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I have run separate EFAs and then CFAs on the second half of the dataset to confirm the solution and the one-factor solution fits well across time points. One weird thing is happening though when I assess configural measurement invariance across time, the loadings for a few of the time points are inverted, so instead of all indicators loading positively for all latent variables, at some points, all loadings are negative, e.g.,

latent variable T1
indicator1 .653
indicator2 .756
indicator3 .465
indicator4 .831
indicator5 .613
latent variable T2
indicator1 -.523
indicator2 -.458
indicator3 -.432
indicator4 -.846
indicator5 -.785
latent variable T3
indicator1 .511

This was not the case for the individual models as they all loaded positively onto the latent variable. Why is this happening?

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The sign of factors is pretty much arbitrary because the analysis finds (you hope) latent factors that don't have any direction. Say that the latent factor at T1 is "happiness" (with positive loadings) then, at T2 it would be "sadness" (with negative loadings).

Now, if some of the loadings changed sign and others didn't, that would need explanation.

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  • $\begingroup$ Yes, that's what I meant. Only the signs at one of the time points changed to negative when I ran the longitudinal model. The remaining ones are all positive. I don't get why that happened. $\endgroup$
    – CatM
    Nov 20, 2023 at 2:11
  • $\begingroup$ No. At T1 they are all positive. At T2 they are all negative. This happened by chance and isn't anything to be concerned about. All the loadings changed sign. $\endgroup$
    – Peter Flom
    Nov 20, 2023 at 11:31
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    $\begingroup$ If you provide (positive) starting values (e.g., +1) for your factor loadings in your CFA software, this should not happen. $\endgroup$ Nov 20, 2023 at 11:56
  • $\begingroup$ @ChristianGeiser does that mean I should change the starting values? Thank you for your help! $\endgroup$
    – CatM
    Nov 20, 2023 at 17:08
  • $\begingroup$ @PeterFlom this is reassuring. It all went back to being positive when I fixed the factor loadings and henceforth the model outputs were as expected. I'm assuming this model can be used then. Thank you for your help! $\endgroup$
    – CatM
    Nov 21, 2023 at 1:31

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