single indicator latent variables and fixed factor scale setting

[Diana Meter]

Hello,

I have a question about including single indicators of latent variables and also using std.lv=TRUE for fixed factor scale setting. The way the syntax below is written, is the model specified correctly? The default is for the residuals for the single indicator latent variables to be fixed to 0, and for the latent variance to be fixed to 1, correct? When a mean structure is requested, I am a little confused by the the presentation of the observed value and the latent value (0) in the results. 

I was under the impression that the defaults in place for cfa and sem in lavaan, while specifying std.lv=T, while designating the single observed variables as single indicators of a latent construct would result in correct estimates in an identified model. I have seen some other ways of specifying models with single indicator latent constructs in lavaan, and so would just appreciate knowing that the way the model is specified is correct.

Thank you very much in advance for your response!
Diana

outcomesnomod<-'

assert=~w1ed_oa_as1 +   w1ed_oa_as3 + w1ed_oa_as4 +   w1ed_oa_as6 + w1ed_ra_as1 +   w1ed_ra_as3 + w1ed_ra_as4 +   w1ed_ra_as6

aggressO=~w1ed_oa_oag1 +  w1ed_oa_oag3 + w1ed_ra_oag1 + w1ed_ra_oag3 

AggressR=~   w1ed_oa_rag2 +   w1ed_oa_rag4 +   w1ed_ra_rag2 +  w1ed_ra_rag4

neuAdult=~w1ed_oa_neu1 + w1ed_oa_neu3 + w1ed_ra_neu1 + w1ed_ra_neu3

neuComf=~ w1ed_oa_neu2 + w1ed_oa_neu4 + w1ed_ra_neu2 + w1ed_ra_neu4

OV =~ w1ov1 + w1ov2 + w1ov3 

RV =~ w1rv1 + w1rv2 + w1rv3

OA=~oa_ave

RA=~ra_ave

accept =~ w1like

reject =~ w1dislike

pop=~ w1pop

unpop=~ w1notpop

depress =~ cesdmean

age1=~ age

OA~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender + age1

RA~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender + age1

OV~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender+ age1

RV~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender + age1

accept~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender + age1

reject~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender+ age1

pop~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender+ age1

unpop~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender+ age1

depress~ assert + aggressO + AggressR + neuAdult + neuComf + w1gender+ age1

'

#robust

fitoutcomesnomod<- sem(outcomesnomod, data=data, missing='fiml', std.lv=TRUE, meanstructure=T,  estimator="MLR",control=list(iter.max=100000000))

summary(fitoutcomesnomod, fit.measures = TRUE, standardized=TRUE, modindices = FALSE )

[Terrence Jorgensen]

I have a question about including single indicators of latent variables and also using std.lv=TRUE for fixed factor scale setting. The way the syntax below is written, is the model specified correctly? The default is for the residuals for the single indicator latent variables to be fixed to 0, and for the latent variance to be fixed to 1, correct?

Yes, that is the default, and I don't see anything wrong with your syntax.

When a mean structure is requested, I am a little confused by the the presentation of the observed value and the latent value (0) in the results. 

I don't see any output in your post, but by default, the mean structure will be identified by setting the latent means to zero, whether std.lv = TRUE or FALSE (same defaults as Mplus).  So you should have an estimated intercept for each indicator and all latent means == 0 (just-identified mean structure).

Terry

[yrosseel]

On 03/01/2016 06:43 AM, Diana Meter wrote:
> I was under the impression that the defaults in place for cfa and sem in
> lavaan, while specifying std.lv=T, while designating the single observed
> variables as single indicators of a latent construct would result in
> correct estimates in an identified model.

To get a better understanding of lavaan's defaults, please see the
lavaan paper:

https://www.jstatsoft.org/article/view/v048i02

in particular section 4.1, and table 3.

Yves.

[Diana Meter]

Thank you both very much for your responses!

Diana

[Diana Meter]

Hello,

I have a follow-up question about single-indicator constructs. If I have a SEM that includes both latent and observed variables, is it more appropriate to include the observed variables without treating them as single indicator constructs? For instance, if I regress my latent construct on age, do I just regress it on that observed variable, or should I create a single indicator construct out of age? 

Are both acceptable ways of modeling?

Does it matter whether or not you request a mean structure in either of these versions of a model? 

I wonder whether the standard error is affected in the single indicator construct version because it is being standardized upon entry into the model, rather than letting it have its naturally occurring intercept and variance. I've done a couple of tests, and the standard errors and p-values do seem to be affected between trials. 

I would appreciate some more information about the most appropriate way to model with a mix of observed and latent variables. Thank you very much in advance!

Best regards,

Diana

[alysh...@gmail.com]

As a follow up to this, I am wondering how to handle path models in lavaan. I have a model of all observed variables and have run the model with just paths, such as below:

Model4 <- ('T2Victim ~ T1Victim + T1Depress 

           T3Victim ~ T2Depress + T2Victim

           w2rel2 ~ T1Depress + w1rel2

           w3rel2 ~ T2Depress + w2rel2

           T2Depress ~ T1Victim + w1rel2 + T1Depress + T1VicImp

           T3Depress ~ T2Victim + T2Depress + w2rel2 + T2VicImp

           

           T1Victim ~~ w1rel2 + T1VicImp

            T2Victim ~~ w2rel2 + T2VicImp

            T3Victim ~~ w3rel2')

Fit4 <- sem(Model4, data=Data2,  estimator="MLR", missing='fiml',fixed.x = FALSE)

I have also run a model creating singe indicator latent variables:

Model3.2 <- ("t1race =~ T1RaceVic

           t2race =~ T2RaceVic

             t3race =~ T3RaceVic

             t1rout =~ w1rel2

             t2rout =~ w2rel2

             t3rout =~ w3rel2

             t1depress =~ T1Depress

             t2depress =~ T2Depress

             t3depress =~ T3Depress

             t1racerout =~ T1VicImp

             t2racerout =~ T2VicImp

             t2race ~ t1race + t1depress 

             t3race ~ t2depress + t2race

             t2rout ~ t1depress + t1rout

             t3rout ~ t2depress + t2rout

             t2depress ~ t1race + t1rout + t1depress + t1racerout

             t3depress ~ t2race + t2rout + t2depress + t2racerout")

The models yield very similar beta weights but the p-values vary. There are more significant paths in the model with latent variables. I am wondering 1) why this might be and 2) which is the correct way to run the path analysis in lavaan. 

Thank you.

[Terrence Jorgensen]

Are both acceptable ways of modeling?

Yes, they will both yields the same regression slopes.  I think what lavaan does behind the scenes is create a single-indicator construct for you, but it keeps all the variance of the observed indicator in the theta matrix instead of setting the indicator's residual variance to zero and putting all the variance in psi.  I think the choice between the two only has a noticeable effect on the standardized solution, but that also might be a matter of setting fixed.x = TRUE or FALSE.  If you want to interpret a "standardized" effect of age on an outcome, then I think you have to make the single-indicator construct in your model syntax.

Does it matter whether or not you request a mean structure in either of these versions of a model? 

Only if you will interpret the mean structure or test any hypotheses about it by adding constraints on intercepts.  

I wonder whether the standard error is affected in the single indicator construct version because it is being standardized upon entry into the model, rather than letting it have its naturally occurring intercept and variance. I've done a couple of tests, and the standard errors and p-values do seem to be affected between trials. 

You should always fit the model to unstandardized variables to make sure your SEs (and therefore Wald z tests) are valid.  The standardized solution is there to show you what the estimates would be if everything were standardized, so you don't need to do any standardizing.  If you make your own single-indicator construct, you would be able to freely estimate the factor loading and set the factor variance to 1, so the factor loading would represent the SD and you could interpret the effect of "standardized age" on the outcome, although that doesn't necessarily mean anything because the SD of age in your sample doesn't necessarily generalize to other samples.

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

[Terrence Jorgensen]

The models yield very similar beta weights but the p-values vary. There are more significant paths in the model with latent variables. I am wondering 1) why this might be and 2) which is the correct way to run the path analysis in lavaan. 

Since you are setting fixed.x = FALSE in the path model, the results should be identical (if you set factor loadings to 1 in Model3.2 and freely estimate the factor variances).  They are both correct because lavaan defines the single-indicator construct behind the scenes if you don't. Notice lambda is an identity matrix in your path model results, and the variances in theta are fixed to zero (my previous post was incorrect):

lavInspect(fit, "coef")

Perhaps your results differ because you aren't using all the same variables?  For instance, it looks like you are using T1RaceVic instead of T1Victim.  Also, you specify residual correlations between endogenous variables at Times 2 and 3 in Model 4 but not in Model 3.2 -- if those are fixed to zero, it will affect other model parameters.

[Diana Meter]

Thank you very much!

Diana