Null model Lavaan: longitudinal CFA

[Amonet]

Dear all, 

In http://quantpsy.org/pubs/little_preacher_selig_card_2007.pdf the authors say that the null model that is commonly used in cross-sectional CFA, i.e. the independence model, is only "one piece of the 'null' expectation for longitudinal models". They refer to other research when stating: "Instead, the appropriate null model is one in which neither the variances nor the means of corresponding indicators change over time". 

This made me wonder: 

1) Does Lavaan select the appropriate null model automatically when specificying a multiple group or longitudinal CFA when using lavaan() function?

2) If 1) is not the case, how can I do this manually? A toy example would be highly appreciated. 

Kind regards,

Amonet 

[Yves Rosseel]

On 03/12/2018 09:16 PM, Amonet wrote:
> 1) Does Lavaan select the appropriate null model automatically when
> specificying a multiple group or longitudinal CFA when using lavaan()
> function?

No, because lavaan() doesn't 'know' if your data is longitudinal or not.

> 2) If 1) is not the case, how can I do this manually? A toy example
> would be highly appreciated.

You can fit your own baseline model. And then use the baseline.model=
argument of the fitMeasures() function. See

?fitMeasures

Yves.

[Amonet]

Dear Yves, 

Thank you for your reply. Would the following syntax give the correct longitudinal model? I am following the earlier mentioned paper and Todd D. Little's book on longitudinal SEM (2013). There the author says the longitudinal null model should have indicators with a constant mean and variance over time (i.e. what I do via m1, m2, m3 and r1 to r4, following your advice from lavaan.org) and no covariances among the indicators (latter is achieved by simply not specifying them).

 

I am in doubt of the specification, because the author of the book and paper doesn't say to restrict or not restrict the covariance between factors. In my syntax they are restricted as I do not specify them. If I do specify them however, then I get a non-positive definite covariance matrix of the latent variables (4 out of 6 corrrelations > 1). The extra model specification I use for that is posted below the first. Your advice would be appreciated. 

Model1 <- ' 

        # latent variables

            Motivation0 =~ 1*V_0_1 + m1*V_0_3 + m2*V_0_4 + m3*V_0_6

            Motivation1 =~ 1*V_1_1 + m1*V_1_3 + m2*V_1_4 + m3*V_1_6

            Motivation3 =~ 1*V_3_1 + m1*V_3_3 + m2*V_3_4 + m3*V_3_6

            Motivation4 =~ 1*V_4_1 + m1*V_4_3 + m2*V_4_4 + m3*V_4_6 

        # residual variances

            

            V_0_1 ~~ r1*V_0_1

            V_1_1 ~~ r1*V_1_1

            V_3_1 ~~ r1*V_3_1

            V_4_1 ~~ r1*V_4_1

            V_0_3 ~~ r2*V_0_3

            V_1_3 ~~ r2*V_1_3

            V_3_3 ~~ r2*V_3_3

            V_4_3 ~~ r2*V_4_3

  

            V_0_4 ~~ r3*V_0_4 

            V_1_4 ~~ r3*V_1_4 

            V_3_4 ~~ r3*V_3_4 

            V_4_4 ~~ r3*V_4_4 

          

            V_0_6 ~~ r4*V_0_6

            V_1_6 ~~ r4*V_1_6

            V_3_6 ~~ r4*V_3_6

            V_4_6 ~~ r4*V_4_6

        # Factor / LV  variances

        

          Motivation0~~Motivation0

          Motivation1~~Motivation1

          Motivation3~~Motivation3

          Motivation4~~Motivation4

        # item covariances constrained to 0

            

'

If I specify the factor covariances, I add this to the above model:

       # factor covariances

            Motivation0 ~~ Motivation1 + Motivation3 + Motivation4 

            Motivation1 ~~ Motivation3 + Motivation4

            Motivation3 ~~ Motivation4    

Thanks,

Amonet

[Amonet]

I forgot to add the lavaan () function syntax part. I use: fit0 <- lavaan(model = Model1, data = data). 

Kind regards

[Christopher David Desjardins]

Hi Amonet,

The paper you cite states "Instead, the appropriate null model is one in which neither the variances nor the means of corresponding indicators change over time." Based on this using the HolzingerSwineford1939 data set, cause I don't have yours, I think it should look like this:


littles.null <- '

# for illustration,
# x1, x4, and x7 are the same indicator over time
# x2, x5, and x8 are the same indicator over time
# and x3, x6, and x9 are the same indicator over time

# constrain variances to be equal
x1 ~~ v1*x1
x4 ~~ v1*x4
x7 ~~ v1*x7

x2 ~~ v2*x2
x5 ~~ v2*x5
x8 ~~ v2*x8

x3 ~~ v3*x3
x6 ~~ v3*x6
x9 ~~ v3*x9

# constrain means to be equal
x1 ~ m1*1
x4 ~ m1*1
x7 ~ m1*1

x2 ~ m2*1
x5 ~ m2*1
x8 ~ m2*1

x3 ~ m3*1
x6 ~ m3*1
x9 ~ m3*1
'
ft.ln <- cfa(littles.null, data = HolzingerSwineford1939)
summary(fit.ln, fit.measures = T)
fitmeasures(ft.ln, fit.measures = c("TLI", "CFI", "chisq", "RMSEA"))
inspect(ft.ln, "cov.ov")
inspect(ft.ln, "mean.ov")

traditional.null <- '
x1 ~~ x1
x2 ~~ x2
x3 ~~ x3
x4 ~~ x4
x5 ~~ x5
x6 ~~ x6
x7 ~~ x7
x8 ~~ x8
x9 ~~ x9
'
fit.tn <- cfa(HS.model, data = HolzingerSwineford1939)
summary(fit.tn, fit.measures = T)
fitmeasures(fit.tn, fit.measures = c("TLI", "CFI", "chisq", "RMSEA"))
inspect(fit.tn, "cov.ov")

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[Amonet]

Hi Christopher, 

I believe you are right. Thanks a lot for your help. 

I didn't think of the 'independence model' as being that, not my brightest moment :) 

For the variables I provided in my question, it the null model would then be (in longitudinal context): 

Model0 <- ' 

# residual variances

V_0_1 ~~ r1*V_0_1

V_1_1 ~~ r1*V_1_1

V_3_1 ~~ r1*V_3_1

V_4_1 ~~ r1*V_4_1

V_0_3 ~~ r2*V_0_3

V_1_3 ~~ r2*V_1_3

V_3_3 ~~ r2*V_3_3

V_4_3 ~~ r2*V_4_3

V_0_4 ~~ r3*V_0_4 

V_1_4 ~~ r3*V_1_4 

V_3_4 ~~ r3*V_3_4 

V_4_4 ~~ r3*V_4_4 

V_0_6 ~~ r4*V_0_6

V_1_6 ~~ r4*V_1_6

V_3_6 ~~ r4*V_3_6

V_4_6 ~~ r4*V_4_6

# equal means 

V_0_1 ~ m1*1

V_1_1 ~ m1*1

V_3_1 ~ m1*1

V_4_1 ~ m1*1

V_0_3 ~ m2*1

V_1_3 ~ m2*1

V_3_3 ~ m2*1

V_4_3 ~ m2*1

V_0_4 ~ m3*1

V_1_4 ~ m3*1

V_3_4 ~ m3*1 

V_4_4 ~ m3*1 

V_0_6 ~ m4*1

V_1_6 ~ m4*1

V_3_6 ~ m4*1

V_4_6 ~ m4*1

'

Thanks again! 

Best wishes

[Christopher David Desjardins]

That looks right to me.

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[Amonet]

Hi,

Sorry to keep bothering you all. 

Applying the help of Christopher as suggested, I fitted the longitudinal null model. 

As Yves suggested, I used fitMeasures(fit, baseline.model = ...). It works when I use the default estimator, i.e. Maximum Likelihood estimation in 'fit'. 

When I use estimator = 'MLM' to get robust SEs and scaled test statistics, it doesn't seem to work: Error in fit.indep@test[[2]] : subscript out of bounds

Is it correct the function doesn't work yet with this estimator? It's not a big problem, as apperantly the adjusted null model is only a very minor (negligible) difference in terms of fit anyways. 

Kind regards

[Yves Rosseel]

You must use the same estimator for the baseline model!

Yves.

[Amonet]

Thanks for the quick reply, it indeed works!

Best wishes

Op woensdag 14 maart 2018 09:08:32 UTC+1 schreef Yves Rosseel:

[Amonet]

Dear Yves,

I just wanted to check if the following is correct:

I specified a null model using 'estimator = 'MLM' for robust SE and robust GoF statistics. I then used this null model as the baseline model to check the goodness of fit of another model that is also estimated using 'estimator = 'MLM'. 

Does fitMeasures(fit = myfit_with_MLM, baseline.model = null_model_with_MLM) compute the robust goodness of fit indices based on the robust statistics of the specified null model? The null model has a baseline.chi.square.scaling.factor of 1.208 (and chisq.scaling factor of 1.058), while "my_fit_with_MLM" has a baseline.chisq.scaling.factor of 1.058 (and chisq.scaling.factor of 1.135). I am somewhat confused by this. 

So in both the null model and the hypothesized model the MLM estimator is used and my question is whether Lavaan 'knows' that I want it to use the robust GoF statistics of the null model to compute the robust GoF statistics of the hypothesized model. Probably this is done automatically, but I wanted to be sure. Sorry if this is a stupid question.

Kind regards

[Terrence Jorgensen]

Does fitMeasures(fit = myfit_with_MLM, baseline.model = null_model_with_MLM) compute the robust goodness of fit indices based on the robust statistics of the specified null model?

Yes, that is correct.  If lavaan sees that you passed a lavaan object to the baseline.model= argument, it will use that instead of fitting the default independence model.

The null model has a baseline.chi.square.scaling.factor of 1.208 (and chisq.scaling factor of 1.058), while "my_fit_with_MLM" has a baseline.chisq.scaling.factor of 1.058 (and chisq.scaling.factor of 1.135). I am somewhat confused by this

Me too.  Whenever I fit my custom null model to the same data with the same arguments, the baseline.chisq.scaling.factor is the same for both my null model and my hypothesized model, because in either case, lavaan fits the same default baseline model to calculate any requested incremental fit indices.

library(lavaan)
example(cfa)
fitMeasures(update(fit, estimator = "MLM"))["baseline.chisq.scaling.factor"] # 1.164138
## custom null model
mod.null <- paste0("x", 1:9, " ~~ foo*x", 1:9)
cat(mod.null, sep = "\n") # more restricted than independence model
fitMeasures(update(fit, model = mod.null, estimator = "MLM"))["baseline.chisq.scaling.factor"] # 1.164138

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

[Amonet]

Thanks a lot for checking this. You're (obviously) right, I must have made some mistake somewhere. The results are now in line what you're telling. 

Kind regards

Op dinsdag 27 maart 2018 11:51:50 UTC+2 schreef Terrence Jorgensen:

[Yves Rosseel]

On 03/20/2018 05:54 PM, Amonet wrote:
> So in both the null model and the hypothesized model the MLM estimator
> is used and my question is whether Lavaan 'knows' that I want it to use
> the robust GoF statistics of the null model to compute the robust GoF
> statistics of the hypothesized model. Probably this is done
> automatically, but I wanted to be sure.

Just to confirm: yes, this is done automatically.

Yves.