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There's been a great deal of chat on SEMNET about single indicator factors. I'm running a model and thought about using a single indicator for an ordered categorical smoking variable. Is constraining the factor variance to equal 1 the best approach for this latent variable? 


If you are not adjusting the indicator to reflect reliability, there is no difference between having a factor with one indicator or using the indicator itself in the analysis. This single indicator issue comes about historically because in some programs you must do this because of how the program is designed. It is simply making the factor equivalent to the observed variable. Then the idea came about to correct the variable for reliability by adjusting the residual variance of a continuous variable. I personally don't think in many cases the reliabiliy is trustworthy enough for these purposes. This is just my opinion 


Thank you for the response. It clears it for me. 


I am running into the same dilemma. I am being advised to adjust my LV to reflect reliability, but I don't know of the exact method (e.g., syntax) to carry that out. I've brought up the idea of just using the observed variable in the analysis, but my mentor is concerned about unreliable variance ending up in the residual term. I haven't totally absorbed his argument, but can you weigh in and possibly guide me as to which syntax to use to include a singleindicator LV adjusted for reliability? Thanks so much. 


Slide 44 of the Topic 1 course handout shows how to do this in Mplus. 

Leslie vdL posted on Tuesday, March 16, 2010  12:32 pm



I have a stupid question, but I am new to SEM: I do not understand why you would want to use a latent variable for a single indicator. Why would you not just use the single indicator? Really only because the program does not allow you to use the indicator? I ask this because I have to study an article in which the authors looked at possible physical attributes that could predict whether a bird survived yes or no. All their physical attributes eventually (through direct and indirect events) lead to the 'dependent variable'  which they call fitness. Fitness is a singleitem factor, with survival as indicator. Survival is measured as: did the bird die (yes=1, no=0). The residual variance was set to 0, because no measurement error was assumed (no live birds considered dead and vice versa). Why would they not simply use the observed variable survival? I hope you can help. 


Sometimes people want to make a correction to a single variable related to the reliability of the variable. That is what is shown on Slide 44 of Topic 1. If you don't want to do this, you should just use the observed variable in the MODEL command. 

Lulu posted on Tuesday, March 16, 2010  12:46 pm



Thank you for the quick reply. I am also new to this forum, and I cannot find the slide 44 of topic 1 you refer to. Could you maybe explain where to find this? 


See the left margin of the homepage under Short Course Handouts. 

Kate Sawyer posted on Wednesday, March 31, 2010  11:25 am



I have a similar question regarding syntax for a latent variable with a single indicator. Here is my situation: I have a longitudinal data set that includes measures of both psychiatric symptoms and cognitive functioning. I want to evaluate a model in which psychiatric symptoms predict cognitive functioning at followup. Unfortunately, half of the individuals in the data set were given one questionnaire to measure psychiatric symptoms, and half were given a different questionnaire. Both questionnaires have good demonstrated validity and can reasonably be assumed to measure the same construct; however, they are different questionnaires. I'm interested in creating a latent variable "Psychiatric symptoms" that is simply the score for whichever psychiatric symptom questionnaire the individual completed and corrects for reliability. Thus, it would be a latent variable with two indicators in that "questionnaire 1" and "questionnaire 2" would both load on "Psychiatric symptoms". But would have one indicator in that any individual would contribute only one questionnaire score (either "questionnaire 1" or "questionnaire 2" depending on which they were administered) to the variable. Is this possible, and if so would you be able to provide example syntax? 


I can't see any way to do what you want unless some people took both measures. You should just look at the two samples separately. 


The code below runs but I can't interpret latent factor mean differences from the output (both means say 0.000). Is there a coding problem? Usevar are SchoolN Q1 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q17 Q18 Q20 Q21 Q23 Q24 Q25 Q26 Q32 Q22 Q27 Q28 Q29 Q30 Q31 Q33 Q34; grouping is SchoolN (1 = one, 2 = two); Analysis: type = general; estimator = mlr; Model: Factor1 by Q1Q32* (A1A23); Q1Q32@1; Factor1@1; Factor2 by Q22Q34* (B1B8); Q22Q34@1; Factor2@1; Factor1 with Factor2 (X1); model two: Factor1 by Q1Q32* (A1A23); Q1Q32@1; Factor1*; [Factor1@0]; Factor2 by Q22Q34* (B1B8); Q22Q34@1; Factor2*; [Factor2@0]; Factor1 with Factor2 (X1); Output: standardized sampstat tech1; 


Mplus fixes the factor means to zero in the first group and lets them free in the second. So when you fix them in the second none is free. 


Model: Factor1 by Q1Q32* (A1A23); Q1Q32@1; Factor1@1; Factor2 by Q22Q34* (B1B8); Q22Q34@1; Factor2@1; Factor1 with Factor2 (X1); model two: Factor1 by Q1Q32* (A1A23); Q1Q32@1; Factor1*; ! take out[Factor1@0]; Factor2 by Q22Q34* (B1B8); Q22Q34@1; Factor2*; ! take out [Factor2@0]; Factor1 with Factor2 (X1); Output: standardized sampstat tech1; Thanks Bengt, So I just delete two lines as above? 


That seems correct. Try it and see. 


Thanks for response Dr Muthen. Yes, it worked out fine. Cheers. 

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