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Description
Suppose a product term is included in the model syntax:
mod <- ' y5 ~ x1 + y1 + x1:y1 '
When analyzing a correlation matrix (or sample-standardized raw data), we can set correlation=TRUE to ensure correct _SE_s (with a GLS estimator):
fit <- sem(mod, data = scale(PoliticalDemocracy),
correlation = TRUE, fixed.x = FALSE)
In this case, the product x1:y1 will not have unit SD, but that is how the model constrains it.
summary(fit)
Variances:
Estimate Std.Err z-value P(>|z|)
.y5 0.360
x1 1.000
y1 1.000
x1:y1 1.000
The product's SD should be a function of the summary statistics of x1 and y1.
Likewise, the covariance of x1 and y1 with x1:y1 is also a function of the x1 and y1 summary stats. But because this only works with fixed.x=FALSE, I guess those formulas wouldn't be applied here
Covariances:
Estimate Std.Err z-value P(>|z|)
x1 ~~
y1 0.382 0.099 3.848 0.000
x1:y1 0.292 0.106 2.742 0.006
y1 ~~
x1:y1 0.238 0.110 2.167 0.030
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