Does the scale of one outcome affect the bivariate correlation?

[andkov]

Fev vs Fev100

Question: will a bivariate model yield the same inference regarding bivariate linear correlation if one of the processes is linearly transformed?

Observations so far by @ampiccinin
Based on the covariances, the fev100 had the desired effect - we can now see slope covariance values larger than 0.00, and the p values become consistently lower - but they vary by how much

[ampiccinin]

While p-values are probably not the best way to compare the results, they are generally what people rely on in drawing conclusions about their data. With this in mind:

Of, for example, the 18 measures in one study:

• 2 have identical p-values both for FEV and FEV100, and based on covariance and correlation. These also have identical (Mplus estimated) correlations, but neither the SEs nor the covariances are exactly the same.

• 1 has n.s. association according to FEV, but "statistically significant" for FEV100 (for cov and corr). Identical estimated correlations, but much smaller SE (.53 vs .14)

• 3 have n.s. association according to FEV and FEV100cov, but "statistically significant" for FEV100corr. Again, with identical estimated correlations, but much smaller SE (~.8 vs .2)

• the rest (12) have slightly smaller SE and p-value for FEV100, but are essentially unchanged between FEV and FEV100.

An additional issue is that the computed correlation CIs (I don't see the SEs in the table) are a lot smaller than the Mplus esimated CIs (e.g., -.94, .96 vs -.05, .07)

Highlighted in the attached file (green, yellow, red, grey/white, and orange, respectively):
pulmonary-meta-fev-vs-fev100-MAP-2017-10-03 - AMP.xlsx

[andkov]

@ampiccinin
A few notes.

1. The computed correlations should not have SE. due to the fact that correlation coefficient is not distributed normally, you can’t just throw a 95%CI from Gaussian onto a point estimate and call it a 95%CI of a correlation.
2. The Mplus estimate this by just throwing a 95CI from Gaussian onto a point estimate and calling this a 95%CI of a correlation.
3. It seems that Mplus, by sssuming that point estimate of a correlation is distributed normally, overestimate its value, compared to Fisher-Z transform employed during our “in-house” computation of the correlation point estimate.