Respected Sir/Madam ... I have three things to get clarified and two questions regarding program code.
C1. Multiple group analysis (MGA) of the Structural part of SEM (assuming either no measurement sections or all dependent variable have only single indicator outcome variable) looks similar to the Dummy independent variable regression, which we usually do as a standard Econometrics technique … am I right!
C2. Now if I’m so … then my second question is… how much does MPlus differ from standard econometric theory for Dummy independent variable regression when we run Multiple Group Analysis in MPlus (for simplicity assuming no measurement section) … Following is the standard procedure that we follow in our standard econometric theory as Dummy independent variable regression (when the dependent variable is continuous) We Estimate the constrained model (i.e. the coefficients for DUMMY and the K interaction terms are all constrained to be zero) … regress Y on all of the X’s. (Total K no. of X’s) For the unconstrained model, regress Y on all of the X’s, DUMMY, and the DUMMY interaction terms. Therefore we get 2K + 2 coefficients to be estimated: 1 intercept, a coefficient for DUMMY, a coefficient for each of the K independent variable, and a coefficient for each of the K interaction terms. Then we do the incremental F test. df1 = K + 1 for the constrained model, and df2 = N-2K-2, where N is the total number of observations F test-statistics i.e. (F df1, df2) = (error sum square Constrained – error sum square Unconstrained)*df2 / (error sum square Unconstrained)*df2 I’m going through MPlus User’s Guide (296-306) but fail to understand the statistics behind the way MPlus handles MGA … however, there is a caveat Professor, I have categorical dependent variable (Y1= 1/0) can I use the same notion of dummy independent variable regression, I mean the partial coefficient with respect to dummy variable at its mean value doesn’t make sense in probit/logit analysis … isn’t it?
C3. I check MPlus Technical Appendices (page 18) plus your article (1989 Presidential Lecture of Psychometric Society) … I couldn’t get what’s the EXCAT TEST STATISTICS that we should use in order to verify group difference, when we have categorical i.e. binary as well ordinal) outcome variable
Questions regarding Program Code
Q1. I’m interested to check the differences in the coefficients (inclusive of the thershold) of structural part of the SEM for two groups … below is my code … could you please tell me how/what to write in the Groups Specific “Model command”.
(Y1 is 0/1, R1-R3 and B1-B3 are 5-scale ordinal)
TITLE:…; DATA: FILE IS d:\datatotal.txt; VARIABLE: ; USEVARIABLES ARE ; CATEGORICAL ARE ; MISSING ARE .; GROUPING IS Fitem (1=comA 0=comB);
These questions are a bit too far-reaching to thoroughly answer, and I need to answer briefly. A key difference between having groups represented by covariates versus multiple-group analysis is that the former approach cannot represent group differences in variances or factor loadings. You can read more about that in standard SEM texts such as Bollen's book (I thought I also treated it in the 1989 Psychometrika article). For multiple-group analysis setups in Mplus, see examples in the Version 3 User's Guide. DIFFTEST can be used whenever you want to test nested models in the WLSMV context.
Sanjoy posted on Wednesday, May 18, 2005 - 4:27 pm
Thanks Professor ... I think I could not make my point clear ... I am interested to check whether there is a SIGNIFICANT group effect (say I have two-grouped data and the regression coefficients vary significantly over the two groups or not)
By default MPlus runs two models for Two groups, assuming factor loadings are SAME and regression coefficients are all DIFFERENT across the groups ... hence this is the UNRESTRICTED model ... is it right? … I suppose this is also the “Baseline Model” as it's been reported in MPlus output?
Now is NOT “holding factor loadings equal across groups” a RESTRICTION by itself! Actually that’s what made me slightly confused.
Again following MPlus example 5.16 and 5.17, there it did NOT do any testing of group specific significance under categorical outcome scenario. These two examples tell us how to specify group specific factor loading.
Kindly let me get it clear once more, in order to Test the Significance of group specific difference (for my case, the dependent variables are ordinal and the restriction is - putting SAME regression coefficients for both the groups)
Step1. Run the model with group command but WITHOUT using the group specific model command …and save the data as DIFFTEST
Step 2. Open another file, and under analysis use “DIFFTEST” and under group specific model command write the restrictions and run it … is it correct!
MODEL: R BY R1-R3; B by B1-B3; Y1 on R B x1 x2 x3 x4; R on B x2 x5; B on R x1 x2 x3;
SAVEDATA: DIFFTEST is d:\grouptest.txt;
therefore by default Mplus is givng us two sets of result for two groups
Now I want to TEST Y1 on R and B are significantly different across the group or not ... I open a new file ...and write the following (pasting only the model section here)
ANALYSIS: DIFFTEST is d:\grouptest.txt; ESTIMATOR=WLSMV; PARAMETERIZATION=THETA; MODEL: R BY R1-R3; B by B1-B3; Y1 on R(1) B(2) x1 x2 x3 x4; R on B x2 x5; B on R x1 x2 x3;
LOOK I did NOT write any group specific model command like "MODEL comB:" etc ... however I found this way of coding works, in output we have same regresiion coefficients for Y1 on R and B for both groups .... DO YOU THINK my code is OK?
Q2. after running DIFFTEST in MPlus Output we get this Chi-Square Test for Difference Testing Value 3.386 Degrees of Freedom 2** P-Value 0.1812
What does this result mean? ... I suppose the difference being considered not statistically significant.
Q3. Can we check NON-Equality (linear) constraint on parameters in MPlus .... say e.g. (y1 is 0/1)
y on x1 x2 x3
and we are interested to check regression co-efficient of Y on X1 is Greater than regression co-efficient of Y on X1
If you ask for TECH1, you can compare the matrices and see whether the pattern of fixed and free parameters is what you want. It is not a good idea to try to decide this looking at the MODEL command alone given that Mplus defaults vary across models.
A chi-square value of 3.386 is not significant for two degrees of freedom.
You can read about MODEL CONSTRAINT in the Mplus User's Guide.