To my knowledge, there is no direct way to get Mplus to compute Cohen's d for you. You can either compute Cohen's d by hand (using the estimated means and variances from the output) or use the model constraint option to define d as a new parameter (in which case you would have to label each parameter in the model statement and then use the labels to write an equation for d in model constraint).

The first option (hand calculation) seems most straightforward to me unless you are doing this for many mean comparisons in which case automation through model constraint may be useful.

Thanks, Christian! Mplus does only report the mean difference since one group is set to 0. Does this formula look correct to you:

((M) / sqrt( (S1+ S2) / 2))

M = the difference in means

S1, S2 = variance of group 1 and 2 (which you get in Mplus via Tech4)

The formula looks OK for equal group sample sizes. In case of unequal group sizes, you might want to consider a pooled SD formula that takes this into account (i.e., a weighted average of the two SDs).

Hey Sebastian, maybe you could think of the standardized estimate as an effect size. It may be neater regressing the latent variable onto a binary variable that represents your grouping variable - the STDY estimate in Mplus will standardize the 'Y' variable, the latent variable, but keep the grouping variable (X) in it's natural metric. So the STDY will tell you the difference in the latent variable means in terms of a standardised effect or z-score. This feels very similar to Cohen's d to me.

Mark

Hi Mark, thanks for your input! This is certainly an interesting idea and I will compare my findings with your proposed strategy.

Since you have already all information you need in the output file of the MI testing output your approach would mean an additional syntax and a bit more of work in Mplus. I also like Cohen's d because it is quite common and easy to understand for a wider audience.

For colleagues interested in this topic: I found a nice online calculator to obtain the pooled SD: https://www.statology.org/pooled-standard-deviation-calculator/. The pooled SD can then be used in the formula mentioned above.