Beta coefficient into effect size PreviousNext
Mplus Discussion > Growth Modeling of Longitudinal Data >
 Johnny Wu posted on Friday, August 03, 2007 - 12:48 pm
Hi Dr Muthen,

I run an LGM, and have i and s factors.

I regress s ON covariate x.

Now I report the beta coefficient, and the p-value. But the reviewers want to know the "effect size."

How can I convert a regression beta coefficient into an "effect size" measure?

-thank you, johnnywu
 Bengt O. Muthen posted on Friday, August 03, 2007 - 5:09 pm
Effect size typically refers to a difference in means for 2 groups, divided by the variable's SD.

Perhaps your covariate x is a dichotomous variable representing 2 groups. In this case you can compute the estimated mean of s for each group and divide by the square root of the estimated variance of s. Alternatively, you can compute the estimated mean of the observed outcome for the 2 x groups and divide by the outcome SD.

See also the standard literature on effect size, including Cohen's writings.
 H Priess posted on Thursday, June 04, 2009 - 3:00 pm
As noted above, effect size often refers to the difference in two groups' means, divided by SD. In the case of latent growth models with binary predictors (e.g., gender), could one use the standardized coefficient "StdY" as a measure of effect size (provided predictor was coded 0,1 so that the coefficient was equal to the group difference), or is this not an equivalent calculation?
 Bengt O. Muthen posted on Thursday, June 04, 2009 - 4:45 pm
So the DV is a growth factor like "i" centered at a certain time point, where StdY makes this DV have SD=1 so the slope on gender is the effect size because it is the mean difference wrt gender in i divided by its SD? Makes sense.
 Sylvana Robbers posted on Tuesday, September 22, 2009 - 4:57 am
I want to know effect sizes in a multigroup LGM (twins versus singletons) with a binary predictor (gender, coded 0,1), but unfortunately Bengt's last post (4.45pm) is too cryptic for me. The influence of gender on the intercept is significant in twins and not in singletons. This could be a power issue, given the smaller sample size for the singleton sample. Could you please clarify how I can use the standardized beta coefficient to check if the effect sizes for sex differences are indeed greater in the twin than in the singleton sample?

Thanks in advance for your time.
 Linda K. Muthen posted on Tuesday, September 22, 2009 - 10:29 am
In the case of a binary covariate, effect size is beta divided by the standard deviation of y.
 Daniel Rodriguez posted on Friday, February 11, 2011 - 8:03 am
What if it's just one group and an effect sizes is needed for the effect of a continuous variable on intercept and slope? For instance, I'm in the midst of preparing a Montecarlo model for a simple LGCM with time invariant and time varying covariates. Now, I will be assessing the effects of various continuous predictors on the level and trend factors. I need to select values for my slopes and those values should correspond to some measure of effect. In this case my dependent variable is caloric intake (continuous variable) measured at three time points. One of my predictors is a measure of anxiety (also continuous). If I want to assume a medium effect based on the Cohen's criterion, how would I determine the start value for my slope? I'd appreciate any guidance you could give.
 Bengt O. Muthen posted on Friday, February 11, 2011 - 10:18 am
Perhaps you can think in terms of how many standard deviations the i and s change as a function of one standard deviation change in the covariate. For instance, a small effect might be that s changes 0.25 SD units.

With growth, there is a choice in what the DV should be - for instance, should it be s or should it be y_t at the last time point? The y_t DV has a difference variance than s, and therefore the effect on y_t is different than the effect on s. The effect on y_t is perhaps more a more tangible concept.
 Daniel Rodriguez posted on Friday, February 11, 2011 - 11:41 am
Yes, thank you very much. This is helpful.
 Justin D. Smith, Ph.D. posted on Friday, October 07, 2011 - 1:36 pm
I need to calculate an effect size for an indirect effect. All the variables in the model are continuous. ???
 Linda K. Muthen posted on Saturday, October 08, 2011 - 3:03 pm
Effect size usually refers to two groups so is more appropriate for a binary x. For a continuous x, you can use StdYX which would give you an effect size for a one unit standard deviation of x.
 Annie Desrosiers posted on Tuesday, July 31, 2012 - 11:48 am
Hi Dr Muthen,

I'm running an LGM for a treatment group effect on 5 times.

Is it possible to test the effect of the group (0 or 1), the effect of another covariate and their interaction in the same model ? And is it possible to have the effect sizes of the 2 mains effect and the effect size of the interaction ?

thank you
 Linda K. Muthen posted on Wednesday, August 01, 2012 - 10:28 am
Yes to the first question. For the second, you may find the following paper helpful:

Preacher, K.J., Rucker, D.D., & Hayes, A.F. (2007). Addressing moderated mediation hypotheses: Theory, methods, and prescriptions. Multivariate Behavioral Research, 42, 185-227.
 Sarah Lowe posted on Tuesday, March 11, 2014 - 7:40 am

I am working on a revision, and the Editor would like an indicator of effect size for cross-lagged paths. My co-authors and I have already provided standardized (stdYX) coefficients and 95% CIs, but it seems like the Editor wants something more.

His suggestion was to 1) run the model with and without each cross-lagged path, 2) calculate the change in R2 for the DV, and 3) convert to an F statistic.

At first, this sounded OK to me, but then I ran the models and noted that some of the R2s were actually *larger* with the (non-significant) cross-lagged path excluded (e.g., .57 with the path, .53 without the path), meaning that the addition of the path was associated with a -R2.

This has me questioning whether this approach to estimating effect size makes sense. I would appreciate your thoughts on this matter.

Thank you!!
 Bengt O. Muthen posted on Tuesday, March 11, 2014 - 12:15 pm
It doesn't sound like the editor's suggestion as you describe it makes sense because when you leave out significant cross-lagged paths the model becomes mis-specified and its estimates are of unknown value. I think standardized CIs make more sense.
 Sarah Lowe posted on Tuesday, March 11, 2014 - 12:39 pm
Thanks - I appreciate your help!
- Sarah
 Mary M Mitchell posted on Tuesday, December 13, 2016 - 8:17 am
Reviewers for a paper want me to calculate effect sizes for the standardized estimates that I got from doing an SEM model with an endogenous factor that has 6 categorical indicator variables. How would I do this? Is it possible? Thanks!
 Bengt O. Muthen posted on Tuesday, December 13, 2016 - 6:26 pm
I don't know how effect size comes into play here. That has to do with differences between groups. Perhaps you want to describe this on SEMNET.
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