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 Jonathan Preszler posted on Thursday, April 12, 2018 - 11:48 am
Hello,

We have a DSEM cross-lagged AR regression model, which included the following (abbreviated) results:

STDYX Standardization
Posterior One-Tailed 95% C.I.
Estimate S.D. P-Value Lower 2.5% Upper 2.5% Significance

Within-Level Standardized Estimates Averaged Over Clusters
P_PP | Q3 ON
Q3&1 0.092 0.055 0.046 -0.019 0.201

P_PO | Q3 ON
SHAPE&1 0.004 0.064 0.472 -0.131 0.133

P_OP | SHAPE ON
Q3&1 -0.125 0.052 0.009 -0.228 -0.024 *

P_OO | SHAPE ON
SHAPE&1 0.176 0.055 0.001 0.071 0.283 *

Between Level
P_OO ON
AGE -0.111 0.122 0.180 -0.342 0.135

SHAPE ON
AGE -0.156 0.112 0.083 -0.373 0.067

When reporting the results, we are unsure about the appropriate terms for the estimated parameters. Specifically, we have confusion about how to understand which are fixed and which are random effects, especially across the between and within levels. We feel we have a good understanding of what these parameters mean conceptually, but we are having a hard time knowing exactly how to label them.
 Tihomir Asparouhov posted on Thursday, April 12, 2018 - 9:43 pm
The standardized parameters are derived from the original model parameters, i.e., they are not the original model parameters, which are reported in the Model Results section.

All parameters on the between level are not random."Within-Level Standardized Estimates Averaged Over Clusters" are also not random.

Note that standardized
P_PP | Q3 ON Q3&1
is the same as the unstandardized so the average across cluster should be close to the mean of P_PP on the between level.

I would recommend reading the following

https://www.tandfonline.com/doi/full/10.1080/00273171.2018.1446819

earlier version available at

http://statmodel.com/download/HamakerAsparouhovBroseSchmiedek&Muthen-MBR.pdf

and

http://psycnet.apa.org/buy/2016-03904-001
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