Re: Power Simsem - Continuous Exogenous - Standardized Betas

[Sunthud Pornprasertmanit]

Hi Ioannis,

If I understand correctly, I think your implementation makes the total variances of Comp, Warm, and Outcome equal to 1, given the exogenous covariance matrix and the regression coefficients. However, I would not say that all betas are therefore conventional standardized effect sizes.

For the dummy variable (Y), if it is coded 0/1, the coefficient is a mean difference between the two groups in the metric of the outcome. If the total variance of the outcome is 1, this coefficient is close to a standardized mean difference, but it is not exactly Cohen’s d, because Cohen’s d uses the within-group SD as the denominator. In a simple model, d = b / SD(e). If you instead force SD(e)=1, then the coefficient for Y is closer to Cohen’s d, but then the total variance of the outcome is not 1 anymore. This also makes the coefficients for continuous predictors less like conventional standardized regression coefficients.

I would not standardize X, Y, X^2, and XY again. For the continuous predictor (X), I believe you already create X as N(0,1) before creating the derived terms, so X is already standardized. That is, create X first, then compute X^2 and XY from that standardized X, while keeping Y as a dummy variable. Then, keep these values and put them into simsem directly. Do not standardize them again.

I am not completely sure whether a multiple-group setup would be better for your purpose. It may be cleaner if the main effect of Y is the focus, because then you can define the outcome variance within each group. In that case, the raw mean difference between groups would correspond more closely to a standardized mean difference. But for the regression setup you described, I would not standardize the dummy variable itself.

Best,
Sunthud