confidence intervals for std.all coefficient (correlation)

[Michael Paul Grosz]

Dear all,

I would like to calculate the confidence intervals for the standardized covariance coeficient of a cfa model.

For example, this is part of the summary of my model:

                   Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all

Covariances:
  RIV.men ~~
    RIV.women         0.218    0.076    2.883    0.004    0.445    0.445

The two latent variables "RIV.men" and "RIV.women" are correlated (r = .445, p = .004). Now I would like to calculate the 90% confidence intervals for the Std.all coefficient (= correlation).
I already tried the CIr function of the package 'psychometric'
CIr(r=.445, n = 91, level = .90)
but it underestimates the size of the confidence intervals because it does not take into account the unreliability of the latent trait estimation.

In lavaan, parameterEstimates() gives the confidence intervals for the unstandardized coeficients:
parameterEstimates(RIV.RIV.fit, ci = TRUE, level = 0.90,
                   boot.ci.type = "perc", standardized = T,
                   fmi = "default")

          lhs op       rhs    est    se      z pvalue ci.lower ci.upper std.lv std.all std.nox

25    RIV.men ~~ RIV.women  0.218 0.076  2.883  0.004    0.094    0.343  0.445   0.445   0.445

Any idea how I could get (from there to) the CIs of the standardized coefficients?

cheers,
Michael

[Yves Rosseel]

What about using std.lv=TRUE?

Yves.

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[Michael Paul Grosz]

Yes, that seems to work. Then I can use parameterEstimates () to get the CIs.
The p-value is slightly different though. .001 instead of .004

Covariances:
  RIV.men ~~
    RIV.women         0.445    0.131    3.404    0.001    0.445    0.445

[Yves Rosseel]

On 11/28/2014 12:36 PM, Michael Paul Grosz wrote:
> Yes, that seems to work. Then I can use parameterEstimates () to get the
> CIs.
> The p-value is slightly different though. .001 instead of .004

That is perfectly normal. p-values for standardized parameters need not
be the same as p-values for unstandardized parameters.

Yves.

[Michael Paul Grosz]

Ok, thanks for the support!
Michael

[Woojae Kim]

That is perfectly normal. p-values for standardized parameters need not
be the same as p-values for unstandardized parameters.

Yves.

Sorry to post a reply to an old thread. But are you sure of the above? Do you mean they need not be the same due to a numerical reason? p-values should be scale invariant. 

[Jae]

I believe I can answer my question. Sorry, Yves, you're right. p-values for testing parameters should not be reparameterization-invariant. Depending on the type of reparameterization, it can still be invariant. But the ones done by the std.lv option will in general change the meaning of parameters, so p-values can change.