest and motivation)? Can I still do multigroup modeling to test for interaction or should I look at the interaction product? 


You can do either. 


Hi, I'm running a multigroup analysis for a zeroinflated poisson regression following the UG 7.25. But first, I ran the regressions separately for each group. I saw that the fit for the multigroup is much more worse compared to the separate models. Shall I use the separate models? Moreover, I used the model constraint block to obtain the results as incident rate ratios. Some exponentiated parameters from the model showed to be significant even if under MODEL RESULTS they are not. Any suggestions about that? Thanks for any assistance you might provide. 


Q1. If no parameter is invariant you need to focus on separate models. Q2. That can happen because the sampling distributions look different for raw and exponentiated estimates. One may be closer to normal than the other. You can do bootstrapping and use the percentilebased confidence intervals to see if you get agreement. 

Tyler Mason posted on Wednesday, February 17, 2016  7:40 pm



Hi, Can you run a multigroup analysis with a model that includes a formative latent variable? I tried and it would not converge. When I removed the formative factor, the model converged. 


It sounds like a problem with the formative factor. Send the output and your license number to support@statmodel.com. 

Irene Dias posted on Sunday, June 05, 2016  10:42 am



Dear profs, Our aim is to compare the regression coef. between girls and boys in one model with two latent variables as predictors(F1,F2) and one latent(F5) and one observed(GPA) as dependents. We also want to control age effects. We used multigroup analysis and ran a model with all paths constrained equal and a second model with no constraints, as follows: Model all paths equal Grouping is gender (1=boys 2=girls); Model: F1 BY D1D5; F2 BY V1V6; F5 BY H1H6; F5 on Age(1); F5 on F1(2); F5 on F2(3); GPA on Age(4); GPA on F1(5); GPA on F2(6); Model paths not constrained equal Same model without (1)(2) and so on.. The difference between the chisquare of the first and the second model was 25.98 (21), ns., and therefore we concluded that the regression paths were invariant, i.e., no gender differences. However, one of the reviewers is saying that our analyses do not allow saying anything about gender differences in the regression coef. Do you see any problem in our approach or in our syntax? Should we not constrain some of the paths and in that case how can we know which ones? We have previously tested configural and scalar invariance for measurement model where factor means were set to zero.Could this be the problem, i.e. should we also constrain factor means to zero when testing the full structural model? 


If you have/impose measurement invariance I think your analysis and conclusions are correct. Factor means and variances can be allowed to be different. 

Irene Dias posted on Sunday, June 05, 2016  2:05 pm



Thank you so much, professor Muthen. Just one additional question: if I want to control for age in the model, is it correct to regress just the dependents (F5 and GPA) on age, or should I also regress F1 and F2? 


The latter. 

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