second order model

[ni wi]

Hello!

I'm trying to fit a second order model to my data, which includes 2 first order factors and 1 second order factor. I think I'm missing something, since the results I'm getting are the same as if the model would have included only 2 correlated factors... Is it reasonable or something is missing?

Here's my syntax:

datar.model<- '

at =~ Q2 + Q3 + Q5 + Q8 + Q10 + Q11 + Q12 + Q15 + Q16 + Q18 + Q21 + Q22 + Q25 + Q28 + Q29 + Q30 + Q33 + Q35 + Q36 + Q37 + Q39 + Q40 + Q41 + Q43 + Q48 + Q49 

hy =~ Q4 + Q7 + Q9 + Q13 + Q17 + Q20 + Q23 + Q26 + Q27 + Q31 + Q34 + Q38 + Q42 + Q44 + Q45 + Q46 + Q47 

ad =~ at + hy

'

fit<- cfa (datar.model, data=datar, estimator="WLSMV", ordered=c("Q2", "Q3", "Q5", "Q8", "Q10", "Q11", "Q12", "Q15", "Q16", "Q18", "Q21", "Q22", "Q25", "Q28", "Q29", "Q30", "Q33", "Q35", "Q36", "Q37", "Q39", "Q40", "Q41", "Q43", "Q48", "Q49", "Q4", "Q7", "Q9", "Q13", "Q17", "Q20", "Q23", "Q26", "Q27", "Q31", "Q34", "Q38", "Q42", "Q44", "Q45", "Q46", "Q47"))

summary(fit, fit.measures=TRUE, standardized=TRUE)

Any help would be much appreciated,

Thanks in advance!

[Michael Paul Grosz]

I also noticed the same pattern when I worked with second-order models so correlating the first-order factors or letting them load on a common second-order factor yielded the same results (even when there were more than two first-order factors). So, I guess this is just a normal pattern.

best,
Michael

[Edward Rigdon]

     A second order model with three first order factors is equivalent to a model with three correlated factors.  With only 2 first order factors, some additional constraint must be imposed to make the second order model statistically identified.  Once that is done, though, you again achieve equivalence between the two approaches.  It may be that the ordered nature of your observed variables is inducing that additional constraint.

--Ed Rigdon

Sent from my iPad

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[yrosseel]

Hm. This can not be. The second-order model is not identified. Can you
show use the full R script and the output of the second-order model?

This is a reproducible example:

# create binary version of the H&S dataset
HS9 <- HolzingerSwineford1939[,c("x1","x2","x3","x4","x5",
"x6","x7","x8","x9")]
HSbinary <- as.data.frame( lapply(HS9, cut, 2, labels=FALSE) )

# two factors only
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6 '
fit <- cfa(HS.model, data=HSbinary, ordered=names(HSbinary))

# add second-order factor 'g'
fit2 <- cfa(c(HS.model, 'g =~ visual + textual'), data=HSbinary,
ordered=names(HSbinary))

gives

Warning messages:
1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats =
lavsamplestats, :
lavaan WARNING: could not compute standard errors!
lavaan NOTE: this may be a symptom that the model is not identified.

2: In lav_model_test(lavmodel = lavmodel, lavpartable = lavpartable, :
lavaan WARNING: could not compute scaled test statistic

as it should.

Yves.

[ni wi]

Oh, my mistake - you are right, it's not identifed. What additinal constraints i need to put?
The model i talked about was second order with 3 first order factors... Sorry for the confusion.

[Yves Rosseel]

On 10/12/2014 03:13 PM, ni wi wrote:
> Oh, my mistake - you are right, it's not identifed. What additinal constraints i need to put?

You could fix the 2nd factor loading to one.

Yves.

[Edward Rigdon]

Dear Ni Wi--
In factor-based SEM, estimation is generally simultaneous. All of the predictors of each dependent variable are gathered together in one equation--as with regression with one dependent. As in such a regression, if you have two correlated predictors, the variance in the dependent which they jointly predict is not credited to either predictor, though it is counted as explained by both predictors together. Factor structures generally minimize this problem as a side effect of identification constraints. Models with the same observed variables loading on multiple factors typically impose orthogonality constraints on the multiple factors, solving both problems at once.
--Ed Rigdon

-----Original Message-----
From: lav...@googlegroups.com [mailto:lav...@googlegroups.com] On Behalf Of ni wi
Sent: Wednesday, October 15, 2014 2:19 AM
To: lav...@googlegroups.com
Subject: Re: second order model

Thank you all!!!
It's not working - could it mean this type of model simply does not fit?
I have one more question regarding bifactor model using lavaan: once a general factor is identified, are the specific factors calculated using the residual variance, after taking into account the general one?

[ni wi]

Thank you Ed, you've confirmed what I thought :) 

בתאריך יום רביעי, 15 באוקטובר 2014 16:58:45 UTC+3, מאת Edward Rigdon:

[ni wi]

Hello all,

It's been awhile, but I need some more clarifications concerning this topic :). I get why the correlated model is nested within the second order model, but what I don't understand is why I'm getting the same results (including the same estimates, fit indices etc.). From what I can see, the only "extra" information I'm getting is the loadings of the first order factors on the second order one - am I right? When I used 7 factors, I got a bit different results. 

בתאריך יום שבת, 11 באוקטובר 2014 12:01:37 UTC+3, מאת Edward Rigdon:

[Edward Rigdon]

     Two different models can be identical in many senses, including in terms of fit.  Methods like exploratory factor analysis have built-in constraints that tend to prevent equivalent models, but factor-based SEM allows users the freedom to do very confusing things, including specifying different models that are empirically indistinguishable.

     A model with three correlated factors is identical to a model with one second order factor and three first order factors with orthogonal residuals.  Both models estimate the same total number of parameters—the three factor covariances in the one model are translated into the three loadings of the second model (or two loadings and a second order factor variance depending on parameterization).  Neither places any effective constraints on the covariance matrix of the factors. Neither model “tests” anything about relations among the first order factors in a chi-square sense (though the second order factor model could be challenged if one or more of the loadings was zero).

--Ed Rigdon

 

From: lav...@googlegroups.com [mailto:lav...@googlegroups.com] On Behalf Of ni wi
Sent: Saturday, November 22, 2014 7:37 AM
To: lav...@googlegroups.com
Subject: Re: second order model

 

Hello all,

[Edward Rigdon]

     I beg your pardon—this model has only two first order factors.  There is some default constraint that makes this model identified, but the reason is still saturation of the covariance matrix of the first order factors.  (The parTable function should make everything clear.)  It doesn’t matter how many indicators the first order factors have.

--Ed Rigdon

 

From: lav...@googlegroups.com [mailto:lav...@googlegroups.com] On Behalf Of ni wi
Sent: Saturday, November 22, 2014 7:37 AM
To: lav...@googlegroups.com
Subject: Re: second order model

 

Hello all,

[ni wi]

Thank you!

בתאריך יום שבת, 22 בנובמבר 2014 17:58:18 UTC+2, מאת Edward Rigdon: