std factor loading is more then 1

[Yuval Moshe]

Hi everyone,
we're fresh students dealing with R and we got some questions about lavaan package,  using it to build a measurement model in CFA. 
one of our factor loadings resulted to be more then 1 and we want to solve this.
look at the line between ABAS to Autistic profile in the picture (1.08)
the code we used is:

mod_meas <- '

  ## latent variable definitions (CFA)

  Accomp_Symp =~ b1 * Sensory + b2 * Sleep_Disturbance + b3 * Stereotypic_Behavior

  Autistic_Profile =~ b4 *ABAS  + b5 * Cognitive + b6 * ADOS

  

  ## covariances

  Accomp_Symp ~~ Autistic_Profile

   

  ## errors

   Sensory ~~ e1 * Sensory

   Sleep_Disturbance ~~ e2 * Sleep_Disturbance

   Stereotypic_Behavior ~~ e3 * Stereotypic_Behavior

   ABAS ~~ e4 * ABAS

   Cognitive ~~ e5 * Cognitive

   ADOS ~~ e6 * ADOS

'

fit_meas <- cfa(mod_meas, data = data)

lay <- get_layout(

  "Sensory",NA,"Sleep_Disturbance",NA, "Stereotypic_Behavior", NA,NA, "ABAS",NA, "Cognitive",NA, "ADOS",

    NA,   NA,  NA,       "Accomp_Symp",    NA,      NA,   NA, NA, NA,        "Autistic_Profile",    NA, NA,

  rows = 2

  )

  

prepare_graph(fit_meas,layout = lay, angle = 30) %>%

         edit_edges((label= est_sig_std)) %>%

         plot()

Thanks in advance,
Yuval

[balal izanloo]

Greetings

standard factor loadings can be greater than one. see some links in bellow

1- http://www.statmodel.com/discussion/messages/9/5074.html?1383773698

2- https://stats.stackexchange.com/questions/266304/in-factor-analysis-or-in-pca-what-does-it-mean-a-factor-loading-greater-than

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[Yuval Moshe]

Thank you!

ב-יום שבת, 3 ביולי 2021 בשעה 13:25:57 UTC+3, b.ez...@gmail.com כתב/ה:

[Yuen Wan Ho]

Hi,

Just looked up the reference shared by Yuval and I spotted that document in the below link is no longer available: 

http://www.ssicentral.com/lisrel/techdocs/HowLargeCanaStandardizedCoefficientbe.pdf

Do you know another link where I can access the document?

Thanks!

Yuen Wan

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/f14df705-655a-4884-b1ac-422ceea2ed6en%40googlegroups.com.

[Terrence Jorgensen]

standard factor loadings can be greater than one

Standardized multiple regression slopes in general can exceed 1 (so, when there are cross-loadings).  But the parameter of interest is a simple regression slope (i.e., the item has no cross-loadings).  Standardized simple regression slopes are zero-order correlations, which are bound by +/-1.  So this is a Heywood case, paired with the negative residual variance (which follows from having a standardized simple slope > 1).  I would recommend looking at the 95% CI of the residual variance to see if it includes admissible (i.e., positive) values, in which case, you cannot reject the H0 that the true residual variance > 0 (and thus the true standardized slope < 1) in the population.  If your model does not fit very badly, then sampling error is the reasonable conclusion.

https://doi.org/10.1177/0049124112442138

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen