Reliability, ordinal omega?

[Jorge Sinval]

After analyzing a model with lavaan (computing the variables as ordinal), if I use the fit object to obtain reliability estimates, they would be ordinal estimates? I saw ordinal alpha and ordinal omega calculated in the package 

userfriendlyscience

with the function

scaleReliability

Any thoughts? Thanks.

[Terrence Jorgensen]

would be ordinal estimates?

Not sure if you have the latest development version of semTools installed, but this is from the latest ?reliability help page:

Regarding categorical indicators, coefficient alpha and AVE are calculated based on polychoric correlations. The coefficient alpha from this function may be not the same as the standard alpha calculation for categorical items. Researchers may check the alpha function in the psych package for the standard coefficient alpha calculation.  Item thresholds are not accounted for. Coefficient omega for categorical items, however, is calculated by accounting for both item covariances and item thresholds using Green and Yang's (2009, formula 21) approach. Three types of coefficient omega indicate different methods to calculate item total variances. The original formula from Green and Yang is equivalent to ω_3 in this function. Green and Yang did not propose a method for calculating reliability with a mixture of categorical and continuous indicators, and we are currently unaware of an appropriate method. Therefore, when reliability detects both categorical and continuous indicators in the model, an error is returned. If the categorical indicators load on a different factor(s) than continuous indicators, then reliability can be calculated separately for those scales by fitting separate models and submitting each to the reliability function.

So only that version of omega takes thresholds into account, giving an estimate of the reliability of the sum of those categorical items.

I saw ordinal alpha and ordinal omega calculated in the package 

userfriendlyscience

with the function

scaleReliability

As that help page shows, it is just a wrapper around the MBESS package's ci.reliability() function, which is written by the same author (and uses the same source code) of the reliability() function in semTools.  So the same applies.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Jorge Sinval]

So the ω_3 from semTools::reliability would give the same results that uerfriendlyscience::scaleReliability would. Nice! Thank you very much for your input, Terry!

[Jorge Sinval]

​​

Just an example:

semTools::realiability

alpha  0.9627

omega  0.9664

omega2 0.9664

omega3 0.9770

avevar 0.8246

userfriendlyscience::scaleReliability

 Ordinal Omega (total): 0.96

 Ordinal Omega (hierarch.): 0.96

  Ordinal Cronbach's alpha: 0.96

Confidence intervals:

     Ordinal Omega (total): [0.96, 0.96]

  Ordinal Cronbach's alpha: [0.96, 0.96]

Curiously the ω_3 is different from the ordinal omega hierarch. Which should be more rigorous to report? (I don't have modifications to the model in the fit object, and I used the std.lv=T, as can be seen, "omega1"="omega2")

*************************************************

Best Regards

Jorge Sinval (BS Psych, MS Psych)

Double PhD Student in Psychology (FFCLRP-USP & FPCEUP)

Mendeley Advisor

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 Nanos gigantum humeris insidentes.

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