# How do you read the coefficients in Structural Equation Model for prediction?

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?

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