Categorical second-order factor analysis

[minoruy...@gmail.com]

Dear lavaan user, I received warning message below while I was analyzing second-order factor model with categorical variables.

-----
Warning messages:
1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :
  lavaan WARNING: could not compute standard errors!

2: In lav_model_test(lavmodel = lavmodel, lavpartable = lavpartable,  :
  lavaan WARNING: could not compute scaled test statistic
-----
model<- 'F1=~v1+v2+v3
               F2 =~v4+v7+v8
               F3=~v5+v6+v9
               F2~~F3
               F3~~F1
               F4=~F1+F2+F3'
fit<- sem(model, std.lv=TRUE,data=dataset1,ordered=c("v1","v2","v3","v4","v5","v6","v7","v8","v9"))
------
#Restrictions on Covariance are needed because unless I restrict these latent variables, the model itself has not converged.
------
lavaan (0.5-16) converged normally after  16 iterations

                                                          Used       Total
  Number of observations                  4162        4533

  Estimator                                         DWLS      Robust
  Minimum Function Test Statistic     586.423          NA
  Degrees of freedom                                22          22
  P-value (Chi-square)                          0.000          NA
  Scaling correction factor                                        NA
  Shift parameter                                    
    for simple second-order correction (Mplus variant)

Model test baseline model:

  Minimum Function Test Statistic      19068.057   14040.988
  Degrees of freedom                                36          36
  P-value                                                    0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.970          NA
  Tucker-Lewis Index (TLI)                         0.951          NA

Root Mean Square Error of Approximation:

  RMSEA                                                    0.079          NA
  90 Percent Confidence Interval          0.073  0.084    NA     NA
  P-value RMSEA <= 0.05                          0.000          NA

Weighted Root Mean Square Residual:

  WRMR                                                        3.051       3.051

Parameter estimates:

  Information                                 Expected
  Standard Errors                           Robust.sem

                            Estimate  Std.err  Z-value  P(>|z|)
Latent variables:
  F1 =~
    v1                     0.665
    v2                     0.608
    v3                     0.751
  F2 =~
    v4                     0.714
    v7                     0.714
    v8                     0.669
  F3 =~
    v5                     0.674
    v6                     0.349
    v9                     0.663
  F4 =~
    F1                    0.270
    F2                    0.247
    F3                    0.720

Covariances:
  F2 ~~
    F3                    0.333
  F1 ~~
    F3                    0.377

Intercepts:
    F1                    0.000
    F2                    0.000
    F3                    0.000
    F4                    0.000

[Terrence Jorgensen]

I don't think your model is identified.  Try removing the covariances between first-order factors (F1, F2, and F3).  Their correlations are supposed to be reproduced by the higher-order factor. 

model<- 'F1=~v1+v2+v3
               F2 =~v4+v7+v8
               F3=~v5+v6+v9

               F4=~F1+F2+F3'

Terry

[yrosseel]

On 04/29/2014 04:09 PM, 柳下実 wrote:
> Terry, Thank you.
>
> Yet, the model you suggested does not work for my data.
>
> Whenever I used that model, I receive the message below.
>
> ------
> Warning message:
> In lavaan::lavaan(model = model, data = dataset1, std.lv <http://std.lv>
> = TRUE, :
> lavaan WARNING: model has NOT converged!
> ------
>
> Does it mean the model itself is not adequat?

It means that lavaan could not find a set of values for the free
parameters that fits your data. It is hard to assess why, without seeing
the data + model. Either your model is wrong (and you should try
alternative models), or you have an unfortunate sample.

Yves.

[柳下実]

Yves, thanks.

Is there anyway to assess why my models perhaps is not good?

Or, is there any good textbooks to learn how to assess models?

By the way just in case, I will let you know what data I am using.
I am using individual data of International Dating Violence Study, 2001-2006 (ICPSR 29583).

Used variables(ordinal data): DOM01, DOM02r, DOM03r, DOM04, DOM05, DOM06, DOM07, DOM08, DOM09.

Used variables can be obtained from individual level data. I only used U.S. sample for SEM.

first-order latent variables: F1=~DOM01+DOM02r+DOM03r
                                           F2 =~DOM04+DOM07+DOM08
                                           F3=~DOM5+DOM6+DOM9

second-order latent variables: F4=~F1+F2+F3

Regards.

Minoru Yagishita

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[yrosseel]

On 05/03/2014 02:34 PM, 柳下実 wrote:
> Yves, thanks.
>
> Is there anyway to assess why my models perhaps is not good?
> Or, is there any good textbooks to learn how to assess models?

I would recommend

Kline, R. B. (2011). Principles and practice of structural equation
modeling. Guilford press.

Does the modeling fit without the second-order latent variable?

Yves.

[yrosseel]

On 05/07/2014 05:52 PM, 柳下実 wrote:
> Thanks, Yves.
>
> I will check the book.
>
> The modeling without the second-order latent variable fit and converged
> after 15 iterations.

It would seem that the second-order latent variable does not work out
for your data. You may try and constrain some of the factor loadings (of
the second-order factor), to see if this helps, and then look at
modification indices afterwards,

F4 =~ 0.2*F3 + 0.2*F2 + 0.5*F1

But sometimes, a second-order factor simply doesn't work.

Yves.