Message/Author 

Tom Booth posted on Monday, September 24, 2012  6:57 am



Is it possible to create a single indicator latent variable based on a binary indicator? I am trying to develop a measurement model where my primary interest is in a secondorder construct. However, my indicator set is suboptimal for estimating a second order construct as I only have two well measured latent factors(>3 indicators with reasonable loadings >0.40). In addition I have a single observed binary variable which could act as a third indicator. I want to discuss and demonstrate/estimate the alternatives whilst acknowledging the problems. I am comfortable describing the issues in the 2 first order factor model (nonidentification at the 2nd order without additional constraints), and can present a bifactor model as an alternative way to get at the general construct (with its different assumptions about the nature of the construct). But it is the estimation and discussion of a model with two first order latent factors and, potentially, a single indicator latent variable from a binary observed indicator with which I am struggling. Thank you in advance for any suggestions. 


You can simply use the binary indicator as a factor indicator for the secondorder factor. It is not necessary to put a factor behind it. If you did, you would obtain the exact same results. 

Tom Booth posted on Tuesday, September 25, 2012  8:55 am



Thanks Linda. Sometimes the answer is the simplest one! When I run this model, I don't get a pvalue for the loading  is this expected? 


If is is the first factor indicator, it is fixed at one to set the metric of the factor so it is not estimated and you would not get a pvalue. 

Tom Booth posted on Tuesday, September 25, 2012  11:15 pm



Hi Linda, The model is set up as follows; usevariable = x1x8 u1 ; categorical = u1 ; model: f1 by x1* x2x3; f1@1 ; f2 by x4* x5x8 ; f2@1 ; f3 by f1* f2 u1; f3@1 ; I do not believe in this coding I have set u1 to be fixed at 1, but in the model output, it is showing as fixed on F3. I am sure I am missing something obvious. Thank you for your help and swift responding. 


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

Tom Booth posted on Thursday, September 27, 2012  4:32 am



Thanks Linda, will do. I am in the process of upgrading to version 7 and getting a new help license so will have to send once this is sorted. 

jiesi G posted on Wednesday, December 18, 2013  3:36 am



Hello, I am running a 4factor CFA using continuous and only one binary indicator. Three of the latent factors have continuous indicators, while the binary indicator was correlated with these 3 factors. The CFA model is set up as follows; usevariable = x1x9 u1 ; categorical = u1 ; ANALYSIS: estimator=WLSMV; model: f1 by x1* x2 x3; f1@1 ; f2 by x4* x5 x6 ; f2@1 ; f3 by x7* x8 x9; f3@1 ; u1 with f1 f2 f3; in the following up SEM analysis, f1 and f2 > f3 > u1, I want to treat the binary indicator as the outcome variable, and use MLR and link=logit to test indirect effect from f1 to u1. my question is whether I can report the correlation matrix in my paper based on this setup CFA input. 


I don't know why you want to report a correlation matrix when your analysis estimates parameters of a path model. The model is sufficient. If you ask for TECH4, Mplus will give you correlations among your 3 factors. I don't think you want a correlation with the binary outcome. 

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