Basic questions on lavaan output

[VS]

Hello all,

I have some very basic questions about the lavaan output, or more specifically the parameterEstimates() function. Can you please comment, if my conclusions are correct? (I took the example from the lavaan-website)

       lhs op     rhs   est    se      z pvalue ci.lower ci.upper
1   visual =~      x1 1.000 0.000     NA     NA    1.000    1.000
2   visual =~      x2 0.553 0.100  5.554      0    0.358    0.749
3   visual =~      x3 0.729 0.109  6.685      0    0.516    0.943
4  textual =~      x4 1.000 0.000     NA     NA    1.000    1.000
5  textual =~      x5 1.113 0.065 17.014      0    0.985    1.241
6  textual =~      x6 0.926 0.055 16.703      0    0.817    1.035
7    speed =~      x7 1.000 0.000     NA     NA    1.000    1.000
8    speed =~      x8 1.180 0.165  7.152      0    0.857    1.503
9    speed =~      x9 1.082 0.151  7.155      0    0.785    1.378
10      x1 ~~      x1 0.549 0.114  4.833      0    0.326    0.772
11      x2 ~~      x2 1.134 0.102 11.146      0    0.934    1.333
12      x3 ~~      x3 0.844 0.091  9.317      0    0.667    1.022
13      x4 ~~      x4 0.371 0.048  7.779      0    0.278    0.465
14      x5 ~~      x5 0.446 0.058  7.642      0    0.332    0.561
15      x6 ~~      x6 0.356 0.043  8.277      0    0.272    0.441
16      x7 ~~      x7 0.799 0.081  9.823      0    0.640    0.959
17      x8 ~~      x8 0.488 0.074  6.573      0    0.342    0.633
18      x9 ~~      x9 0.566 0.071  8.003      0    0.427    0.705
19  visual ~~  visual 0.809 0.145  5.564      0    0.524    1.094
20 textual ~~ textual 0.979 0.112  8.737      0    0.760    1.199
21   speed ~~   speed 0.384 0.086  4.451      0    0.215    0.553
22  visual ~~ textual 0.408 0.074  5.552      0    0.264    0.552
23  visual ~~   speed 0.262 0.056  4.660      0    0.152    0.373
24 textual ~~   speed 0.173 0.049  3.518      0    0.077    0.270

1) 1 to 9: est represents the unstandardized factor loadings (lhs contains latent factors, rhs the manifest indicators); lower and upper CI indicate the 95% range in which est is allocated
2) 1 to 9: se represents the standard error of est
3) 1 to 9: z-value and p-value indicate the significance of factor loading (is the beta weight "meaningful"?)
-------------------
4) 10-18: est represents the unstandardized (error) variance of manifest indicators,
5) 10-18: se represents the standard error of est
6) 10-18: z-value and p-value indicate the significance of error variance - what does this mean?
------------------
7) 19-21: est represents the latent factor loadings
------------------
8) 22-24: est represents the intercorrelations between factors

Thanks a lot!!

[Mikko Rönkkö]

Hi,

Comments below

Yes, for the first part. I am not sure fi I understand what you mean by “95% range in which est is allocated”, but be sure not to confuse credibility intervals and confidence intervals.

2) 1 to 9: se represents the standard error of est

Yes.

3) 1 to 9: z-value and p-value indicate the significance of factor loading (is the beta weight "meaningful”?)

No. The p-value tells you the probability of obtaining result as or more extreme as this given the sample size and population model with nil (i.e. 0) effect. In other words, how likely it would be to obtain this kind of result purely by change.

Whether the result is meaningful is your interpretation and does not depend on the p-value. 

-------------------
4) 10-18: est represents the unstandardized (error) variance of manifest indicators,
5) 10-18: se represents the standard error of est

Yes to both.

6) 10-18: z-value and p-value indicate the significance of error variance - what does this mean?

It is a test of whether the variances are zero in the population. In other words, you could interpret this as tests if any of the indicators are completely free of measurement error and correlated perfectly with the latent variable. Such indicators would be highly unusual if even possible.

------------------
7) 19-21: est represents the latent factor loadings

No, these are the factor variances.

------------------
8) 22-24: est represents the intercorrelations between factors

Covariances, not correlations.

Mikko

Thanks a lot!!

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[VS]

Dear Mikko,

THANKS a lot!!

[isomitzi]

Hi,

Comments below

Hello

Regarding:

 8) 22-24: est represents the intercorrelations between factors

how would you use this information in your analysis? also, how do you get the correlations values?  

[Mikko Rönkkö]

HI,

On 19 Sep 2015, at 23:07 , isomitzi <israel....@gmail.com> wrote:

On Monday, September 14, 2015 at 1:15:05 PM UTC+3, Mikko Rönkkö wrote:

Hi,

Comments below

On 14 Sep 2015, at 13:05 , VS <vs.stud...@gmail.com> wrote:

Hello all,

I have some very basic questions about the lavaan output, or more specifically the parameterEstimates() function. Can you please comment, if my conclusions are correct? (I took the example from the lavaan-website)

       lhs op     rhs   est    se      z pvalue ci.lower ci.upper

22  visual ~~ textual 0.408 0.074  5.552      0    0.264    0.552
23  visual ~~   speed 0.262 0.056  4.660      0    0.152    0.373
24 textual ~~   speed 0.173 0.049  3.518      0    0.077    0.270

------------------
8) 22-24: est represents the intercorrelations between factors

Covariances, not correlations.

Regarding:
 8) 22-24: est represents the intercorrelations between factors

how would you use this information in your analysis? also, how do you get the correlations values?  

inspect(fit,”cov.lv”) will give you the factor covariance matrix containing the values. I hope that this is what you were asking about.

Mikko

[isomitzi]

Thank you for the quick answer.
i was actually asking about the correlations values.  

[Mikko Rönkkö]

Hi,

inspect(fit,”cov.lv”) will give you the factor covariance matrix containing the values. I hope that this is what you were asking about.

Mikko

Thank you for the quick answer.
i was actually asking about the correlations values.  

inspect(fit, “cor.lv”)

Mikko

[Veneta Slavchova]

Dear Mikko, is it possible to conduct a significance test on the intercorrelations between latent variables?

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[Mikko Rönkkö]

Hi,

If you do a CFA, you will get the significance tests. Are you doing a CFA or a structural regression model? If the latter, then why not CFA if you are interested in the correlations.

Mikko

[Veneta Slavchova]

Thanks for quick reply! I am doing a CFA. When I inspect the summary function I only see significance tests for covariances between LV, but I want it for cor.LV

[Mikko Rönkkö]

Hi,

The significance (p-values) are exactly the same because the latent variable correlation matrix simply a rescaled version of the covariance matrix. You can also  inspect the standardized solution.

Mikko

[Veneta Slavchova]

thanks big time

[Yves Rosseel]

On 09/24/2015 01:24 PM, Mikko Rönkkö wrote:
> Hi,
>
> The significance (p-values) are exactly the same because the latent
> variable correlation matrix simply a rescaled version of the covariance
> matrix.

Unless std.lv = TRUE was used to begin with, this is generally not true.
The p-values of unstandardized (say, covariance) parameters are not the
same as the p-values of the corresponding standardized (here,
correlation) parameters. The sampling distributions are different. In
fact, it can happen that the p-value for the covariance is significant,
while the p-value for the correlation is not.

The standardizedSolution() output will give p-values for standardized
parameters.

Yves.

[Veneta Slavchova]

Thanks for correction! Is it correct to speak about Pearson correlation in this context? Or what kind of correlation are we talking about?

[Yves Rosseel]

On 09/24/2015 02:14 PM, Veneta Slavchova wrote:
> Thanks for correction! Is it correct to speak about Pearson correlation
> in this context? Or what kind of correlation are we talking about?

Given that the latent variables are continuous, we can call them Pearson
correlations.

Yves.