Latent variable scores of a single-item construct

[jista]

Dear pls mates,

when modeling an endogenous construct with only one item (the exogenous constructs have all more than two indicators) there is only a limited amount of scores for the latent variable.
The single item was formally measured with a 7-point Likert scale (like all the other indicators) and z-standardized before modeling.

The amazing thing is that the resulting latent variable scores also show only 7 different values for all cases (n=53) - how can this be? What’s wrong?

Thanks for your support!

[Diogenes]

Hi Sebastian,
nothing is wrong.
See an example:
- scale 1 to 7
- mean = 5
- standard deviation = 1.5
Possible values
raw // standardized (xi - mean)/sd
1 // -2.667
2 // -2.000
3 // -1.333
4 // -0.667
5 // 0.000
6 // 0.667
7 // 1.333

Best regards.

Bido