Single indicator latent variables!
Message/Author
 Sanjoy posted on Monday, March 21, 2005 - 5:57 pm
Prof. Linda and Bengt Muthen

Dear Madam and/or Sir

this is my model situation, "f's " are the three latent variables and their corresponding indicator variables are Y's ... X's share some common elements between them

f1 = function of (f2, f3 and X1)
f2 = function of (f3 and X2)
f3 = function of (f2 and X3)

f1 has only one indicator Y1 which is binary
f2 has only one indicator Y2 which is ordered categorical (five scale)
f3 has only one indicator Y3 which is ordered categorical (five scale)

I have three quick questions ... kindly suggest me what to do or rectify if I'm wrong

Q1. Is it OK if I fit three equations using only "ON" statement ... I have tried to fit "f1 by Y1, f2 by Y2, f3 by Y3" and then "f1 on f2 f3 X1" and so on ... then in the output it's showing warning no convergence ... but if you write "Y1 ON Y2 Y3 X1", "Y2 ON Y3 X2" and so on ... it runs nicely, and the result is OK too

Q2. why is it happening such ...though it's all single indicator variable, we still have "measurement section" of the SEM, don't we, why can't we mention them by "BY" statement ... and that's primarily how Statistics of SEM differs from Econometrics, where we usually don't model dependent variable with measurement error, errors in Econometrics come from the explanatory side (please correct me if I'm wrong)

Q3. our system is Non-recursive, I need to check whether it's been identified or not ...I suppose MPlus would have informed me if it wasn't (please correct me if I'm wrong)... nonetheless, I need the algebra behind this, I have to report it in my dissertation ...please suggest me a comprehensive reading

Thanks and regards ... sincerely, Sanjoy
 bmuthen posted on Monday, March 21, 2005 - 6:14 pm
With single indicators you cannot estimate separately a measurement error variance and a factor variance. This is described in SEM books. This implies that when you use BY you try to estimate a factor variance and it is not identified. When you use ON you do not estimate a factor variance and the model is identified. You should use ON here, but it would be equivalent to using BY if you also fix the factor variance (e.g, to 1).
 Sanjoy posted on Tuesday, March 22, 2005 - 8:36 pm
Thank you Sir ... below is the model Statement for my second model where I'm using three latent variable, one of them "Y1" has one indicator and two of them have three indicator variables

CATEGORICAL ARE Y1 R7-R9 B6-B8;
ANALYSIS: PARAMETERIZATION=THETA;
ESTIMATOR=WLSMV;
MODEL: B by B6-B8; !equation 1
R by R7-R9; !equation 2
Y1 on B R X7-X12; !equation 3
B on R X2 X8 X9 X11 X15 X9 X10; !equation 4
R on B X5 X9 X10 X12; !equation 5

up to this result is OK ... But

my QUESTION is I want to put some parameter constriant, following page 423 of Mplus User's Guide I have tried but it didn't work ...could u kindly rectify me please

I WANT TO CHECK, say for equation 3, parameter coefficients associated with B and R both are equal to zero ... this is what I have done

MODEL: B by B6-B8;
R by R7-R9;
Y1 on B(p1) R(p2) X7-X12;
B on R(p3) X2 X8 X9 X11 X15 X9 X10;
R on B(p4) X5 X9 X10 X12;
MODEL CONSTRAINT: p1 EQ 0;
p2 EQ 0;

Nothing is happening, I guess I grossly misunderstood the "labeling thing" ... besides it'a also saying X7 to X12 aren't being used

thanks and regards ...Sanjoy
 Linda K. Muthen posted on Wednesday, March 23, 2005 - 6:55 am
You can only have one label per line. Try the following.

MODEL: B by B6-B8;
R by R7-R9;
Y1 on B(p1)
R(p2)
X7-X12;
B on R(p3)
X2 X8 X9 X11 X15 X9 X10;
R on B(p4)
X5 X9 X10 X12;
MODEL CONSTRAINT: p1 EQ 0;
p2 EQ 0;
 Sanjoy posted on Wednesday, March 23, 2005 - 11:18 am
Thank u madam ... But... the problem remains, it's saying

"
*** ERROR in Model Constraint command
Unknown parameter label in MODEL CONSTRAINT: 0
in assignment: 0 =
"

this is what I have written
MODEL: B by B6-B8;
R by R7-R9;
Y1 on B(C1)
R(C2)
X7-X12;
B on R X2 X8 X9 X11 X15 X9 X10;
R on B X5 X9 X10 X12;
! C1 and C2 are the model constraints on parameters
MODEL CONSTRAINT: C1 EQ 0;
C2 EQ 0;

I can send u the data set if u think that would be required

thanks and regards ... sanjoy
 Linda K. Muthen posted on Wednesday, March 23, 2005 - 3:19 pm
I think you should be saying c1 = 0; and c2 = 0; although you could just say in the MODEL command y1 ON b20; and r@0;
 Linda K. Muthen posted on Wednesday, March 23, 2005 - 4:54 pm
I should have said y on b@0;
 Sanjoy posted on Wednesday, March 23, 2005 - 7:11 pm
Thanks ..."@0" worked nicely
also, under model constraint I put different model constraints like b1=-b2; that ran perfectly too

however, for the SAME model where "@0" worked nicely I have tried to fit the same constraint on the SAME parameters writing c1=0
it does not work then

the below one works NICELY

MODEL: B by B6-B8;
R by R7-R9;
Y1 on B@0
R
X7-X12;
B on R X2 X8 X9 X11 X15 X9 X10;
R on B X5 X9 X10 X12;

the below version did NOT work

MODEL: B by B6-B8;
R by R7-R9;
Y1 on B(C1)
R X7-X12;
B on R X2 X8 X9 X11 X15 X9 X10;
R on B X5 X9 X10 X12;
MODEL CONSTRAINT: C1 = 0;

it's saying

"
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.

"

thanks and regards ...Sanjoy
 Linda K. Muthen posted on Wednesday, March 23, 2005 - 8:42 pm
If you are interested in me looking at this further, you need to send full outputs of that which worked and did not work along with your license number to support@statmodel.com.
 Simon O. F. posted on Wednesday, November 04, 2009 - 11:04 am
Hi,

I'm testing some path models (single item variables) and for some models, I got no degree of freedom left. I was wondering if it is normal in path models or should I report something else then the fit indices like R-square ?

Thanks in advance,
 Linda K. Muthen posted on Wednesday, November 04, 2009 - 5:48 pm
If you have no degrees of freedom, the model is saturated and model fit is not relevant.
 Cecily Na posted on Sunday, November 28, 2010 - 12:23 pm
Dear Linda,
I'm working on a model with 3 latent factors. Each factor has only one single indicator. One single indicator is categorical and the other two are counts (continuous?)
Here is the syntax
f1 by criminal;
f2 by partner;
f3 by drug;
f1 ON f3;
f2 ON f3;
f2 ON f1;

I believe, in order to identify the model, I need to set the variance of the single-indicator at 0, and fix the path between the indicator and factor to 1. Can you show me how to do it in Mplus?
 Linda K. Muthen posted on Monday, November 29, 2010 - 5:53 am
For count and categorical variables, you don't need to fix the residual variances to zero as these parameter are not estimated. When you have only one indicator, you can work with the observed variables rather than factors that are equal to the observed variables, for example,

criminal on drug;
partner on drug;
partner on criminal;

It is not necessary to create factors that are the same as the observed variable.
 Cecily Na posted on Monday, November 29, 2010 - 6:42 am
Thanks a lot for the prompt reply!
 Gregory Stevens posted on Thursday, December 09, 2010 - 8:16 am
Dear Drs. Muthen,
I have a question about a model where parcels (in the form of scale averages) are used as single indicators for latent factors. In our model, I have set the residual variances of the indicators (factor variance X (1-reliability)) and then specified the measurement and structural models.

Sample Model command:
avg_w@.061;
avg_z@.124;
avg_y@.004;
f_w BY avg_w;
f_z BY avg_z;
f_y BY avg_y;
f_y ON f_w f_z;

When I run something like this in Mplus, I get fit indices that are way outside of typical bounds (i.e., CFI of 0, RMSEA of 4.5), leading me to believe that I am perhaps missing something about Mplus' default behavior or perhaps an additional setting somewhere. This model will run fine both (1) without the commands to set the error variances, and (2) with single item indicators for the factors. Unfortunately, our participant to parameter ratio will not allow us to use the latter alternative, so we have set on using the parcels.

We have also run this model using AMOS, which demonstrated adequate model fit; unfortunately, that program doesn't handle interactions of latent factors, so we would like to figure out how to get Mplus to accept our single-indicator models.

Thank you very much for your assistance,
Greg
 Linda K. Muthen posted on Thursday, December 09, 2010 - 12:03 pm
When you have a single-indicator, the residual variance should be fixed at

(1– reliability) * sample variance
 ylam posted on Tuesday, November 05, 2013 - 5:16 pm
Hi,
I am testing a SEM model with 3 latent continuous latent variables and one observed indicator (AP). the fit index is acceptable with the following command:

IV by v1-v3;
C by c1 c2;
O by o1-o3;

O on C AP IV;

However, when I change the independent variable into a single indicator latent variable, "NO CONVERGENCE" noted. Is there any thing inappropriate with the following revised command? OR is there anything I miss and how could I fix it?

IV by v1@1;
C by c1 c2;
O by 01-03;
O on C AP IV:

Further, if I wanna to test the moderating effect of C in the relationship bw IV and O, does the following appropriate?

model:
O on C IV;
CxIV | C XWITH IV;
O on CxIV;
output: tech8;

Last, in assessing the mediating effect of IV -> C -> O, with the command O ind C IV, I m not sure whether the result has exclude the effect of AP? or after controlling other possible indicator/latent in the model?

Thank you very much.
 Bengt O. Muthen posted on Tuesday, November 05, 2013 - 5:56 pm
Q1 Saying

IV by v1@1;

makes the model non-identified because you estimate 2 variances - one for IV and one for v1. Fix the latter at zero.

Q2 Your XWITH command does handle moderation.

Q3 For your mediation model your substantive theory has to guide you. You don't have to exclude AP.
 ylam posted on Tuesday, November 05, 2013 - 6:22 pm
Dear Dr Muthen, thanks for your prompt reply.

A follow-up question regarding the mediation model:
how about if I wanna to know the mediating effect of C in the relationship bw AP and O with "O on C AP", does it ok to interpret? in this case, is the effect from IV being controlled? OR I could only test the mediating with latent variable only?

Thanks again.
 Bengt O. Muthen posted on Wednesday, November 06, 2013 - 8:38 am
It is better if you send this kind of general modeling question to SEMNET.
 PAJ Stat posted on Tuesday, January 28, 2014 - 1:29 pm
Hello,
I am running a SEM with a single indicator latent variable. I know I have to fix error measurement ( 1-realibility)*variance). Here is my code:
Y BY X@1;
X@0.05;
However, i have an error message, the model is not identified. Surprisingly, when I add Y@0.05; it works pretty well. Is it adequate to add the measurement error to the latent variable?
Thank you
 Linda K. Muthen posted on Tuesday, January 28, 2014 - 1:56 pm
No. Please send the output and your license number to support@statmodel.com. You must have some other misspecification.
 Maren Schulze posted on Wednesday, May 06, 2015 - 1:00 am
Dear Sir or Madam,

I have a model with six latent factors of which one only has a single indicator.

I have tried two models:

a)
f1 BY x1@1;
f1@1;

-> here, the standardized path coefficient is larger than 1

b)
x1 ON f1;

-> here, I get an error message that "f1" is unknown - have I misunderstood your explanation in the first post

How am I supposed to specify the model correctly?

Thank you very much.

Kind regards
 Linda K. Muthen posted on Wednesday, May 06, 2015 - 10:54 am
The proper specification is

f1 BY x1@1;
x1@0;

This makes f1 identical to x1. You may as well use x1 in the model.
 Constanze Eib posted on Monday, March 21, 2016 - 6:22 am
Hello,

I want to estimate a model where a latent difference score (between T1-T2) moderates a relationship (between T2-T3). I only have a single indicator latent variable though. Should this work at all? It gives me the error : estimated covariance matrix could not be inverted.

I built the latent variables like this:
iv1 by item1@1;
item1@0;
iv2 by item2@1;
item2@0;
iv3 by item3@1;
item3@0;
(it couldn't converge with (1-rel)*var)

The latent diff score:
iv2 ON iv1@1;
diff12 BY iv2@1;
diff12 ON iv1*;

The interaction:
iv2xdiff | iv2 XWITH diff12;

Estimation:
DV3 ON iv2 diff12 iv2xdiff ;

Is there something wrong with my syntax or is it generally not possible to have interactions with single indicator latent variables?

Many thanks for your help!
 Bengt O. Muthen posted on Monday, March 21, 2016 - 6:47 am
You can have interactions between single-indicator latent variables.

I don't see how this is a latent diff score:

The latent diff score:
iv2 ON iv1@1;
diff12 BY iv2@1;
diff12 ON iv1*;

I don't see where iv3 is used.

If you have questions about this, please send output including TECH1 to Support along with your license number
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