Heywood case for LATENT variables

[Jie Ren]

I am currently examining whether language learning is correlated with inhibitory control for 2-year-old toddlers. I treated language and inhibitory control as two latent variables and there are four different measurements for each of the two latent variables. I ran the following model using lavaan, but the model ends up with a negative variance value for one of the LATENT variables SWITCH which measures Inhibitory control (of course the program sent a warning saying that some estimated ov variances are negative). 

LANGUAGE=~a*WordComp + b*WordProd + c*SentComp+ d*SentProd

SWITCH=~e*Post2+f*Pre2+g*Post1+h*Pre1

LANGUAGE~~w*SWITCH

As you can see, the model is really not a huge one. However, I am really a novice in SEM though I have received formal statistical training with a master's degree in Biostatistics. I wonder whether I could learn from your insight about this. What could have happened so that the estimated variance is negative? Any suggestion about how to solve this problem would be appreciated. 

[Stas Kolenikov]

Ken Bollen and I published a paper on Heywood cases a few years ago: http://journals.sagepub.com/doi/10.1177/0049124112442138

-- Stas Kolenikov, PhD, PStat (ASA, SSC)  @StatStas
-- Senior Scientist, Abt Associates @AbtDataScience
-- Program Chair (2018), Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
 

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