Path analysis / standardized coeffici... PreviousNext
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 Holger Muster posted on Friday, November 25, 2011 - 2:36 am
Hi all,

herewith a question concerning standardization in path analysis:

I have a set of observed variables, one is binary. The binary variable is the dependent variable in the first sub-model and one of the covariates in the second sub-model.

Applying "OUTPUT:STANDARDIZED;" I only get STDXY and STD standardization, not STDX. However, from my understanding for both sub-models I only should use STD-coefficients as standardized path weights. Right?
 Linda K. Muthen posted on Friday, November 25, 2011 - 9:48 am
For a binary x, use StdY. You will need to compute it from what you get.
 Holger Muster posted on Monday, November 28, 2011 - 8:28 am

thanks for your comment.

If I use StdY for all my covariates just because one of my covariates is binary, do you think the standardized coefficients (=path weights) are comparable? To guarantee that, would not STD be better?

A second question: Which standardization is recommended given a binary dependant variable in path analysis? From my current understanding I believe STD is recommended because for StdXY and StdY I would use standard deviation of a binary variable which does not make sense.

BR Holger
 Linda K. Muthen posted on Monday, November 28, 2011 - 11:33 am
You should use StdY for binary covariates and StdYX for all others. The choice of standardization is based on the covariate not the dependent variable.
 Holger Muster posted on Tuesday, November 29, 2011 - 2:21 am
sorry, but if the dependent variable is binary and all covariates would be continuous, use of StdYX does not make sense from my perspective because StdYX means the resulting "standardized coefficient bStdYX is interpreted as the change in y in y standard deviation units for a standard deviation change in x" (user guide v6, page 642) where y is the dependant binary variable and hence change in y standard deviation units does not make sense. Would you agree?

Thus if I'm right what would be the correct standardization given a binary dependent variable? Would that be STD?
 Linda K. Muthen posted on Tuesday, November 29, 2011 - 11:39 am
It would be StdYX where y is y* the latent response variable underlying the observed categorical variable y.
 dvl posted on Monday, April 23, 2012 - 8:05 am

I am doing a path analysis and my outcome variable is dichotomous. I have a binary independent variable (regression 1) next to a continuous independent variable (regression 2). I am figuring out which standardized coefficients I have to use. My output only represents STDYX and STD. My STD coefficients are the same as my original non-standardized coefficients.

I have understood that in case that the independent variable is dichotomous I should use STDY (regression 1). In case that the independent variable is continuous I should use STDYX (regression 2). Is this true?

In order to compare all standardized coefficients from both regressions do I have to use OR stdy OR stdyx? In other words, do I have to choose one standardization method or can I compare STDY and STDYX across the different regressions?

Could please tell me how I calculate stdy from the information I get? Then I am sure that my calculation is right.
 Linda K. Muthen posted on Monday, April 23, 2012 - 12:39 pm
You can combine different standardized coefficients.

If you have StdYX, you divide it by the standard deviation of x to get StdY.
 dvl posted on Saturday, May 12, 2012 - 3:40 am

I am running a path analysis (no latent variables). I have a dichotomous independent variable, a continuous mediating variable and a binary outcome variable.

When I study the standardized effect of the dichotomous variable I will use the stdy value (I calculate this value myself). The standardized effect of the continuous mediating variable on the binary outcome variable is a STDYX value.

Now, what do I have to do when I want to study the indirect effect of the dichotomous independent variable on the binary outcome variable. Can I just look at the STDYX value for the indirect effect and divide it by the standard deviation of x?
 Linda K. Muthen posted on Sunday, May 13, 2012 - 10:39 am
You would use StdY for the indirect effect. That is how you would obtain it.
 Minnik Findik posted on Monday, May 21, 2012 - 7:50 am
Dear Linda,
I am running a path analysis. All my variables are categorical (binary) except for 1. Am I correct at assuming I should use stdY estimate? And my next question is mplus do not automatically give me that estimate. How can I compute it? And will it have the same p value as the model results??
Best wishes
 Linda K. Muthen posted on Monday, May 21, 2012 - 11:29 am
The choice of StdY versus StdYX is based on whether a covariate is binary or continuous. Use StdY for a binary covariate and StdYX for a continuous covariate. See the STANDARDIZED option in the user's guide for the formula.
 Minnik Findik posted on Monday, May 21, 2012 - 1:18 pm
Dear Linda,
what if the covariate is an ordinal (0,1,2)independent variable hence, can not be defined as categorical. Does that mean I will be using StdYX?
Kind regards.
 Linda K. Muthen posted on Monday, May 21, 2012 - 1:51 pm
An ordinal covariate is treated as continuous. Use StdYX.
 Marco Bardus posted on Sunday, July 29, 2012 - 2:38 am
Dear Drs. Muthén,

I am running a path analysis with a count outcome (or with a binary outcome - not in the example below) censored below variable.

I managed to calculate indirect effects using MODEL CONSTRAINT. But How do I get the standardized estimates of the effects?
Should it be beta = B*SDx/SDy? Where do I get SDx and SDy of the total effects? There might be something I am overseeing.

CENSORED = bpad (bi);

intmean ON attmean (a);
intmean ON snmean (b);
intmean ON pbcmean (c);
bpad ON intmean (d);
attmean WITH snmean pbcmean;
snmean WITH pbcmean;

new(ad bd cd);
ad = a*d;
bd = b*d;
cd = c*d;
 Linda K. Muthen posted on Sunday, July 29, 2012 - 9:47 am
This is correct for censored but would not be correct for count. See the following paper which is available on the website:

Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.

The standardization is correct. You get the x variances from TYPE=BASIC and the y variances from the RESIDUAL output.
 Winnie Yang posted on Friday, November 14, 2014 - 6:55 am
Dear Dr. Muthen,

I am running a mediation testing whereby I am using model constraint. Under "model results" I am able to see whether the new parameter c1 is significant, I am wondering if there is any way I can also see the significance (p-value) of C1 under standardized model results?

new (c1);

Many thanks
 Linda K. Muthen posted on Friday, November 14, 2014 - 7:24 am
We don't provide standardized estimates on new parameters. You would need to do that yourself in MODEL CONSTRAINT.
 Winnie Yang posted on Friday, November 14, 2014 - 8:36 am
Dear Linda,

I see. Thanks for your quick response! It may sound silly to ask, but could you please advise me on how to set up the formula. Namely, what would be the formula for calculating standardised estimates. Many thanks.
 Bengt O. Muthen posted on Friday, November 14, 2014 - 1:19 pm
You use the usual standardization formula of multiplying by the X SD and dividing by the Y SD. You need to give a parameter label to the X variance in the Model for use in this Model Constraint standardization, and you need to express the model-implied Y variance in Model Constraint for use in the standardization.
 Alvin  posted on Monday, May 04, 2015 - 4:02 pm
Hi Dr Muthen, I am doing a full SEM model and most of the indirect paths in my model are significant (calculated using bootstrapped 95% CI). However, I notice the effect sizes are quite small ( <0.10). Some of the standardized coefficients are actually 0. Is this common? Thanks
 Bengt O. Muthen posted on Monday, May 04, 2015 - 4:33 pm
You can get significance for small effects if sample size is large.
 Annika Martin posted on Wednesday, April 27, 2016 - 3:25 am
I run a negative binomial model with path analyses on count data. My predictors are continious variables. There seems to be no problem with the model estimation but the p-values for the standardized (STD, STDYX and STDY) and unstandardized parameters do not agree.
Which parameters do I use in a negative binomial model to report my results and why?
 Bengt O. Muthen posted on Thursday, April 28, 2016 - 6:56 pm
Standardization with respect to Y is a strange thing for count Y. With respect to X is reasonable. Note that you can do bootstrapping to see if confidence intervals agree when you take into account non-symmetric estimate distributions.
 Jiseun Lim posted on Thursday, February 23, 2017 - 12:12 am
Hi Dr Muten.
Does it make sense to compare the sizes of two standardized coefficients (STD) when dependent variable is binary variable, and independent variables are binary or ordinary variables?
 Bengt O. Muthen posted on Thursday, February 23, 2017 - 6:16 pm
No, STD is standardizing only latent variables which it sounds like you don't have.
 Jiseun Lim posted on Thursday, February 23, 2017 - 9:30 pm
Dear Bengt,

I see. Thanks for your quick response. I'll change the previous question a little. Does it make sense to compare the size of a standardized coefficient (STDY, Y- bianary, X-binary) to another (STDYX, y-binary, x-ordinary)?
 Bengt O. Muthen posted on Friday, February 24, 2017 - 4:55 pm
It's not wrong.
 K. N. posted on Thursday, August 10, 2017 - 9:26 am
Dear Drs. Muthén,

I’m testing a boostrapped mediation model where all variables are observed, continuous variables. There are no specified covariates or latent variables in the model.

I’d like to report the standardized estimates for my indirect effects. Which of the three forms of standardized estimates I should report? I have read the details in the user manual regarding the standardized command, as well as the above posts, but am still unsure as to which to report.

Thank you in advance.
 Bengt O. Muthen posted on Thursday, August 10, 2017 - 4:32 pm
The indirect effect is from X to Y, so the regular regression rules hold:

If X is cont's, use STDYX

if X is binary, use STDY
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