Standardised output in multilevel SEM
Message/Author
 Xu, Man posted on Wednesday, November 05, 2008 - 9:07 am
I was wondering how the standardised path coefficients in the multilevel SEM are derived.
1.Are level 1 standardised coefficients obstained by unstandardised beta being multiplied with ratio between sd of predictor and sd of level 1 dependent latent variable? And are level 2 standardised coefficients obstained by unstandardised beta being multiplied with ratio between sd of predictor and sd of level 2 dependent latent variable?
2.also, if I define an extra parameter, say a variable that is the net effect of a level 2 contextual variable (level 2 beta minus level 1 beta of the same variables), should i calculate the standardised coefficient of this variable according to which method above??
3. how do i do if I have a latent cross level interaction term and I am interested in deriving its standardised coefficient?
 Bengt O. Muthen posted on Thursday, November 06, 2008 - 8:34 am
Multilevel modeling often does not use standardized coefficients. So one question is if you really need them.

1. Mplus standardizes to the variance on within for within relationships and to the variance on between for between relationships. Another choice is to standardize to the total variance, within+between. As always, yes, you multiply the raw coefficient by the ratio of the SD's for the IV divided by the DV.

2. If you have to standardize, you should do it with respect to the SD's of the variables in the relationship, which in this case are the between-level variables, I believe.

3. Cross-level interaction means a random slope so here you have a within-level DV variance that is a function of the IV values - so it is not clear which DV SD one should use. This is probably an argument against standardizing with respect to the DV - you can still standardize wrt the IV (multipling by the IV SD).
 Kätlin Peets posted on Monday, March 21, 2011 - 1:16 pm
Hi,

I have a question concerning standardized vs unstandardized between-level estimates. I am not sure which estimates (stand. or unstand) I should trust. It seems that the significance of the parameters varies sometimes quite a bit depending on whether I look at the stand. vs unstand. output.

My second question concerns the situation where I regress the intercept on several (four) between-level covariates. It seems that some of the x and y associations become stronger (and significant) when other covariates are in the model. However, I don't think the multicollinearity is an issue here as the highest correlation between the covariates is .27. What does it indicate (does it matter that the number of clusters is only 33?)?
 Bengt O. Muthen posted on Monday, March 21, 2011 - 5:04 pm
Standardized and unstandardized significance agree except in unusual situations. Standardized may have a more well-behaved sampling distribution and therefore be preferred. If you want to know more, send relevant info to support.

Remember that with several covariates the slopes are partial regression coefficients, so representing the effect when other covariates are held constant. So the meaning is different.
 joon hyung park posted on Tuesday, March 20, 2012 - 10:42 pm
Hi. I have same question concerning standardized vs unstandardized between-level estimates.

If I look at the unstandardized output, some parameters are not significant but if I look at STDYX (or STDY) standardization, these are significant.

However STD standardization shows same patterns as the unstandardized one.

Which estimates are preferred?
 joon hyung park posted on Wednesday, March 21, 2012 - 5:18 am
Dear Dr.Muthen

You can see the output at
http://joonpark77.tistory.com/333

I found a posting saying,
"The raw and standardized coefficients have different sampling distributions. This is why their significances may differ (Linda)."

What do you suggest to use?
 Linda K. Muthen posted on Wednesday, March 21, 2012 - 9:14 am
I would use raw coefficients. It depends on what is commonly reported in your discipline. Check journals where you would normally publish and see what is reported.
 Melvin C Y posted on Thursday, May 10, 2012 - 4:45 am
I would like to compare the multilevel contextual effects of prior ability (1-7 scale) and SES (regression score) on achievement (irt scaled score). Generally, unstandardized estimates are preferred. But as prior ability and SES are usually highly related, I think my best chance is to run separate analysis. My question is: how do I compare the estimates if they are measured on different metrics? It appears that the stdYX estimates would be the best option here.

My second question is: if I add more L2 variables (all on 1-7 scale), is it still advisable to use Stdyx estimates? Or should I standardize the contextual variables first before running them in Mplus? In this way, I can interpret the contextual variables in standardized units but keep the metrics of my L2 variables.

Thank you.
 Linda K. Muthen posted on Thursday, May 10, 2012 - 1:19 pm
This question is better suited to a general discussion forum like SEMNET.
 Rod Bond posted on Monday, May 13, 2013 - 8:03 am
Hi,
I am running the following 2-level model:
VARIABLE:
WITHIN are height testost meanf0 df ;
MODEL:
%WITHIN%
mascul ON testost height df meanf0;
meanf0 on testost height;
df on testost height;
df with meanf0;
height with testost;

Clusters are participants who provide a number of judgments of mascul; The WITHIN variables are different task characteristics that do not vary between clusters (each participant completes the same set of tasks).
I get the message: A NON-POSITIVE DEFINITE FIRST-ORDER DERIVATIVE PRODUCT MATRIX and all standard errors for the within model equal zero except those involving mascul. Am I doing something wrong here?
Thanks.
 Linda K. Muthen posted on Monday, May 13, 2013 - 8:47 am
 Alex Leung posted on Saturday, March 25, 2017 - 12:40 pm
Dear Drs. Muthen,

I have a question about interpreting the results of my model. Is the result from a multilevel model still meaningful if the between level of analysis is significant but the within level is not?

On average, x does not predict y...but groups with higher x tend to have higher y?

Thanks!
 Bengt O. Muthen posted on Sunday, March 26, 2017 - 6:03 pm
Yes, meaningful. You may discuss it further on Multilevelnet.