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I understand that in regression, the beta weight can be used for prediction. For example: Depression =~ 1 + 0.5*Loneliness Suppose that depression and loneliness are measured with Likert Scale from 1 to 7, then a score of 4 on the Loneliness scale would mean a score of 3 on the depression scale.

How do I make such interpretation in structural equation model?

For example (example taken from lavaan website):

               Estimate  Std.err  Z-value  P(>|z|)   Std.lv  Std.all
Latent variables:
ind60 =~
x1                1.000                               0.670    0.920
x2                2.180    0.139   15.742    0.000    1.460    0.973
x3                1.819    0.152   11.967    0.000    1.218    0.872
dem60 =~
y1                1.000                               2.223    0.850
y2                1.257    0.182    6.889    0.000    2.794    0.717
y3                1.058    0.151    6.987    0.000    2.351    0.722
y4                1.265    0.145    8.722    0.000    2.812    0.846
dem65 =~
y5                1.000                               2.103    0.808
y6                1.186    0.169    7.024    0.000    2.493    0.746
y7                1.280    0.160    8.002    0.000    2.691    0.824
y8                1.266    0.158    8.007    0.000    2.662    0.828

Regressions:
dem60 ~
 ind60             1.483    0.399    3.715    0.000    0.447    0.447
dem65 ~
 ind60             0.572    0.221    2.586    0.010    0.182    0.182
 dem60             0.837    0.098    8.514    0.000    0.885    0.885

Suppose that ind60, dem60, and dem65 are measured with 7-point Likert Scale. Then what would be the score of dem60 if the score of x1, x2, and x3 were to be 3? And also, what would be the score of y1, y2, y3, and y4?

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    $\begingroup$ Have you tried lavPredict() in the lavaan package? $\endgroup$ – Randel Jul 30 '15 at 17:10
  • $\begingroup$ If your data are likert ratings, as in your example, you should not be using linear regression & making predictions in the way you describe. $\endgroup$ – gung - Reinstate Monica Jul 30 '15 at 23:19
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Just like in regression, except that your variables are latent.

A 1 unit increase in ind60 is associated with an increase of 1 unit in x1, 2.18 units in x2, etc. The reason to fix the loading of the first item to 1 is to identify the variance of the latent variable, and make it meaningful. (The other thing to do is to fix the variance of the latent variable to 1 to identify it).

You ask: "What would be the score of dem60 if the score of x1, x2, and x3 were to be 3?" That's the wrong way around. Dem60 is the (hypothesised) cause of x1, x2 and x3. You can ask what the predicted values of x1, x2 and x3 are, if dem60 has a score of (say) 1, but you need to know the intercepts, and they're not presented here. (The intercepts / means of the latents are usually 0).

If ind60 increases 1 unit, dem60 increases 1.483 units. If dem60 increases 1.483 units, y1 increases 1.000*1.483 = 1.483 units.

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