Some general bits on effect size for multilevel models (someone more knowledgeable about STATA can give details for that software). Effect size for a coefficient, or for the model, and if the model it is important for multilevel models to look at which level? http://www.bristol.ac.uk/cmm/software/support/support-faqs/pval.html provides much information. A good paper on this is:

@article{RightsSterba2019,

author = {Rights, Jason D. and Sonya K. Sterba},

title = {Quantifying explained variance in multilevel models: An integrative framework for defining {R}-squared measures},

journal = {Psychological methods},

volume = {24},

year = {2019},

pages = {309-338},

doi = {doi:10.1037/met0000184},

}

Araceli Rojo One method for estimating the effect size in a multilevel model in STATA is to utilize the Cohen's d statistic. Cohen's d is a standardized mean difference that may be used to compare two groups' means. It is determined by dividing the difference in averages between the two groups by the pooled standard deviation.

After fitting your multilevel model, use the estat effectsize command in STATA to compute Cohen's d for continuous dependent variables. The command computes the standardized mean difference between the independent variable's groups.

After fitting the multilevel model, you may use the estat esize command to size categorical independent variables. The standardized mean difference between the group means and the grand mean is returned by this command.

Here's an example of how to utilize STATA's estat effectsize command:

xtmixed yvar xvar || group: || _cons, cov(unstructured)

estat effectsize

In a mixed-effects model with the random effect 'group,' this would produce the effect size statistics for the variable 'xvar' on the dependent variable 'yvar'.

Alternatively, you may use the predict command to compute the effect size, and then divide the change in means by the pooled standard deviation.

It is crucial to remember that effect sizes might be sensitive to outliers; thus, before performing your analysis, verify for the presence of outliers in your data and treat them properly.

It is also worth mentioning that Cohen's d is not the only approach to calculate impact magnitude; other methods include:

- Hedges' g is a variant of Cohen's d that accounts for bias in small sample sizes.

- R-square, the percentage of the total variation in the outcome variable explained by the predictor factors.

- For multilevel models, the intraclass correlation coefficient (ICC) is used.

It is critical to select the impact size measure that is most suited to your data and research issue.